Multi task selection including part mix, tool allocation and process plans in CNC machining centers using new binary PSO

This paper proposes a new binary PSO for solving multi-task selection problem concerning various issues such as Part mix, Tool allocation and Process plans in CNC machining centers. The mathematical formulation of considered selection problem emerges as highly constrained and 0-1, combinatorial optimization, which further belongs to the category of NP-hard problems. The proposed Binary PSO variant embeds a new sigmoid function namely “Gompertz function” as a binary number generator with an additional benefit of controlling its parameters so as to induce the combined effect of sigmoid as well as linear function. The corresponding variant is termed as “Gompertz Binary Particle Swarm Optimization (GBPSO)”. Before applying GBPSO for considered selection problem, the efficacy of proposed GBPSO is tested on a set of 0-1 Multi-dimensional knapsack problems and results are compared with standard binary PSO. Thereafter two test cases for considered optimal selection problem are solved and analyzed using GBPSO. The simulation results manifest the superiority of proposed variant over standard BPSO for solving benchmark problems and practical application as well.