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\def\editors	{\href{mailto://mike.strub@weyerhaeuser.com} {Editor:~Mike R.~Strub}}
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\author{	{\href{mailto://\citeemail}{Yong~\citename}}$^1$, 		% Change only the first name of the first author
		{\href{mailto://pbettinger@warnell.uga.edu}{Pete Bettinger}}$^2$, 		% Complete for other
		{\href{mailto://biomat@uga.edu}{Chris J.~Cieszewski}}$^3$, 
		{\href{mailto://rongxia.li@umit.maine.edu}{Rongxia Tiffany Li}}$^4$
}\affiliation{	\small\it{$^1$Graduate Research Assistant, $^{2,3}$Professor, {\href{http://www.warnell.uga.edu}{WSFNR, University of Georgia, Athens, GA 30602 USA}}} \\ 
		\small\it{$^4$Post Doctoral Research Associate, SFR, University of Maine, Orono, ME 04469 USA}
}\def\yourtitle	{{Trends in spatial forest planning}} 				%need double {{ for \\ e.g.: {{Title \\ Subtitle}}
\def\yourkwords	{Spatial forest planning, Mathematical programming, Heuristics, Modeling techniques, GIS}
\def\yourabstract{ 
Both mathematical and heuristic methods have advanced rapidly in spatial forest planning over the past 20 years. The review presented here is broader in both scope and depth (more analysis within spatial forest planning models). We conduct here a world-wide literature review and extensive analysis of the status and trends over the past two decades in spatial forest planning. In our investigation, we hope to understand the roles of objective and constraint functions in spatial forest planning. The literature review results suggest that methods used in forest planning have shifted somewhat from exact analytical solution techniques to heuristic techniques. In an effort to incorporate complex relationship into forest plans, other solution methods have also been evaluated for adoption in the planning process. Besides the economic and commodity production objectives, there is a noticeable increase in the proportion of ecological and social concerns in objective functions. In Europe, multi-parameter objective functions now seem to be in vogue, containing little or no constraints. In the U.S., single-parameter objective functions are still common, with multiple concerns recognized as constraints. In addition to the economic and commodity production constraints, adjacency and green-up relationships have recently been considered as important constraints in many areas of the world. Vector data are found to be more popular than raster data in the forest planning process, particularly in real-life applications of methods. In theoretical applications of methods, both vector and raster data are commonly used. Limitations in mixed integer programming, heuristic parameter selection processes, modification and enhancements to heuristics, and measurements of heuristic solution quality are some of the gaps we have identified.  
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% Continue with the first Section: 

\section{Introduction} 
Although theoretically spatial order has always been a factor in the 
development of strategic and tactical forest plans, physically, 
incorporating spatial concerns into forest planning methods has advanced 
rapidly only over the past 20 years. This advance is coincident with the 
advances made in computer hardware and software technology, and satellite 
technology and geographic information systems (GIS), as well as changes in 
human values associated with forest conditions. Interestingly, while changes 
in forest structure occur globally, most of the concern related to the 
timing and juxtaposition of management activities is in developed countries. 
Forest regulations and voluntary efforts of managing forests for 
sustainability in these countries are the main areas of spatial forest 
planning concerns [29]. In addition, as many wildlife-habitat 
relationships continue to be better understood or advanced, the evaluation 
of these and other concerns has prompted advances in spatial forest planning 
concepts as well. 

Certain laws and directives guide the use of spatial forest planning 
methods, and thus the need to adhere to regulations, to comply with the 
guidelines of voluntary certification programs, and to operate within 
published forest plans [29]. U.S. National Forests, for example, are 
regulated by the National Forest Management Act (United States Congress 
1976), which provides guidance regarding the appropriate size of harvest 
units. In simply perusing the published forest plans, one can find 
information on the maximum sizes of clearcuts, the dispersion of the 
openings created, and guidance for the management of habitat patches on 
various national forest lands. Some U.S. states also have passed 
laws that limit the size of clearcutting activities on privately-owned land 
[29, 44]. Canadian provinces may also have regulations relating to the size, 
shape, and pattern of areas to be clearcut, as may other governments, such 
as Sweden, the United Kingdom, and Australia [44]. Further, voluntary 
certification programs and habitat conservation plans may contain inferences 
to compliance issues, such harvest planning strategies that contain goals 
related to the spatial management of forest land [29]. These laws and 
directives typically stem from the desire to alleviate the effects of forest 
management on forest fragmentation and other ecological processes, the 
creation of frost pockets that hinder reforestation, and public pressure 
related to aesthetic quality [44].

Over the last two decades, a number of researchers and practitioners have 
performed and reported reviews related to forest planning. For example, 
Church et al. (1998) describe how forest management issues are closely 
related to other similar issues in the location sciences. In addition, the 
quantitative basis for measuring spatial structure as a prerequisite to 
implementing forest landscape management has previously been characterized, 
and ecological goals assessed at the landscape level, especially those 
objectives concerning the negative effects of habitat fragmentation, have 
been discussed [11, 136]. Nowadays, in some areas of the world, forest 
landscape management uses an ecosystem-based approach, which requires 
different management paradigms, modeling approaches, and software 
engineering techniques. As a result, Baskent et al. (2000) discuss recently 
introduced planning methods one might use to design an ecosystem-based 
forest management plan. Although we recognize that others have also 
suggested that spatial forest planning is a trend in natural resources 
management. One review discussed the necessary factors that have led to its 
adoption and also describes why the planning process may be avoided 
[29].

A number of types of forest management problems related to the location 
sciences have been classified to emphasize the locational issues in forest 
management [58]. As early as 1990, researchers introduced the idea of 
heuristic simulation, and provided a brief review of its capabilities for 
accommodating spatial forest plans [71]. Besides North America and 
Europe, some developing countries also have accumulated significant research 
on spatial forest planning; for instance, Epstein et al. [72] provide a 
review on the application of operations research systems in Chilean forest 
industries. Besides the conventional single-objective plans, a review of 
multiple criteria decision support in forest management illustrates how 
these methods could be beneficial for one or more types of spatial forest 
planning problems [127]. Martell et al. (1998) review methods for 
strategic forest management, short-term forest planning, forest operations, 
and forest fire management, and discuss the opportunities and challenges for 
operational researchers. Nurullah et al. (2000) review the need for spatial 
stratification as a method to organize the geographical information. Murray 
(1999) reviews some specific constraint functions also have been reviewed, 
such as the unit and area restriction models, two basic kinds of adjacency 
constraints in harvest scheduling. One of the most common spatial 
constraints in forest planning is related to the adjacency and green-up of 
clearcut harvests, an area of research that has stimulated researchers and 
practitioners to find more efficient solution processes for spatial forest 
planning problems. As early as 1990, reviews concerning the analysis of 
adjacency constraints have been presented [217, 242]. Due to the 
combinatorial complexity of spatial forest planning problems, forest 
planning problems have become much more difficult to solve. Reviews of 
combinatorial problems induced by spatial forest harvest planning were 
presented by Weintraub et al. (2000a) and Weintraub and Murray (2006). 
Weintraub (2007) further reviews some traditional mathematic programming 
techniques, such as the use of integer programming for spatial forest 
planning. 

