Integration of directed searches in particle swarm optimization for multi-objective optimization

While a wealth of endeavors in optimization studies are devoted to the realization of the two ultimate goals, which are: 1) to minimize the distance between the found solutions from the true Pareto front and 2) to maximize the diversity among the found Pareto solutions in both objective and parameter spaces; only lukewarm efforts are given to the development and utilization of approximating techniques of non-dominated sets in continuous multi-objective optimization studies. In this regard, a directed search method embedded in a vector particle swarm optimization (PSO) algorithm, as an exploiting search phase to improve the efficiency of the algorithm, is proposed to steer the searches toward the desired direction. The proposed strategy excludes gradient computations of the Jacobian in determining the corresponding desired direction in the parameter space. The components of the PSO algorithm are also redesigned accordingly. The performances with the application of the proposed algorithm on two case studies are reported and compared with those of three well developed vector evolutionary algorithms.