Advanced equilibrium optimizer for electric vehicle routing problem with time windows

Electric Vehicle Routing Problem with Time Windows (EVRPTW) is often used in the transportation area. EVRPTW is difficult to solve by the traditional precise method. The meta-heuristic algorithm is often used to solve EVRPTW and can obtain approximate optimal solutions. Equilibrium optimizer (EO), as a meta-heuristic algorithm, is simple to implement by software and hardware. Given the shortcomings of EO, such as low convergence precision and fall into local optima easily, we propose an advanced equilibrium optimizer (AEO). In AEO, we improved EO with multi-population method, novel quantum operator, and FPA-inspired pollination operator. Multi-population method constitutes the algorithm structure of AEO. The novel quantum operator and FPA-inspired pollination operator effectively enhance EO’s global exploration capabilities, improving the convergence accuracy and stability of EO. Then we test the AEO by CEC2013. Experiment results and Friedman’s mean rank show that AEO has better performance in convergence than differential evolution (DE), flower pollination algorithm (FPA), grey wolf optimizer (GWO), particle swarm optimization (PSO), and EO. Finally, AEO also is applied to solve EVRPTW. From the test results of the instances, AEO is more suitable to solve the EVRPTW than some comparison algorithms.