A comprehensive review of mathematical forest planning in North American 
literature was presented by Bettinger and Chung (2004), providing forest 
managers and researchers who are involved in forest planning tasks with a 
good grasp of the trends in forest planning techniques associated with the 
change in the forest management planning environment. In contrast, the 
review presented here is broader in both scope (world-wide) and depth (more 
analysis within spatial forest planning models). Previous reviews have 
discussed the conceptual frameworks of spatial forest planning, and included 
a discussion of the spatial configuration related to the forest patches. In 
addition, various management approaches that could be used to conceptualize 
spatial forest planning problems were posed, along with a discussion of 
challenges related to spatial forest planning [14]. Compared to this, 
our forthcoming review considers a more extensive analysis of the status and 
trends over the past two decades. In our investigation, we hope to 
understand the roles of objective and constraint functions in spatial forest 
planning. The configuration of the objective function, for example, may 
provide information regarding shifts in what researchers and land managers 
want their spatial forest plans to accomplish. Constraint functions may also 
illustrate that more restrictions are being placed on forest plans, or that 
a different set of restrictions now applies, as opposed to twenty years ago. 
Thus, our objective is to expend a greater effort understanding the current 
status, trends, and gaps in the spatial forest planning literature.

\section{Methods}
We conducted an extensive literature review of peer-reviewed spatial forest 
planning research based on a full search of twenty-three international 
journals and a limited examination of 19 other journals whenever there was 
an indication, through the review, that relevant spatial forest planning 
literature might be located there. This review is mainly concerned with the 
use of techniques for problem-solving, and not necessarily about how 
problems are structured or about how models are built. These latter two 
concerns are more difficult to understand given the various manners in which 
research results are presented. Therefore, we developed a classification 
process and used it to categorize the papers in various ways, including (a) 
the methods used to accommodate the planning model, (b) the types of 
objectives and constraints that were recognized, and (c) the size of 
problems that were being addressed. The full classification that we used can 
be found in Tables 1 through 3. We examined papers published from January 
1989 and through December 2007. 

Because of the complexity of natural resource management problems today, and 
given our previous knowledge of the literature, we expected that much of the 
literature reported the development, testing, and analysis of new techniques 
for accommodating spatial forest planning issues. The two basic groups of 
techniques involve heuristic methods and traditional mathematical 
programming methods. In our assessment, mathematical programming methods 
were sub-divided (Table 1) into exact techniques (linear programming, goal 
programming, integer programming, mixed integer programming (MIP), and 
non-linear programming) and other techniques (dynamic programming, 
simulation, and others). We consider exact techniques as those that are 
generally deemed to guarantee the location of an optimal solution to a 
planning problem. Heuristics and other techniques generally cannot provide 
this guarantee. Heuristic techniques were subdivided into seven commonly 
used methods (genetic algorithms (GA), Monte Carlo integer programming 
(MCIP), simulated annealing (SA), tabu search (TS), threshold accepting 
(TA), the raindrop method, and other heuristic methods). 


\begin{table}[htbp]
\begin{center}
\caption{Categories for forest-level planning techniques described in 
peer-reviewed articles.}
\begin{tabular}{|l|l|}
\hline
Major categories& Sub categories  \\
\hline
\raisebox{-9.00ex}[0cm][0cm]{Heuristics}& Genetic algorithms \\
\cline{2-2} 
 & Monte Carlo integer programming \\
\cline{2-2} 
 & Stimulated annealing \\
\cline{2-2} 
 & Tabu search \\
\cline{2-2} 
 & Threshold accepting \\
\cline{2-2} 
 & Raindrop \\
\cline{2-2} 
 & Other heuristics \\
\hline
\raisebox{-6.00ex}[0cm][0cm]{Exact techniques}& 
Goal programming \\
\cline{2-2} 
 & Integer programming \\
\cline{2-2} 
 & Linear programming \\
\cline{2-2} 
 & Mixed integer programming \\
\cline{2-2} 
 & Non-linear programming \\
\hline
\raisebox{-4.50ex}[0cm][0cm]{Other techniques}& 
Dynamic programming \\
\cline{2-2} 
 & Qualitative analysis \\
\cline{2-2} 
 & Simulation \\
\cline{2-2} 
 & Others \\
\hline
\end{tabular}
\label{tab1}
\end{center}
\end{table}

The type of forest planning methods applied to spatial planning problems is 
of interest from a number of perspectives: (a) some methods are more 
well-understood by practitioners than others, (b) some methods have been 
demonstrated over time to be robust or simply adequate, and (c) some methods 
are better for addressing certain problems than others, from both 
computational speed and computational complexity perspectives. We know that 
some research papers describe the use of up to eight planning techniques 
[24], while most describe only one or two. In these cases, a number of 
planning techniques may have been recorded as being used, all arising from a 
single paper. In cases where two or more techniques are present in a 
research paper, this usually suggests that a validation or comparison of 
techniques is performed. Further, in some instances a single technique 
(e.g., tabu search) may have been examined using several different 
formulations or modifications [201]. In cases such as these, the 
number of times a technique is noted as being used is limited to one 
instance. In other words, various modifications to techniques are not 
recorded beyond the fact that the type of technique is used. 

Deciphering the formulation of planning problems is relatively 
straightforward in most research papers, but this is not universally the 
case. While a formal description of a planning problem may seem requisite, a 
number of papers have been published where it is difficult to ascertain the 
objective or constraints under analysis. We began our assessment of the 
literature with a preliminary categorization of the elements within the 
objective and constraints. The categories evolved as our assessment grew, 
however. Table 2 represents the major categories and sub-categories of 
objective functions that we determined. As we suggested, we began with a 
smaller set, and found that it needed expansion as the literature search 
proceeded, since some objectives were not assumed \textit{a priori}. For example, economic 
and commodity production objectives are the most obvious forest planning 
objectives. In addition, we assumed wildlife habitat objectives would be 
found in the literature. However, during our search, we located research 
that used measures commonly considered as constraints (e.g., adjacency) in 
the objective function of planning problems. 



\begin{table}[htbp]
\begin{center}
\caption{Objective functions categories for forest-level planning 
peer-reviewed articles.}
\begin{tabular}{|l|l|}
\hline
Major categories& Sub categories \\
\hline
& Maximize net present value \\
\cline{2-2} 
Economic and  & Maximize revenue \\
\cline{2-2} 
commodity production & Minimize discounted costs \\
\cline{2-2} 
 & Wood flow \\
\hline
\raisebox{-1.50ex}[0cm][0cm]{Wildlife habitat}& Maximize acres in habitat \\
\cline{2-2} 
 & Maximize species \\
\hline
Forest structure&  \\
\hline
Biodiversity&  \\
\hline
Recreation&  \\
\hline
\raisebox{-10.50ex}[0cm][0cm]{Other objectives}& Fire \\
\cline{2-2} 
 & Entomology \\
\cline{2-2} 
 & Adjacency \\
\cline{2-2} 
 & Landscape metrics \\
\cline{2-2} 
 & Minimize shape index \vspace{-.05in}\\
 & or clustering \\
\cline{2-2} 
 & Minimize site disturbance \\
\cline{2-2} 
 & Regeneration area \\
\cline{2-2} 
 & Water yield \\
\hline
\end{tabular}
\label{tab2}
\end{center}
\end{table}


