Matrix-Probabilistic Particle Swarm Optimization for Supply Chain Optimization

This paper presents a novel approach to supply chain optimization using a matrix-based adaptation of Particle Swarm Optimization (PSO). We address the challenge of applying PSO, originally designed for continuous problems, to the discrete, multi-dimensional nature of supply chain systems. Our method evolves through two versions: Matrix-based Binary PSO (MBPSO) and its improved variant, Matrix-Probabilistic PSO (M-PPSO). Both versions represent solutions as matrices, allowing for complex interactions between supply chain entities. MBPSO uses binary values to indicate interactions but suffers from local optima issues. To overcome this limitation, we developed M-PPSO, which employs probabilities for a more nuanced representation. We evaluate these versions against traditional PSO and Binary PSO on benchmark problems, including the Rastrigin function and the Knapsack problem. Results show that M-PPSO significantly outperforms MBPSO, resolving local optima issues and achieving consistent optimal solutions within fewer iterations. M-PPSO also enables more realistic modeling by allowing buyers to interact with multiple sellers for the same product. This research contributes to the field by demonstrating the efficacy of matrix-based PSO in handling the complexities of supply chain optimization, offering a promising direction for future applications in discrete, multientity optimization problems.