ON THE DISTRIBUTION OF PARETO OPTIMAL SOLUTIONS IN ALTERNATIVE SPACE – THE INVESTIGATION OF MULTI OBJECTIVE PERMUTATION FLOW SHOP SCHEDULING PROBLEMS

The paper presents a study of the search space topology in the context of global optimization under multiple objectives. While in mono criterion problems a single global optimum has to be identified, multi objective problems require the identification of a whole set of equal. Pareto optimal alternatives. It is unclear up to now, however, whether Pareto optimal solutions appear relatively concentrated in search space, or whether their relative positions are rather distant. This open issue is addressed to the multi objective permutation flow shop scheduling problems. Distance metrics is introduced to asses numerical evaluation of the concentration of Pareto sets. It can be seen that independent from the chosen optimality criteria, Pareto optimal alternatives appear relatively concentrated in alternative space. The result holds for an extensive range of generated problem instances for which the exact global optima are known as well as for benchmark instances taken from literature. The importance of the results can be seen in the context of metaheuristic local search approaches for which meaningful implications derive.