An improved probability-based discrete particle swarm optimization algorithm for solving the product portfolio planning problem

Product Portfolio Planning (PPP) is one of the most critical decisions for companies to gain an edge in the competitive market. It seeks for the optimal combination of products and attribute levels offered for customers in the target market, which is a NP-hard combinatorial optimization problem. In this paper, a Probability-based Discrete Particle Swarm Optimization (PDPSO) algorithm is proposed to solve the PPP problem. In PDPSO, the particle is encoded as discrete values, which can be straightforwardly used to represent the product portfolio with discrete attributes. PDPSO adopts a probability-based mechanism to update particles. Specifically, a probability vector is used to decide the probability of three search behaviors, i.e., learning from the personal best position, global best position, or random search. In experiments, the search performance of PDPSO has been compared with that of a Genetic Algorithm (GA) and a Simulated Annealing (SA) algorithm on generated PPP problem cases with different sizes. The results indicate that PDPSO obtains significantly better optimization results than GA and SA in most cases and obtains desirable/near-optimal solutions on various PPP problem cases. A case study of notebook computer portfolio planning is also presented to illustrate the efficiency and effectiveness of PDPSO.