An analysis of Monte Carlo integer programming, simulated annealing, and tabu search heuristics for solving spatial harvest scheduling problems

Heuristics are commonly used to solve spatial harvest scheduling problems. They can generate spatially and temporally feasible solutions to large problems that traditional mathematical programming techniques are unable to solve. A common complaint about heuristics is that the quality of the solutions is unknown. We compared three heuristic techniques commonly used to solve spatial harvest scheduling problems: Monte Carlo integer programming, simulated annealing, and tabu search. Five hundred solutions to four problems, which had between 3000 and 5000 0–1 integer variables, were generated with each heuristic technique. In addition to the heuristic solutions, the optimal solution value was found to each problem using integer programming. Simulated annealing found the highest solution value for three of the four planning problems, and was less than 1% from the highest objective function value in the fourth problem. Tabu search located the best solution for the fourth planning problem. Monte Carlo integer programming had the lowest objective function for all four problems. Tabu search had the smallest range of solutions, followed by simulated annealing. Monte Carlo integer programming had the largest range of solutions. Using the Anderson–Darling statistics, the hypothesis that the solutions from each heuristic technique were distributed as a Weibull distribution was rejected for 10 of the 12 set of values. For the two solutions where the Weibull distribution was not rejected, the estimated optimal solution was found to be an unreliable estimate of the actual optimal solution. It appears that the reliability of using extreme value statistics to estimate the optimal solution is dependent on the quality of solutions generated by the heuristic procedure.