Multiobjective variable mesh optimization

in Annals of Operations Research (2016)

In this article we introduce a new multiobjective optimizer based on a recently proposed metaheuristic algorithm named Variable Mesh Optimization (VMO). Our proposal (multiobjective VMO, MOVMO) combines ... [more ▼]

In this article we introduce a new multiobjective optimizer based on a recently proposed metaheuristic algorithm named Variable Mesh Optimization (VMO). Our proposal (multiobjective VMO, MOVMO) combines typical concepts from the multiobjective optimization arena such as Pareto dominance, density estimation and external archive storage. MOVMO also features a crossover operator between local and global optima as well as dynamic population replacement. We evaluated MOVMO using a suite of four wellknown benchmark function families, and against seven state-of-the-art optimizers: NSGA-II, SPEA2,MOCell, AbYSS,SMPSO,MOEA/DandMOEA/D.DRA. The statistically validated results across the additive epsilon, spread and hypervolume quality indicators confirm that MOVMO is indeed a competitive and effective method for multiobjective optimization of numerical spaces. [less ▲]

Reasoning With Various Kinds of Preferences: Logic, Non-Monotonicity, and Algorithms

in Annals of Operations Research (2008), 163(1), 89114

As systems dealing with preferences become more sophisticated, it becomes essential to deal with various kinds of preference statements and their interaction. We introduce a non-monotonic logic ... [more ▼]

As systems dealing with preferences become more sophisticated, it becomes essential to deal with various kinds of preference statements and their interaction. We introduce a non-monotonic logic distinguishing sixteen kinds of preferences, ranging from strict to loose and from careful to opportunistic, and two kinds of ways to deal with uncertainty, either optimistically or pessimistically. The classification of the various kinds of preferences is inspired by a hypothetical agent comparing the two alternatives of a preference statement. The optimistic and pessimistic way of dealing with uncertainty correspond on the one hand to considering either the best or the worst states in the comparison of the two alternatives of a preference statement, and on the other hand to the calculation of least or most specific “distinguished” preference orders from a set of preference statements. We show that each way to calculate distinguished preference orders is compatible with eight kinds of preferences, in the sense that it calculates a unique distinguished preference order for a set of such preference statements, and we provide efficient algorithms that calculate these unique distinguished preference orders. In general, optimistic kinds of preferences are compatible with optimism in calculating distinguished preference orders, and pessimistic kinds of preferences are compatible with pessimism in calculating distinguished preference orders. However, these two sets of eight kinds of preferences are not exclusive, such that some kinds of preferences can be used in both ways to calculate distinguished preference orders, and other kinds of preferences cannot be used in either of them. We also consider the merging of optimistically and pessimistically constructed distinguished preferences orders. [less ▲]