\begin{table}[htbp]
\begin{center}
\caption{Constraint categories for forest-level planning peer-reviewed 
articles.}
\begin{tabular}{|l|l|}
\hline
Major categories& Sub categories \\
\hline
& Net present value \\
\cline{2-2} 
Economic and  & Revenue \\
\cline{2-2} 
commodity production & Budget \\
\cline{2-2} 
 & Wood flow \\
\hline
\raisebox{-3.00ex}[0cm][0cm]{Aquatics}& 
Stream sediment \\
\cline{2-2} 
 & Stream temperature \\
\cline{2-2} 
 & Water yield \\
\hline
Forest structure & \vspace{-.05in} \\ 
or inventory&  \\
\hline
Adjacency&  \\
\hline
Road-related&  \\
\hline
Wildlife&  \\
\hline
Minimum or maxaximum &  \vspace{-.05in}\\ 
harvest age&  \\
\hline
\raisebox{-7.50ex}[0cm][0cm]{Other constraints}& Fire \\
\cline{2-2} 
 & Entomology \\
\cline{2-2} 
 & Biodiversity \\
\cline{2-2} 
 & Carbon \\
\cline{2-2} 
 & Optimal bucking \\
\cline{2-2} 
 & Processing capacity or  \vspace{-.05in} \\
 & materials \\
\hline
\end{tabular}
\label{tab3}
\end{center}
\end{table}

With each forest and landowner comes a different set of objectives and 
constraints. The ideal situation of each landowner behaving rationally with 
economic or ecological objectives and institutional constraints on budgets 
and timing considerations does not necessarily hold. As a result, a wide 
variety of constraints were anticipated in the assessment of the literature. 
For example, we planned to locate economic and commodity production 
constraints as well as those related to habitat, adjacency, and forest 
structure (e.g. ending inventory). Some forest-level constraints were 
unexpected (entomology, carbon) and were represented by few papers; 
therefore the ``other'' category contains several diverse natural resource 
planning constraints. In a number of cases the constraints used in various 
research papers were embedded informally as thoughts within the text, and 
therefore required a careful reading of the methodology of each paper.

Over a period of six months, the main 23 journals we targeted were 
systematically reviewed by first viewing the titles of manuscripts to 
determine whether further analysis was necessary. The reference work within 
the literature we located led to other sources of research outside of our 
initial area of search. We also consulted the vitae of numerous scientists 
working in this field, if those vitae were available over the Internet. When 
we felt we had exhausted our search, we began to synthesize the 
contributions made thus far in spatial forest planning.

\section{Results}
Developing a comprehensive review of spatial forest planning literature is 
somewhat difficult given all of the potential venues in which peer-reviewed 
literature might be located. Some journals provide efficient access through 
the Internet, while others do not. In addition, our organization (University 
of Georgia) does not necessarily provide researchers direct, no-cost access 
to every journal. Undeterred, 245 papers were located that report results or 
discussion on spatial forest planning activities. We found over half of the 
papers on spatial forest plannings in either \textit{Forest Science} (27.1{\%}), the \textit{Canadian Journal of Forest Research} (16.5{\%}), 
\textit{Forest Ecology and Management} (7.6{\%}), or the \textit{European Journal of Operational Research} (5.1{\%}). These results were not unexpected since 
spatial forest planning approaches represent advances or new developments in 
operations research methods applied to natural resource management. These 
advances are better suited to journals that accommodate theoretical 
research, rather than journals that accommodate applied research transfer to 
forest managers. A number of other journals contained several papers on 
spatial forest planning, including \textit{Silva Fennica}, \textit{Scandinavian Journal of Forest Research}, \textit{The Forestry Chronicle}, and \textit{Ecological Modelling}. These findings were expected, 
since these journals have forestry or natural resource management as their 
main emphasis. A few other journals that do not have forestry or natural 
resource management as their main emphasis contained as many papers as 
these, however, including \textit{Operations Research}, \textit{Journal of Environmental Management}, and \textit{Annals of Operations Research}. Some papers were located through limited 
searches in journals such as \textit{Tree Physiology}, \textit{Water Resources Bulletin},\textit{ Location Science}, \textit{Nonlinear Analysis}, and \textit{Discrete Applied Mathematics}. The difficulty for researchers and 
managers new to the field is that at least 42 journals serve as sources for 
spatial forest planning literature. As a result, the ability to locate 
pertinent research may require a considerable commitment of time. 

The number of peer-reviewed forest planning papers increased at a rate of 
about 1.5 papers per year during the 1990s (see Figure 1). The largest 
number of papers appearing in our literature review occurred in 2000. The 
rate of publication of papers has declined slightly since 2000. With the 
exception of a few odd years (e.g., in 2004, only 5 papers were located in 
the journals.), the rate of publication seems to be between 10 and 15 papers 
per year. While implementation of these techniques into real-world planning 
effects remains a challenge, we may be seeing the end of the exploratory 
phase of spatial forest planning. A number of the early papers on this 
subject described new methods for incorporating spatial concerns in a forest 
plan or described new problem-solving methods for spatial forest planning 
problems. Advances in these areas may continue, however many further example 
applications may not be seen as novel. In essence, we may be transitioning 
into a phase of competitive testing and analysis, which may require an 
expanded effort of a research team to produce a peer-reviewed manuscript.

\begin{figure}[htbp]
\centerline{\includegraphics[width=3.9in,height=2.5in]{17-81-1-SP.eps}}
\caption{Number of publications in the spatial forest planning literature, 
by year.}
\label{fig1}
\end{figure}

\subsection{Solution Techniques for Spatial Forest Planning Problems}
The results from our survey show that during the 1990s, exact methods were 
mainly used for problem solving or validation purposes (Figure 2). However, 
since about 2000, heuristics have become just as frequently used. Although 
linear programming and its derivatives are still illustrated in recently 
published papers, they are generally used to generate the exact or the 
``relaxed'' solutions to a problem in order to validate heuristic methods 
(and other methods as well), or are limited to solving various small-size 
problems. Simulation methods are used consistently in research papers 
throughout this time span, however to a much lesser extent than heuristics. 
The results also show that dynamic programming has shown value as a 
forest-level planning technique, rather than simply as a stand-level 
optimization technique. It is important to realize that dynamic programming 
produces optimal solution to individual subproblem in some specific paper 
[107], and its combination with other approaches to get a non-exact solution 
to the master problem in the same paper.

It is well known that one of the disadvantages of heuristic methods is that 
one cannot prove the solution located is the best solution to the problem, 
whereas exact methods provide a guarantee of optimality. However, as problem 
sizes increase, it may be impossible to solve large problems using tractable 
analytical methods [150]. In addition to the common exact and heuristic 
methods, researchers have continuously attempted to solve spatial forest 
planning problems with new methods. Each year several of these new methods 
appear in journals. However, in some cases these new techniques cannot be 
applied to the wider range of forest planning problems without encountering 
some computational issues (e.g., [20]). For example, an optimized method 
based on cellular automata has been applied to solve spatial forest planning 
problem [93]; fuzzy multicriteria approval method which is based on approval 
voting has been used in forestry decision support [122], and ant colony 
optimization has been adopted for the risk management of wind damage in 
forest planning [247].

