A scalable parallel cooperative coevolutionary PSO algorithm for multi-objective optimization.

We present a parallel multi-objective cooperative coevolutionary variant of the Speed-constrained Multi-objective Particle Swarm Optimization (SMPSO) algorithm. The algorithm, called CCSMPSO, is the first multi-objective cooperative coevolutionary algorithm based on PSO in the literature. SMPSO adopts a strategy for limiting the velocity of the particles that prevents them from having erratic movements. This characteristic provides the algorithm with a high degree of reliability. In order to demonstrate the effectiveness of CCSMPSO, we compare our work with the original SMPSO and three different state-of-the-art multi-objective CC metaheuristics, namely CCNSGA-II, CCSPEA2 and CCMOCell, along with their original sequential counterparts. Our experiments indicate that our proposed solution, CCSMPSO, offers significant computational speedups, a higher convergence speed and better or comparable results in terms of solution quality, when evaluated against three other CC algorithms and four state-of-the-art optimizers (namely SMPSO, NSGA-II, SPEA2, and MOCell), respectively. We then provide a scalability analysis, which consists of two studies. First, we analyze how the algorithms scale when varying the problem size, i.e., the number of variables. Second, we analyze their scalability in terms of parallelization, i.e., the impact of using more computational cores on the quality of solutions and on the execution time of the algorithms. Three different criteria are used for making the comparisons, namely the quality of the resulting approximation sets, average computational time and the convergence speed to the Pareto front.