Ordinal comparison of heuristic algorithms using stochastic optimization

The performance of heuristic algorithms for combinatorial optimization is often sensitive to problem instances. In extreme cases, a specialized heuristic algorithm may perform exceptionally well on a particular set of instances while fail to produce acceptable solutions on others. Such a problem-sensitive nature is most evident in algorithms for combinatorial optimization problems such as job shop scheduling, vehicle routing, and cluster analysis. The paper proposes a formal method for comparing and selecting heuristic algorithms (or equivalently, different settings of a same algorithm) given a desired confidence level and a particular set of problem instances. We formulate this algorithm comparison problem as a stochastic optimization problem. Two approaches for stochastic optimization, ordinal optimization and optimal computing budget allocation are applied to solve this algorithm selection problem. Computational testing on a set of statistical clustering algorithms in the IMSL library is conducted. The results demonstrate that our method can determine the relative performance of heuristic algorithms with high confidence probability while using a small fraction of computer times that conventional methods require.