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.5in]{17-82-1-SP.eps}}
\caption{Type of mathematical programming technique in the spatial forest 
planning literature, by year.}\label{fig2}
\end{figure*}


Researchers initially considered exact techniques (table 4) as the most 
appropriate way to solve spatial forest planning problems. Goal programming 
(8 papers), integer programming (14 papers), mixed integer programming (29 
papers), linear programming (64 papers) and non-linear programming (6 
papers) have been used to solve economic and commodity production objective 
function problems, yet the problem size is usually limited to less than 
about 1,000 management units. Large and more complicated problems may 
require use of heuristics such as GA (15 papers), MCIP (17 papers), SA (33 
papers), TS (25 papers), TA (4 papers), and the raindrop method 32]. 



\begin{table*}[htbp]
\begin{center}
\caption{Related papers for forest-level planning techniques described in 
peer-reviewed articles.}
\begin{tabular}{|l|l|}
\hline
Technique categories & 
Literature \\
\hline
Genetic algorithms& 24, 42-45, 70, 75, 76, 148, 152, 163, 194, 225, 246, 247 \\
\hline
Monte Carlo integer programming& 8, 24, 41-43, 61, 67, 76, 89, 117, 139, 174, 177, 200, 201, 227 \\
\hline
Stimulated annealing& 12, 15, 24, 40, 41, 50, 54, 65, 66, 92, 93, 120, 146, 149, 150, 166, 172,  \vspace{-.05in} \\
& 185-188, 191, 194, 206, 208, 213, 220, 222-224, 246, 247 \\
\hline
Tabu search& 17, 20-22, 24, 27, 30, 31, 41-45, 47, 52, 92, 134, 142, 164, 166, 172, 191, \vspace{-.05in} \\
& 194, 201, 246 \\
\hline
Threshold accepting& 24, 25, 50, 91, 191 \\
\hline
Raindrop& 32 \\
\hline
Other heuristics& 2, 5, 7, 24, 57, 60, 63, 66, 74, 84, 92, 93, 103, 121, 125, 130-132, 134, 137,\vspace{-.05in} \\
&  140, 148, 152, 156, 166, 170, 178, 184, 191, 192, 194, 204, 207, 226, 230,  \vspace{-.05in} \\
& 231, 233, 234, 238, 241, 243, 244, 247 \\
\hline
Goal programming& 19, 38, 56, 69, 133, 138, 181, 237 \\
\hline
Integer programming& 7, 17, 21, 64, 82, 83, 156, 168, 169, 210-212, 240, 241 \\
\hline
Linear programming& 5, 15, 18, 20, 21, 33, 34, 39, 42, 45, 46, 48, 49, 55-57, 62, 64, 67, 68, 77, \vspace{-.05in} \\
& 79, 81, 88, 95, 98, 100, 103-106, 109, 115, 118, 141, 147, 153, 160, 162, \vspace{-.05in} \\
& 167, 168, 171, 173, 175, 177, 184, 186, 196, 199, 200, 202, 203, 205, 213, \vspace{-.05in} \\
& 215, 220, 226, 227, 229, 230, 233, 236, 238, 243 \\
\hline
Mixed integer programming& 2, 33, 35, 53, 60, 62, 73, 74, 96, 97, 101, 142, 157-159, 167, 174, 179, 180, \vspace{-.05in} \\
& 198, 218, 219, 230, 231, 233, 234, 238, 243, 245 \\
\hline
Non-linear programming& 99, 100, 102, 104, 106, 237 \\
\hline
Dynamic programming& 36-38, 107, 108, 110, 189 \\
\hline
Qualitative analysis& 114 \\
\hline
Simulation& 3, 10, 26, 28, 59, 85-88, 110, 113, 115, 119, 144, 162, 173, 182, 216, 239 \\
\hline
Others& 1, 4, 6, 9, 51, 80, 81, 90, 94, 122-126, 128, 143, 151, 154, 161, 176, 193, \vspace{-.05in} \\
& 195, 197, 214, 218, 221 \\
\hline
\end{tabular}
\label{tab4}
\end{center}
\end{table*}

MCIP is one of the earliest heuristic methods used in forest planning and it 
helped illustrate the importance of heuristic methods to the forest managers 
by allowing the solution of spatial forest planning problems that could not 
be solved using traditional exact methods. Some advantages of MCIP are that 
it is computationally fast, conceptually simple, and easy to program and 
modify [174]. Thus, it is not uncommon to find that about 70{\%} of forest 
planning problems used the MCIP method on real (not theoretical) data. 
Within forest planning, it has been applied to problems related to economic 
[8] and commodity production problems [61, 117, 200], and those 
involving adjacency constraints [67, 139, 175], wildlife habitat [89], 
and road system management issues [174]. The literature indicates that 
around 65{\%} of the MCIP examples were published before 2000. After that, 
MCIP has typically been used as a method with which to compare against other 
recently developed heuristic methods. 

The concepts that form the basis for SA were first published by Metropolis 
et al. (1953) and are based on an algorithm that simulates the cooling of 
materials in a heat bath, a process known as annealing [24]. Generally 
speaking, SA is implemented as a 1-opt process, where changes to a single 
decision variable are considered. If the changes lead to a less desirable 
solution, the SA criterion is employed to determine whether or not to accept 
the proposed change in the solution. We determined that the number of papers 
describing SA for solving spatial forest planning problems is 33, which is 
the largest group among all the heuristic methods. Within forest planning, 
SA has been applied to problems related to economics [186, 220], 
commodity production [12, 150, 206], recreation [40], landscape design 
[54, 187, 188], adjacency issues [65, 213], road system management 
issues [66], regeneration [120], biodiversity [146], forest 
structure [149, 185], and wildlife habitat [224]. These results also 
illustrate that SA is widely used throughout the world, thus one of the most 
common heuristic techniques in natural resource planning and research. The 
locations of the work include Oceania, Asia, U.S.A., Europe, and Canada. 
Most papers, however, involve the latter three areas of the world. 

TA is similar to simulated annealing in how it operates. However, TA accepts 
every new (proposed) solution that is not much worse (within a threshold) 
than the previous current solution, whereas in SA there is only a 
probability that a less desirable proposed solution would replace the 
current solution [24]. We only located four TA papers in the literature, 
and three of them [24, 50, 191] are used to compare with other heuristic 
methods. Only one paper [25] relied on the unique TA method to assess 
the ecological and economic goals in a forest plan.

Tabu search, which is one of the most extensively used heuristic methods for 
solving forestry-related problems, is a hill-climbing algorithm and 
combinatorial optimization technique. The search process arrives at the best 
solution by incrementally adding (or removing) decision choices to (or from) 
a solution, yet avoiding a continual re-selection of a subset of these 
choices based on their influence on the objective function [21]. Tabu 
search is also generally implemented as a 1-opt process, however 
improvements have been noted with the addition of intensification (2-opt) or 
diversification (frequency analysis or strategic oscillation) processes. 
Tabu search analyzes a ``neighborhood'' of proposed changes to a solution 
prior to selecting one, changes are then considered off-limits for a number 
of iterations of the model. Within forest planning it has been applied to 
problems related to economics [17, 45, 172, 194], commodity production 
[20, 21, 164, 191], stream sediment and temperature [27], adjacency 
issues [41, 43, 44, 47, 92], wildlife habitat [22, 30, 43], road 
system management issues [135, 201], and forest structure [52]. The 
literature illustrates that the size of the planning problems in the 25 tabu 
search papers we located are larger than 100 management units (75{\%} of 
them among 100 to 1,000 units, others were larger than 1,000 units). There 
are usually two types of decision procedures in tabu search: a change to 
single-decision choices (1-opt moves) and changes to two-decision choices 
(2-opt moves). Since 1999, almost half of tabu search papers have discussed 
the advantages and disadvantages of using combinations of 1-opt and 2-opt. 
The use of 2-opt moves allowed the tabu search procedure to find better 
solutions because the changes in the objective function value are not as 
severe as with using a 1-opt neighborhood alone, where changes are made 
simply to the status of individual harvest units [21].

