Stepwise monogamous pairing genetic algorithm method applied to a multi-depot vehicle routing problem with time windows

Ting Yee Lim, Xin Ju Ng, Choo Jun Tan, Chee Peng Lim

Abstract: Evolutionary computation (EC) is a powerful tool for global optimization across various domains, including healthcare logistics. However, the prevalence of local optima in complex problems often hinders the ability of the populations to find optimal solutions, leading to premature convergence. More daunting is that complex optimization problems motivated from real-world challenges continue to pose huge hurdles for EC, with many remaining unresolved. To fill this gap, we propose a new framework named SW-MopGA (Stepwise Monogamous Pairing Genetic Algorithm), which hinges on two innovations. First, a controller for diversity maintenance is introduced into MopGA to generate perturbed opposite solution via opposition-learning when necessary. In doing so, the algorithm is able to maintain population diversity effectively, which alleviates the risk of premature convergence. Second, SW-MopGA proposes a two-step framework: Initially, the population undergoes evolution on a simplified version of the originally complex problem. Solutions derived from the simplified problem serve as building blocks (stepping stones) upon which more intricate blocks are constructed for the final problem—a form of incremental evolution. Numerical analysis on two real-world cases in the logistics healthcare sector demonstrates the effectiveness of SW-MopGA. The problems are formulated as a multi-depot vehicle routing problem with time windows (MDVRPTW). Overall, the combined effect of the two innovations resulted in up to 18% and 8% savings in terms of total travel time and distance, and vehicles used, respectively on an off-peak day scenario; while approximately 17% and 7% savings for the same criteria on a peak-day scenario, compared to the baseline MopGA. Additionally, SW-MopGA improved the best-known solution of three instances in the MDVRPTW benchmark dataset. Finally, algorithmic insights are provided. In general, our initial study shows encouraging outcomes for incremental evolution and its potential for other real-world complex optimization models.