Design of efficient multiobjective binary PSO algorithms for solving multi-item capacitated lot-sizing problem

In this paper, a multi-item capacitated lot-sizing problem with setup times and backlogging (MICLSP_SB) is addressed with respect to two conflicting objective functions. This nondeterministic polynomial time (NP)-hard problem consists of finding optimal production plans while minimizing, simultaneously, the total cost and the total inventory level. To effectively solve the considered problem, two new versions of multiobjective binary particle swarm optimization are designed. In the first proposed version "standard multiobjective particle swarm optimization" (S-MOBPSO) algorithm, two main contributions are introduced. First, a new particle encoding and decoding method is developed to treat the MICLSP_SB decision variables. Second, the overall violation minimization method and the constraint handling method are combined to effectively handle the problem constraints. To further enhance the overall performance, an improvement procedure that minimizes the capacity constraints violations is developed and embedded into the S-MOBPSO algorithm. This second version is named improved MOBPSO (I-MOBPSO). An illustrative example is presented to explain the application of the proposed algorithms. Five performance metrics are considered to measure and evaluate the effectiveness of the proposed algorithms. Experimental results demonstrate the efficiency of the S-MOBPSO and I-MOBPSO algorithms compared to each other as well as the basic MOBPSO and nondominated sorting genetic algorithm II.