Genetic algorithms are a population-based, nature-inspired random search 
technique, and were first developed by Holland (1975) in an attempt to 
locate global optimal solutions to complex problems. With genetic 
algorithms, a population (set) of solutions is generated. These are then 
combined randomly or deterministically to create new solutions. The new 
solutions are then modified slightly through ``mutations.'' The population 
is then updated, and the search continues until stoppings criteria have been 
recognized. In concept, the method is not very appropriate for solving 
spatial forest-planning problems unless limited amounts of genetic material 
(pieces of forest plans) are incorporated into new solutions. However, as 
its development proceeded and given successful application in other areas, 
such as strategic planning, machine learning and so on, since about 2000, 
researchers and practitioners have successfully applied GAs to spatial 
forest planning problems. Within forest planning, it has been applied to 
problems related to economics [152], commodity production [75], 
adjacency issues [148], forest structure [76], wildlife habitat 
[163], and landscape design [225]. Some researchers have conducted 
comparisons between GA and other heuristic methods, such as SA, and TS. For 
each iteration of a GA model, there may be multiple changes to a forest 
plan, and thus GA is relatively slow compared to some of the other heuristic 
methods. Opinions vary on the application of GAs to spatial forest planning 
problems. In the study of Bettinger et al. (2002), it was concluded that a 
basic GA was not as good as SA and TS. The same conclusion was attained by 
Liu et al. (2006), who suggest that simulated annealing is more efficient 
than genetic algorithms for forest harvest scheduling problems. However, 
Pukkala and Kurttila (2005) pointed out that GA might be better than SA and 
TS in spatial problems. However, they also concluded that GA was not good in 
very simple problems, and the improved performance of GA in the most 
difficult problems can result from the fact that it was the only technique 
where a move could imply more than one change in the solution [194]. 
For spatial problems, the best GA algorithms may be those that transfer 
limited genetic material in the development of new (child) solutions. There 
still exist fertile areas of subjects to research, including variable 
mutation rates and crossover probabilities, or the use of dynamic penalty 
functions, with parameters self-modified with the convergence process 
[75].

\subsection{Objective Function Components}
The economic and commodity production concerns of landowners continue to 
account for the majority of objectives in spatial forest planning problems 
presented in the literature (Figure 3). However, long-term sustainable 
forest management challenges have prompted researchers to pay more attention 
to wildlife habitat, forest structure, biodiversity, recreation, and other 
objectives. As a result, about one-third of the spatial forest planning 
papers accommodate other goals in the objective function of the problems 
presented. These are either single-objective optimization problems, or more 
commonly, goal programming problems that use various forms of utility 
functions. Interestingly, in Europe, utility functions have become common 
aspects of spatial forest planning [143], yet in North America, penalties 
are more commonly added to single parameter objective functions [12]. Why 
this is the case has yet to be understood, but may be related to the goals 
and objectives of both the planners and the land managers. 

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.5in]{17-83-1-SP.eps}}
\caption{Objectives contained in the spatial forest planning literature, by 
year.}\label{fig3}
\end{figure*}


The maximization of net present value (97 papers), revenue (28 papers), and 
wood production (76 papers) are still the highest-level issues of 
researchers and practitioners, as is the minimization of discounted costs 
(20 papers). Policy makers and private landowners continue to balance 
economic and commodity production objectives with other non-product 
objectives, however. Objectives which include maximizing area in habitat (19 
papers) and maximizing wildlife species populations (9 papers) dominate the 
non-product objectives that researchers and practitioners have considered 
(table 5). The population and habitat of a wildlife species is mostly 
affected by the landscape features and spatial distribution factors that are 
considered in a spatial forest planning process. Forest structure (16 
papers), biodiversity (11 papers), recreation (12 papers) are also hot 
topics in spatial forest planning. Other objective function components have 
included those related to entomology (Hof et al. 1997), adjacency of 
harvests (8 papers), landscape metrics (6 papers), shape indexes or 
clustering (3 papers), site disturbances (3 papers), regeneration areas 
(Jorgensen et al. 1992), and water yield (4 papers). Papers that describe 
single-objective problems represented about 69.1{\%} of the literature. 
Papers describing two-parameter objective functions represented about 
19.1{\%} of the literature, and the rest of the literature include more than 
three components in the objective function. As a result, we have seen an 
increase in the use of multiple objective function problems in spatial 
forest planning over the past ten years.



\begin{table*}[htbp]
\begin{center}
\caption{Related papers for objective functions categories in forest-level 
planning peer-reviewed articles.}
\begin{tabular}{|l|l|}
\hline
Objective categories& Literature \\
\hline
Maximize net present value& 
2, 4-8, 17-20, 27, 31, 36-39, 41-46, 50, 52, 53, 56, 57, 60, 62-64, 66, 69, 70, \vspace{-.05in} \\
& 73, 75-77, 80, 81, 90, 93, 107-109, 116, 122, 123, 126, 130, 134, 135, 140, \vspace{-.05in} \\
& 141, 143, 150, 152, 153, 157, 162, 164, 166, 169-173, 175, 185-188, 190, \vspace{-.05in} \\
& 194, 198-200, 202, 205, 206, 209, 213, 214, 219-221, 223, 230, 231, 233, \vspace{-.05in} \\
& 234, 236, 238, 241, 243-245 \\
\hline
Maximize revenue& 
1, 32, 33, 48, 56, 65, 83, 102, 104, 105, 110, 121, 128, 138, 146, 158, 159, \vspace{-.05in} \\
& 161, 168, 174, 192-194, 196, 208, 218, 221, 227 \\
\hline
Minimize discounted costs& 
20, 48, 61, 74, 89, 98, 99, 102, 103, 110, 113, 142, 154, 179, 180, 189, 201,  \vspace{-.05in} \\
& 214,233, 234, 240 \\
\hline
Wood flow& 
10, 15, 20-22, 26, 30, 32, 34, 40, 47, 54, 55, 61, 67-70, 79, 82, 84-88, 91, \vspace{-.05in} \\
& 100-102, 115, 117, 119, 121, 123-126, 128, 130-133, 137, 142, 148-151, 156, \vspace{-.05in} \\
& 160, 176, 177, 181, 182, 184, 195-197, 199, 200, 206, 211, 212, 215, 216,  \vspace{-.05in} \\
& 221, 224, 229, 238,243, 246, 247 \\
\hline
Maximize acres in habitat& 
1, 4, 22, 24, 49, 100, 137, 161, 163, 179, 180, 191, 194, 196, 197, 202, 203, \vspace{-.05in} \\
& 207, 240 \\
\hline
Maximize species& 
33, 88, 96, 101, 126, 181, 186, 191, 204 \\
\hline
Forest structure& 
40, 69, 91-93, 100, 125, 143, 149, 185, 191-193, 197, 221, 245 \\
\hline
Biodiversity& 
19, 106, 122, 125, 131, 132, 140, 149, 194, 197, 222 \\
\hline
Recreation& 
1, 40, 122, 123, 126, 128, 133, 143, 161, 181, 194, 195 \\
\hline
Fire& 
214 \\
\hline
Entomology& 
97 \\
\hline
Adjacency& 
3, 9, 92, 93, 144, 150, 239, 247 \\
\hline
Landscape metrics& 
54, 91, 100, 225, 246, 247 \\
\hline
Minimize shape index or clustering& 
187, 188, 219 \\
\hline
Minimize site disturbance& 
3, 126, 134 \\
\hline
Regeneration area& 
93, 120 \\
\hline
Water yield& 
95, 151, 197, 234 \\
\hline
\end{tabular}
\label{tab5}
\end{center}
\end{table*}

