A Symbiotic Organisms Search algorithm with adaptive penalty function to solve multi-objective constrained optimization problems

Abstract

Many real world engineering optimization problems are multi-modal and associated with constrains. The multi-modal problems involve presence of local optima and thus conventional derivative based algorithms do not able to effectively determine the global optimum. The complexity of the problem increases when there is requirement to simultaneously optimize two or more objective functions each of which associated with certain constrains. Recently in 2014, Cheng and Prayogo proposed a new metaheuristic optimization algorithm known as Symbiotic Organisms Search (SOS). The algorithm is inspired by the interaction strategies adopted by the living organisms to survive and propagate in the ecosystem. The concept aims to achieve optimal survivability in the ecosystem by considering the harm and benefits received from other organisms. In this manuscript the SOS algorithm is formulated to solve multi-objective problems (termed as MOSOS). The MOSOS is combined with adaptive penalty function to handle equality and inequality constrains associated with problems. Extensive simulation studies are carried out on twelve unconstrained and six constrained benchmark multi-objective functions. The obtained results over fifty independent runs reveal the superior performance of the proposed algorithm over multi-objective colliding bodies optimization (MOCBO), multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm II (NSGA-II) and two gradient based multi-objective algorithms Multi-Gradient Explorer (MGE) and Multi-Gradient Pathfinder (MGP). The engineering applications of the proposed algorithm are demonstrated by solving two constrained truss design problems.