An interval space reducing method for constrained problems with particle swarm optimization

Abstract

In this paper, we propose a method for solving constrained optimization problems using Interval Analysis combined with Particle Swarm Optimization. A Set Inverter Via Interval Analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a Space Cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified Particle Swarm Optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100,000 runs on a set of wellknown benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.

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“…Essas características fazem do PSO um método muito útil para selecionar pregões que maximizam os lucros do fornecedor considerando atributos como incerteza (Nojavan et al, 2015), informação incompleta (Soleymani, 2011) e o comportamento e racionalidade limitada dos agentes (Zhu et al, 2006). Machado-Coelho et al (2017) explicam que o PSO funciona por meio da geração aleatória r de s_size soluções para o problema dentro de um espaço n-dimensional chamadas de partículas. Na primeira iteração, as melhores partículas ou soluções são guardadas em um vetor de memória chamado de pbest.…”