\subsection{Constraint Components}
Two constraints have dominated forest-planning problems over the last twenty 
years: (1) those that are fragmentation related, or involve harvest size or 
adjacency issues; and (2) those that involve economic measures or commodity 
production goals (Figure 4). The economic and commodity production 
constraints represent some of the more traditional constraints in forest 
plans. Economic and commodity production constraints (table 6) include those 
related to net present value [51], revenue (10 papers), budgets (9 papers), 
and even wood-flow (113 papers). Adjacency and green-up relationships, which 
address the juxtaposition of harvests and habitat, are perhaps the single 
most widely used spatial constraints in forest planning today [32]. The 
papers that involve adjacency relationships are numerous (90 papers). While 
we are unable to determine cause or effect, spatial forest planning problems 
seem to have become more complex as time proceeded through our analysis, and 
there has been a shift from a reliance on exact techniques or Monte Carlo 
simulation to the use of various heuristics. In addition, the constraints 
incorporated into these manuscripts have become more complex in recent 
years, using functional relationships related to wildlife habitat, 
biodiversity, aquatic resources and others. We assume the need to 
incorporate the complex relationships prompted the exploration of 
alternative solution methods, however, one could argue that the use of 
alternative solution methods allows a more extensive set of resource 
evaluation rules to be incorporated into forest plans. In addition, 
validating these problems (when solved with heuristics) becomes problematic 
because exact methods often are incapable of solving the full problem.

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.5in]{17-84-1-SP.eps}}
\caption{Constraints contained in the spatial forest planning literature, 
by year.}\label{fig4}
\end{figure*}


Other constraint functions (table 6) that have been considered include those 
related to forest structure or inventory (60 papers), road management (20 
papers), wildlife (30 papers), minimum or maximum harvest ages (40 papers), 
and aquatics, which includes stream sediment (7 papers), stream temperature 
(2 papers), water yield (5 papers). In addition, other noteworthy 
constraints include fire, entomology, biodiversity, carbon, optimal bucking, 
processing capacity or materials. 


\begin{table*}[htbp]
\caption{Related papers for constraint categories for forest-level planning 
peer-reviewed articles.}
\begin{center}
\begin{tabular}{|l|l|}
\hline
Constraint categories& 
Literature \\
\hline
Net present value& 
.51 \\
\hline
Revenue& 
48, 138, 166, 168, 174, 175, 181, 202, 208, 238 \\
\hline
Budget& 
55, 68, 82, 117, 133, 141, 164, 179, 181 \\
\hline
Wood flow& 
2, 5, 6, 8, 15, 18, 20, 21, 24, 26, 27, 31, 40-49, 52, 53, 60-65, 67, 68, 70, 73, \vspace{-.05in} \\
& 75-77, 79-82, 84, 90, 96, 98, 99, 103-106, 108, 109, 113, 115, 116, 133-135, \vspace{-.05in} \\
& 137, 138, 141, 142, 148, 153, 157-162, 164, 166, 168, 169, 171, 173-178, \vspace{-.05in} \\
& 181, 183, 186,187, 189, 190, 196, 198, 199, 201, 205, 206, 209, 211, 215, \vspace{-.05in} \\
& 218-220, 222, 223, 226, 229-231, 233, 236, 238, 241, 243, 245 \\
\hline
Stream sediment& 
27, 31, 151, 220, 231, 233, 238 \\
\hline
Stream temperature& 
27, 31 \\
\hline
Water yield& 
35, 133, 151, 205, 220 \\
\hline
Forest structure or inventory& 
5-7, 17-19, 21, 28, 39, 46, 51, 52, 57, 59, 62, 64, 65, 68, 76, 77, 80, 83, 95, \vspace{-.05in} \\
& 104-106, 109, 110, 116, 117, 120, 138, 156-158, 160-162, 171, 173, 175, 176, \vspace{-.05in} \\
& 182, 185, 186, 188, 189, 196, 198, 200, 202, 205, 208, 209, 216, 227, 229, \vspace{-.05in} \\
& 230, 241 \\
\hline
Adjacency& 
7, 9, 10, 15, 17, 24, 26, 32, 36-38, 41-45, 52, 53, 60, 61, 63-67, 76, 81-88, 90, \vspace{-.05in} \\
& 94, 100, 107, 108, 111, 117-119, 134, 139, 144, 146, 148, 149, 151, 154, \vspace{-.05in} \\
& 156-159, 166-170, 174-177, 184, 185, 190, 198, 200, 201, 208-213, 215, \vspace{-.05in} \\
& 216, 218-220, 222, 223, 226, 227, 230, 239, 241, 243 \\
\hline
Road-related& 
2, 10, 60, 66, 74, 82, 104, 105, 134, 142, 166, 174, 177, 189, 201, 231, 233, 238 \\
\hline
Wildlife& 
25, 30, 33, 34, 42, 49, 50, 62, 87, 89, 94, 100, 101, 103, 106, 133, 147, 151, \vspace{-.05in} \\
& 161, 172, 180, 181, 200, 202-204, 220, 224, 227, 240 \\
\hline
Minimum or maximum & 8, 19, 24-26, 28, 30, 34, 42-44, 51, 65, 67, 77, 83-88, 95, 98, 102, 103, 109, \vspace{-.05in} \\
harvest age& 111, 148, 159, 161, 171, 176-178, 182, 212, 216, 227, 243, 244 \\
\hline
Fire& 
199 \\
\hline
Entomology& 
97, 162 \\
\hline
Biodiversity& 
19, 133, 146 \\
\hline
Carbon& 
135 \\
\hline
Optimal bucking& 
73, 141 \\
\hline
Processing capacity or materials& 
6, 48, 80 \\
\hline
\end{tabular}
\label{tab6}
\end{center}
\end{table*}

\subsection{Type of Data used in Forest Planning Research}
The type of the data that has been used in spatial forest planning research 
is characterized as hypothetical and real, and raster and vector. We used 
our best judgment, where necessary, to make these determinations. Raster 
data and vector data are the two basic GIS data structures that we 
considered in the review. Raster data is characterized by regular-shaped 
grid cells (pixels) obtained from satellites or other geoprocessing methods. 
This data structure can be manipulated quickly by a computer, thus 
computations are generally more efficient. Vector data includes points, 
lines, and polygons (irregularly shaped), which are derived from air photo 
image interpretation, digitizing, and land surveys. Since this data is 
relatively easy to obtain and use, it is not uncommon to find that vector 
data is more prevalent in forest planning problems compared to raster data 
(Figure 5). Within the 245 papers we located, we determined that 50 used 
raster data, 107 used vector data, and 10 used both, which means that about 
one-third of the papers did not explicitly refer to one of these two data 
structures (we considered the review papers to not mention either of them). 
Although it is hard to argue against the fact that vector data is prevalent 
in the planning process, the trends indicate that researchers and 
practitioners may be suggesting that a single data structure is not enough 
to satisfy the needs of complex spatial forest planning and research. In 
order to further describe the type of data used, we classified it as real or 
hypothetical (Figure 6). It seems obvious that researchers would want to 
test their methods on real data, but due to the complexity of the planning 
problems, researchers at many times resort to testing their methods on 
hypothetical data. Among the 245 papers we reviewed, 140 used real data, 72 
used hypothetical data, and 5 used both. Through our interpretation of the 
literature, we concluded that 143 of the papers represent applications and 
87 lacks an example of the use of the techniques in applied spatial forest 
planning, and of course 18 are review papers (Figure 7). As a result, many 
of the applied research papers utilize hypothetical data. Two reasons for 
this include the difficulty in obtaining large databases describing actual 
landscapes, and the inability to obtain permission to illustrate an 
organization's data in a published research paper.

