Sim-heuristic algorithm for solving bi-objective stochastic optimization problems

Bi-objective stochastic constrained optimization problems (BSCOP) involve bi-objective stochastic functions and deterministic constraints. BSCOP is NP-hard because of exponential growth in computational complexity. A sim-heuristic algorithm can solve NP-hard problems, where the simulation addresses model uncertainty and interacts with the metaheuristic approach, which explores the search space to identify a near-optimal solution. A sim-heuristic approach that combines leaf in wind optimization with ordinal optimization (LWOO), is presented to solve BSCOP efficiently. The LWOO approach comprises three phases: surrogate model, universal exploration, and local exploitation. The Kolmogorov–Arnold Network (KAN) serves as a surrogate model to efficiently evaluate solution performance. In universal exploration, a refined leaf in wind optimization is developed to select N promising solutions from the whole search space. An advanced optimal computing budget allocation is utilized in local exploitation to identify a near-optimal solution from the N promising solutions. The LWOO approach is employed for production planning in reconfigurable manufacturing systems. The purpose is to find the optimal system configuration, task allocation to the workstation, and buffer allocation to simultaneously maximize expected throughput while minimizing the total buffer capacity. A reconfigurable manufacturing system consisting of 3 workstations with 2 inter-station buffers serves as a practical example. The LWOO approach was compared with four heuristic methods to validate the performance. Experimental results demonstrate that the LWOO approach consistently produces optimal and reliable solutions within a reasonable timeframe.