Priority based ∊∊ dominance: A new measure in multiobjective optimization

Dominance is a fundamental concept in Multiobjective Optimization (MOO) where a solution is said to dominate the other if it is better in at least one objective, and same as or better in the other objectives. Given a pair of solutions, if neither dominates the other, then the solutions are said to be non-dominated. In real spaces, a large number of non-dominated solutions can exist in principle, making convergence of MOO techniques rather slow. Relaxed forms of dominance have been proposed in the literature for faster convergence. One such form is the ∊∊-dominance, which in principle, partitions the space into ∊∊-sized grids. The value of ∊∊ is often user defined and the performance of ∊∊-dominance based multiobjective evolutionary algorithms (∊∊-MOEAs) critically depends on the value of ∊∊. In this article we propose a novel way of determining the value of ∊∊, which is different for each objective function, based on the correlation between them. We call this approach Priority Based ∊∊ (PBE) as the method ranks the objectives according to their priority before calculating the ∊∊ values. PBE is incorporated in an archived simulated annealing based MOO technique called AMOSA. AMOSA has been earlier shown to outperform several well-known MOO techniques especially for many objective optimization. PBE based AMOSA, referred to as PBE-AMOSA, is found to comprehensively outperform AMOSA, MOEA/D-DE, the conventional ∊∊ based version ∊∊-AMOSA and ∊∊-MOEA both in case of benchmark test problems and 0/1 knapsack problem.