Particle Swarm Optimization (PSO) is a well-known technique for numerical optimization with real-parameter representation. Like other meta-heuristics, PSO is usually designed for the goal of finding a single optimal solution for a given problem. However, many scientific and engineering optimization problems have convoluted search spaces with a large number of optima. This paper explores the ability of a cooperative combinatorial PSO (CCPSO) used in tandem with explicit diversity strategies to discover sets of high-quality and diverse solutions. This idea has been pursued in numerical optimization in several PSO variants, but no explicit PSO has been developed to handle multimodal combinatorial problems. A protein sequence redesign problem is selected to assess the exploratory ability of multimodal CCPSO by evaluating both the quality and diversity of the solutions obtained.

Particle Swarm Optimization (PSO) is a well-known, competitive technique for numerical optimization with real-parameter representation. This paper introduces CCPSO, a new Cooperative Particle Swarm Optimization algorithm for combinatorial problems. The cooperative strategy is achieved by splitting the candidate solution vector into components, where each component is optimized by a particle. Particles move throughout a continuous space, their movements based on the influences exerted by static particles that then get feedback based on the fitness of the candidate solution. Here, the application of this technique to side-chain packing (a proteomics optimization problem) is investigated. To verify the efficiency of the proposed CCPSO algorithm, we test our algorithm on three side-chain packing problems and compare our results with the provably optimal result. Computational results show that the proposed algorithm is very competitive, obtaining a conformation with an energy value within 1% of the provably optimal solution in many proteins.