۱- Introduction

۲- Related works

۳- Constrained multi-swarm particle swarm optimization without velocity

۴- Simulation results

۵- Conclusion

References

Abstract

The original particle swarm optimization (PSO) is not able to tackle constrained optimization problems (COPs) due to the absence of constraint handling techniques. Furthermore, most existing PSO variants can only perform well in certain types of optimization problem and tend to suffer with premature convergence due to the limited search operator and directional information used to guide the search process. An improved PSO variant known as the constrained multi-swarm particle swarm optimization without velocity (CMPSOWV) is proposed in this paper to overcome the aforementioned drawbacks. Particularly, a constraint handling technique is first incorporated into CMPSOWV to guide population searching towards the feasible regions of search space before optimizing the objective function within the feasible regions. Two evolution phases known as the current swarm evolution and memory swarm evolution are also introduced to offer the multiple search operators for each CMPSOWV particle, aiming to improve the robustness of algorithm in solving different types of COPs. Finally, two diversity maintenance schemes of multi-swarm technique and probabilistic mutation operator are incorporated to prevent the premature convergence of CMPSOWV. The overall optimization performances of CMPSOWV in solving the CEC 2006 and CEC 2017 benchmark functions and real-world engineering design problems are compared with selected constrained optimization algorithms. Extensive simulation results report that the proposed CMPSOWV has demonstrated the best search accuracy among all compared methods in solving majority of problems.

Introduction

The field of optimization has received significant attention in recent years as a promising tool for decision making. Depending on the objective function used to describe a specific goal to be achieved by an optimization problem, the optimal combination of decision variables obtained can either lead to the smallest objective function value for minimization problems or the largest objective function value for maximization problems. Majority of the real-world engineering application such as product development are considered as the constrained optimization problems (COPs). The objective functions used to describe the preliminary design model of product are generally represented using a set of analytical equations, while the product specifications are formulated as technical constraints. The presence of optimization constraints tend to reduce the feasible regions of search space, resulting in the COPs become more difficult to solve as compared to the unconstrained counterparts (Mezura-Montes & Coello Coello, 2011; Michalewicz & Schoenauer, 1996; Runarsson & Xin, 2000). In order to solve the COPs successfully, the optimal set of decision variables obtained not only need to optimize the objective functions, but also to satisfy all technical constraints (Mezura-Montes & Coello Coello, 2011; Michalewicz & Schoenauer, 1996; Runarsson & Xin, 2000).