CS-PSO: chaotic particle swarm optimization algorithm for solving combinatorial optimization problems

Combinatorial optimization problems are typically NP-hard, due to their intrinsic complexity. In this paper, we propose a novel chaotic particle swarm optimization algorithm (CS-PSO), which combines the chaos search method with the particle swarm optimization algorithm (PSO) for solving combinatorial optimization problems. In particular, in the initialization phase, the priori knowledge of the combination optimization problem is used to optimize the initial particles. According to the properties of the combination optimization problem, suitable classification algorithms are implemented to group similar items into categories, thus reducing the number of combinations. This enables a more efficient enumeration of all combination schemes and optimize the overall approach. On the other hand, in the chaos perturbing phase, a brand-new set of rules is presented to perturb the velocities and positions of particles to satisfy the ideal global search capability and adaptability, effectively avoiding the premature convergence problem found frequently in traditional PSO algorithm. In the above two stages, we control the number of selected items in each category to ensure the diversity of the final combination scheme. The fitness function of CS-PSO introduces the concept of the personalized constraints and general constrains to get a personalized interface, which is used to solve a personalized combination optimization problem. As part of our evaluation, we define a personalized dietary recommendation system, called Friend, where CS-PSO is applied to address a healthy diet combination optimization problem. Based on Friend, we implemented a series of experiments to test the performance of CS-PSO. The experimental results show that, compared with the typical HLR-PSO, CS-PSO can recommend dietary schemes more efficiently, while obtaining the global optimum with fewer iterations, and have the better global ergodicity.