New Hybrid Discrete PSO for Solving Non Convex Trim Loss Problem

Trim loss minimization is the most common problem that arises during the cutting process, when products with variable width or length are to be produced in bulk to satisfy customer demands from limited available/stocked materials. The aim is to minimize inevitable waste material. Under various environmental and physical constraints, the trim loss problem is highly constrained, non convex, nonlinear, and with integer restriction on all variables. Due to the highly complex nature of trim loss problem, it is not easy for manufacturers to select an appropriate method that provides a global optimal solution, satisfying all restrictions. This paper proposes a discrete variant of PSO, which embeds a mutation operator, namely power mutation during the position update stage. The proposed variant is named as Hybrid Discrete PSO (HDPSO). Binary variables in HDPSO are generated using sigmoid function with its domain derived from position update equation. Four examples with different levels of complexity are solved and results are compared with two recently developed GA and PSO variants. The computational studies indicate the competitiveness of proposed variant over other considered methods.