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.6in]{17-85-1-SP.eps}}
\caption{Vector and Raster data in the spatial forest planning literature, 
by year.}\label{fig5}
\end{figure*}


\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.3in]{17-86-1-SP.eps}}
\caption{Real and theoretical data in the spatial forest planning 
literature, by year.}\label{fig6}
\end{figure*}


\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.4in]{17-87-1-SP.eps}}
\caption{Type of papers in spatial forest planning literature, by year.}\label{fig7}
\end{figure*}


\subsection{Geographic Location of the Problems}
While the importance of forest planning has been realized worldwide, 
research on forest planning is costly and the objectives nowadays do not 
concern economic or commodity production. Thus, developing countries may be 
short of such funds for conducting forest-planning research or may not place 
high importance on its use in forest management. In the literature, the 
countries or continents where most of the published forest planning problems 
are geographically situated (Figure 8) are: USA (68 papers), Canada (34 
papers), and Europe (48 papers). However, researchers and practitioners have 
also solved some spatial forest planning problems in Oceania (6 papers), 
South America (7 papers), Asia [54, 241], and Africa [181]. 

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.5in]{17-88-1-SP.eps}}
\caption{Location of spatial forest planning analyses, by year.}\label{fig8}
\end{figure*}


\subsection{Spatial Concerns}
As we noted earlier, spatial forest planning is used to examine patterns and 
trends in the spatial development of landscapes, and focuses on forestry and 
natural resource management activities and the specific tools used to 
develop, implement, and evaluate forest plans and alternative policies 
[9]. These are core elements of spatial forest planning. Control of 
these concerns has been accomplished through the objective function and 
constraints of the problem formulation (see tables 5 and 6, and sections 3.2 
and 3.3). Therefore, given the structure of the model being used and the 
creativity of the planner, there are a number of ways by which one can 
acknowledge and accommodate spatial concerns in forest plans. An increase in 
the spatial restrictions or objectives in forest planning problems is 
evident by the results (Figure 9). In our classification of objectives, 
spatial objectives include those related to wildlife habitat (some 
maximizing acres in habitat are not spatial), forest structure, adjacency, 
and many others. The spatial constraints include adjacency, aquatics, forest 
structure or inventory, wildlife, and road management. Only 37 papers among 
245 papers we found used non-spatial models. Among these, a few attempt to 
address hypothetical problems [16, 98, 99, 102, 113, 115, 203, 209] and 
related these to potential practical application. 

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.5in]{17-89-1-SP.eps}}
\caption{Number of papers that include spatial goals, by year.}\label{fig9}
\end{figure*}


\subsection{The use of Geographic Information Systems (GIS)}
Since the introduction of GIS in natural resource management, there has been 
a logical increase in the application of GIS to forest planning (Figure 10). 
The role of GIS technology in spatial forest planning has, however changed 
significantly, from the source of input to the analysis tool of spatial 
models. One vital function of GIS is the ability to address locational 
issues, and to manage information in digital form, through an attribute 
database. GIS has also traditionally been used in forestry to store maps in 
electronic form and to make calculations, such as areas and distances 
[14]. However, if the spatial restrictions or objectives were not 
included in a forest planning problem formulation, and subsequent spatial 
analysis was necessary, GIS is used to only address these post-plan 
development issues. More recently, its use has been extended to analyses of 
potential land uses and other complex problems, which have a spatial 
context. However, it is not uncommon to see GIS used as an input facilitator 
rather than as an analysis tool. 

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.5in]{17-90-1-SP.eps}}
\caption{GIS use in spatial forest planning literature, by year.}\label{fig10}
\end{figure*}


\section{Discussion}
There are still many important areas in quantitative forest planning that 
need to be further studied. Although we have discussed that MIP methods are 
limited by problem size and are difficult to use for solving spatial 
problems, researchers and practitioners still attempt to use innovative 
formulations of MIP to obtain exact answers. For example, two MIP 
harvest-scheduling formulations have been developed to solve area-based 
adjacency problems [59]. Forest planning problems with patch size 
constraints or objectives that are essential for wildlife habitat concerns 
have also been addressed with new formulations of MIP [198]. Finding 
ways to apply exact methods, especially mixed integer programming, to very 
large problems without running into restrictions of the number of 
constraints, or without requiring extensive computational time to solve the 
problems is an area worth further research.

As we know, a large number of new algorithms appear every year in the area 
of operations research, and applying those algorithms to forest planning 
practice is an interesting topic. One relevant classification of heuristic 
methods is to separate heuristics that are based on populations of solutions 
from heuristics that are based on a single change to a solution (point-based 
algorithms). A point-based algorithm will only have one unique solution per 
iteration, and we update the best one with the new obtained solution if it 
is better than the best we have found before. With a point-based algorithm, 
we only need to define the current solution and use a metaheuristic to 
obtain a new solution. With a population-based algorithm, we have to define 
the current population and new population in each iteration. Additionally, 
we also need to initiate the population size and define the maximum 
population size allowed. Other population-based heuristic methods like 
particle swarm optimization, which has been successfully used in other areas 
including optimization of artificial neural networks, image processing, and 
computational biology, could also been applied in forest planning. More 
discussion of the advantages and disadvantages should follow, and they 
should be tested against various standard forest planning problems.

No matter what heuristic techniques one adopts to solve spatial forest 
planning problems, choosing the appropriate parameters seems to require the 
most attention. This issue is treated lightly in many papers, thus a broader 
explanation of the parameters for typical forest planning problems is needed 
in future work. One might ask whether there ways to estimate the parameters 
based on the type and size of a problem (figure 11), rather than needing to 
perform a number of trials to locate the acceptable range of parameters. 
Ultimately we need to find ways to estimate the appropriate parameters 
rather than have the user try to identify them, taking this process out of 
their hands.

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5.5in,height=2.5in]{17-91-1-SP.eps}}
\caption{Size of the problem in spatial forest planning literature, by 
year.}\label{fig11}
\end{figure*}


Addressing limitations of the search process is also an area requiring more 
work. As we discussed, it is probably better for GA to swap small amounts of 
genetic material during each iteration of a spatial forest planning process, 
because the transfer of large amounts of genetic material during the 
crossover results in numerous violations of spatial constraints. The same is 
true in spatial forest planning problems when the mutation rate is high. 
After addressing these types of limitations, GA and its modifications could 
be more effectively used for spatial forest planning problems. Recently, an 
intelligent mechanism of combining standard heuristic methods such as TS, 
SA, TS, and the raindrop method has been developed by Li (2007). Using such 
a mechanism to study how to intelligently combine GA with other heuristics 
is new, and needs additional research to determine the most effective meta 
heuristic model.

