Abstract:

This research proposes an odd-even dimension RUNge Kutta algorithm (ODRUN) to solve global optimization and a well-known NP-hard problem in inventory management. The rpoposed algorithm integrates odd-even dimensional, fourth-order Runge-Kutta method, and neighbor search strategies. This hybrid approach significantly improves population diversity, avoids local optima, and enhances convergence accuracy. To validate the performance of the proposed algorithm, a widely recognized benchmark function suit from CEC2022 is first employed. Results confirm that ODRUN achieves an overall effectiveness ratio of 66.67% across three statistical indicators (best, mean, and standard deviation) for 12 benchmark functions. The test shows this algorithm is ranked first compared to seven state-of-the-art metaheuristic algorithms. Furthermore, ODRUN is applied to the joint replenishment problem with imperfect items and trade credit. Numerical examples from 600 randomly generated large-scale instances highlight that the algorithm’s performance remains unaffected by an increase in problem scale. The significant cost savings brought by the ODRUN algorithm, with the maximum improvement ratio in average cost and best-found total cost ranging from 14.81% to 19.5%, are achieved in comparison to other algorithms. In conclusion, ODRUN is an effective and robust tool for complex optimization problems.

Key words: metaheturitics, RUNge Kutta algorithm, odd-even dimension search strategy, neighbor search strategy, joint replenishment problem with imperfect items and trade credit