On Pathological Fitness Landscapes for Constrained Combinatorial Optimization

Population-based search methods such as evolutionary algorithms follow gradients in the fitness landscape under the assumption that high quality solutions will lead to even better ones. Most real-world optimisation problems, however, have constraints which lead to infeasible solutions that may disrupt these gradients. As a result, high quality solutions may lie in regions that are often unreachable from regions in the fitness landscape where the preponderance of feasible solutions lie. In such cases, the make-up of the initial population as well as critical aspects of the search strategy become the crucial factors in determining whether or not high quality regions are ever reached. In this paper, we present examples of pathological landscapes that arise by considering the constrained component deployment optimisation problem for which standard evolutionary algorithms are almost certain to fail to reach the regions where high quality solutions lie. We indicate how some simple modifications can help alleviate this problem.