The Open Operational Research Journal, 2010, 4, 1-11 1 1874-2432/10 2010 Bentham Open Open Access Informed Development of Meta Heuristics for Spatial Forest Planning Problems Rongxia Li 1 , Pete Bettinger *,2 and Kevin Boston 3 1 School of Forest Resources, Forest Bioproduct Research Initiative, University of Maine, Orono, ME 04469, USA 2 Warnell School of Forestry and Natural Resources, University of Georgia, Athens, GA 30602, USA 3 Department of Forest Engineering, Resources & Management, Oregon State University, Corvallis, OR 97331, USA Abstract: In this research application paper, the usefulness of an intelligent mechanism (a cubic spline smoothing technique) for determining when to switch from one algorithm to another within a meta heuristic search process is explored. We concentrated on a typical planning problem for a southern United States forestry company where the net present value of management activities is maximized subject to wood flow and harvest adjacency constraints. We found that more than 75% of the 3-algorithm meta heuristics examined produced consistently better solutions than the best standard heuristic (threshold accepting) in terms of mean and maximum solution values. However, a 2-algorithm meta heuristic (threshold accepting + tabu search) performed the best in terms of the average solution value and the absolute maximum solution value, improving solution quality 1.4% over the best standard heuristic solution value. Results also indicate meta heuristics which began a search with a relatively fast, stochastic search process (simulated annealing or threshold accepting) and end a search with a relatively slow, deterministic search process (e.g., tabu search) produced better solutions than other model configurations for the problem examined. Further, results suggest that the time to switch from one heuristic to another should be based on when the improvement in solution quality stagnates. Without recognizing this point, a search process may switch prematurely or be computationally wasteful. Keywords: Operations research, forest planning, combinatorial optimization. INTRODUCTION Spatial forest planning has gained wide acceptance over the past decade, as people have gradually recognized the importance of tactical planning, and as forest sustainability concepts have been more closely integrated with planning processes [1]. Knowing the exact location of management activities can help forest managers better understand forest planning problems, account for spatial restrictions and wildlife habitat concerns, and thus allow them to make appropriate decisions. Many forest regulations and voluntary guidelines require or suggest that harvesting activities follow certain rules regarding clearcut sizes and landscape patterns [1]. Therefore, involving spatial components in forest planning processes helps planners more closely model operational issues. However, it is widely acknowledged that spatial forest planning problems can be difficult to solve [2], especially for those with green-up or adjacency constraints that control the timing and juxtaposition of harvests, since they are combinatorial in nature [1, 3-5]. Using exact math- ematical methods (mixed integer programming and integer programming) to solve large spatial forest planning problems can be difficult, and can involve an excessively long comput- ational times. *Address correspondence to this author at the Warnell School of Forestry and Natural Resources, University of Georgia, Athens, GA 30602, USA; Tel: 706-542-1187; Fax: 706-542-8356; E-mail: pbettinger@warnell.uga.edu For these reasons, heuristic methods have been explored for addressing spatial forest planning problems, and they have been accepted as a practical approach to generate near- optimum solutions in a reasonable amount of time. The most commonly used heuristic methods in the field of forestry include simulated annealing [2, 4, 6-9], tabu search [10-12], genetic algorithms [12-14], threshold accepting [15, 16], and Monte Carlo random search [17]. Some of the heuristic methods have been enhanced to further explore the solution space and possibly improve the quality of solution values. For example, Richards and Gunn [18] designed an oscillating reactive tabu search and found it can improve solution values by about 20%. Bettinger et al. [5] developed 2-opt tabu search and also obtained better results over standard tabu search. Other forestry research efforts have shown that combining two algorithms may allow one to locate better solutions [12, 15]. However, this combination has generally been limited to two heuristic algorithms, and the decision criteria for switching processes has been relatively rote and determined by the experiences and expertise of the researcher (i.e., change after x number of iterations). While our assessment includes only the heuristic techniques commonly used in forest management and planning, applications and demonstrations of soft computing tools for decision support in fields other than forest management may inspire researchers to adapt the concepts to forestry problems. Advances in other areas of operations research include the use of neural network algorithms