Modified particle swarm optimization for a multimodal mixed-variable laser peening process

Optimization problems that result in shock, impact, and explosion type disciplines typically have mixed design variables, multiple optimal solutions, and high computational cost of an analysis. In the optimization literature, many researchers have solved problems involving mixed variables or multiple optima, but it is difficult to find multiple optima of a mixed-variable and high computation cost problem using an particle swarm optimization (PSO). To solve such problems, a mixed-variable niching PSO (MNPSO) is developed. The four modifications introduced to the PSO are: Latin Hypercube sampling-based particle generation, a mixed-variable handling technique, a niching technique, and surrogate model-based design space localization. The proposed method is demonstrated on the laser peening (LP) problem. The LP process induces favorable residual stress on the peened surface to improve the fatigue and fretting properties of the material. In many applications of LP, geometric configurations and dimensional integrity requirements of the component can constrain implementation of an optimal solution. In such cases, it is necessary to provide multiple alternatives to the designer so that a suitable one can be selected according to the requirements. It takes 24–72 CPU hours to perform an LP finite element analysis.