Since heuristics cannot guarantee optimality, the development of a measure 
of quality is necessary. What we usually do in validations heuristic results 
is to assess the solution value, solution running time, complexity of 
programming codes, and various statistics including maximum value, minimum 
value, mean, standard deviation, and the estimated global optimum. These are 
often compared against results generated by other heuristic techniques, or 
ideally against an exact solution generated by traditional mathematical 
programming techniques. However, if the exact solution is elusive, a 
comparison against other heuristics only provides relative validation. One 
might logically ask about the quality of solutions generated by the other 
heuristics, and whether this comparison sheds light on overall solution 
quality. As a result, one gap in the literature is the development of a 
solution quality index. This opens an area of research for professional 
statisticians to apply new statistics to validate heuristic results. 

Another fertile area of research involves integrating the theories and 
technologies of heuristics with relationships developed in other areas. For 
example, we could develop effective partnerships between landscape ecology 
and forest planning. Landscape ecologists have made significant 
contributions to the subject the conservation biology. Since forestry 
entails the alteration of landscapes, the theory and tools of landscape 
ecology could be integrated into a forest planning process. As the field of 
landscape ecology grows, its concepts and tools (e.g. remote sensing, GIS, 
spatial statistics, spatially explicit modeling) are increasingly being used 
in ecological disciplines including forestry [78]. As we know, modeling 
ecological processes across scales, including scaling up and scaling down, 
is essential in landscape ecology. In forest planning, we divide the 
planning into strategic, tactical and operational levels. We will also face 
the scaling up and scaling down problem. We could work together with 
landscape ecologists to integrate these problems. For example the objective 
function with respect to maximizing acres in wildlife habitat, Bettinger et 
al. (2002) mentioned that could be divided to strata-based goals, 
minimum-patch-size goals, and complementary-patch goals, to illustrate that 
the range of factors one can consider. 

At this time, we have not considered the publications from the conference 
proceedings, graduate-level dissertations and public agencies and advances 
have been reported in these gray literature, so we leave this job for other 
researchers. In addition, although we have found theoretical papers in our 
review that do not specifically relate to spatial forest planning, we did 
not study the relationship between these and any related applied paper. This 
should be a time-consuming, but interesting job, because we may eventually 
infer the kinds of theory in that may have successful application in forest 
planning. 

\section{Conclusions}
We investigated the difference between the early period (1995 and prior) and 
recent period (2000 and after) with respect to spatial forest planning 
research (Figure 12). The results illustrate that researchers and 
practitioners have relied more on heuristic techniques in the latter period 
than the early period. At the same time, we find that researchers and 
practitioners still attempt to use traditional, exact methods no matter what 
the period is being considered. Due to the increase in the complexity of the 
planning environment, the type of objective function has shifted slightly 
from commodity production to other concerns. When the constraint components 
in the papers are considered, we find that reliance on wildlife, aquatics, 
and biodiversity constraints have not changed much as time has passed. 
However, less emphasis has been placed on economics or commodity production 
in the latter period than the early period, and more emphasis has been 
placed on other constraints in the latter period. 

\begin{figure*}[htbp]
\centerline{\includegraphics[width=5in,height=4in]{17-92-1-SP.eps}}
\caption{Differences between the early period and recent period.}\label{fig12}
\end{figure*}


The type of spatial forest planning problems being solved has evolved over 
the past 20 years. The trends suggest that forest-level planning 
publications have increased in the journals examined over the past fifty 
years, however the number of publications seem to have stabilized in the 
last few years [23], and perhaps has been decreasing since 2002. While we 
found the rate of publication easing in the last few years, the reason for 
this is not clear. For example, one could argue that the science has matured 
significantly, and that novel approaches to illustrating solutions to 
complex management problems are becoming moot. In fact many approaches to 
spatial forest planning have been proposed. Perhaps the questions now lie 
with determining efficient methods for designing constraint sets, or with 
designing adaptive heuristics that leave parameterization to the algorithm 
rather than the user. The rate has not eased due to a reduction in available 
journals. In fact it is arguable that the aims and scope of many 
international journals leave open the opportunity to publish spatial forest 
planning research. In addition, a number of new online journals have 
appeared in the last decade, providing more outlets for research results. 
One aspect concurrent with the maturing of the science relates to the 
validation of results. Perhaps higher standards in this area have influenced 
the quality of peer-reviewed literature, although we did not test this 
hypothesis here. 

It is difficult to predict which methods will dominate quantitative forest 
planning in the future. The two comprehensive reviews we located both 
discussed the possibility that the hierarchal structure could be divided 
into strategic, tactical and operational planning. Strategic forest plans 
attempt to develop broad strategies related to harvest levels, habitat 
levels, and economic expectations. Tactical forest plans determine where 
activities will be placed on a landscape and may require integer decision 
variables [23]. The operational level involves the determination of a land 
use plan for an area of the forest, and forest operations problems that 
represent short-term issues, such as harvesting, production, hauling, 
planting, pest control, fire management, and road building and maintenance 
[166]. Since exact methods have the advantage of ensuring that the 
solution one finds is optimal, the use of these seems valuable for all three 
levels of planning. However, most planning problems we now face are either 
tactical or operational, and involve complex problems with discrete integer 
variables, thus researchers and practitioners have embarked upon solving 
these problems using heuristic methods. 

From this extensive and world-wide forest planning review, we are convinced 
that the past 20 years represents the seminal period for the development of 
the spatial forest planning methods. The literature review results convince 
us that methods used in spatial forest planning have shifted from exact 
algorithms to heuristic techniques. At the same time, researchers and 
practitioners have attempted to adopt various other methods to solve forest 
planning problems. In addition to the economic and commodity production 
objectives, an increase in ecological and social objectives has been noted. 
Besides economic and commodity production constraints, adjacency and 
green-up relationships are now also considered important constraints for 
industrial and managers in North America. Compared with raster data, vector 
data are more often used in the planning process. Hypothetical data are used 
by researchers to introduce new methods or compare various methods. To the 
extent that forest planning is of concern to forest policy makers, 
hypothetical examples are of as much value as specific real-life examples, 
although it was not unexpected to find that 35{\%} of the papers failed to 
address a real-life problem. The geographic extent of the papers we located 
is world-wide, however not evenly spread across the world: the United 
States, Canada, and Europe provide most of the work in this area. Spatial 
restrictions or objectives in the process are the trend for the forest 
planning problems. GIS technology is a widely-used tool in forestry and 
natural resource management, yet thus far has had limited application 
(generally used as an input tool) in the forest planning process. More 
research should be conducted to continue to integrate GIS with forest 
planning algorithms. The gaps in knowledge that we have identified leave 
room for further investigation into mixed integer methods, applications of 
new heuristics to spatial problems, exploration of appropriate heuristic 
parameters, development of a solution quality index, integration with other 
fields utilizing spatial relationships, and a broader examination of the 
non-peer-reviewed literature.

\section*{Acknowledgements}
This research was supported by the USDA Cooperative State Research Service's 
McIntire-Stennis program (project number GEOZ-0138-MS). We appreciate the 
thoughful comments of the reviewers of the manuscript.

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