The rapid growth of electric vehicles (EVs) has led to significant challenges in providing efficient and sustainable charging solutions. This paper addresses the battery swapping station (BSS) recommendation problem by proposing a novel conflict-free genetic algorithm (CFGA) integrated with a Nash equilibrium seeking (NES) approach to identify optimal Nash equilibrium (ONE) solutions to such a non-cooperative optimization problem. The CFGA employs specialized crossover and mutation operators to generate offspring that satisfy the constraints of the problem, ensuring that each EV decides a unique battery swap strategy without conflict. Firstly, an order crossover operator is proposed to preserve the order of genes in the chromosomes. Secondly, a replacement and exchange mutation operator is proposed to enhance mutation diversity. The resulting optimal solution is then used as the initial strategy for the NES, which iteratively converges to the ONE. The proposed CFGA with NES algorithm is evaluated under both small-scale and large-scale cases, demonstrating its effectiveness in achieving a balance between costs for EVs and utilization for BSSs. The study's findings have practical implications for the smart grid and EV integration, offering a robust method for optimizing EV infrastructure and operations.

Multimodal optimization problems (MMOPs) have multiple global optima, hence the algorithm must preserve population diversity to locate multiple global optima and ensure the precision of the obtained solutions simultaneously. To achieve these, the niching technique is widely applied. Although the niching technique shows encouraging performance, some niches may continuously evolve even though accurate enough global optima in their regions have been found. This may cause the waste of computational resources and the inefficiency of search behavior. To maintain population diversity and accuracy, and to break through the mentioned deficiency, an optimal peaks detected-based differential evolution (OPPDE) algorithm is proposed, which has three novel components. Firstly, to maintain population diversity, OPDDE designs a parameter-insensitive OPTICS-based niching strategy to automatically partition niches. Secondly, to avoid wasting computation resources on founded global optima and enhance search efficiency, OPDDE designs an optimal peaks detection strategy that uses historical information to identify the founded global optima. Thirdly, a dynamic step local search strategy is used to refine solutions. The proposed OPDDE algorithm generally superiors some state-of-the-art algorithms regarding both the accuracy and completeness of solutions, according to experiments on widely used MMOP benchmarks.

Dynamic multiobjective optimization poses great challenges to evolutionary algorithms due to the change of optimal solutions or Pareto front with time. Learning-based methods are popular to extract the changing pattern of optimal solutions for predicting new solutions. They tend to use all variables as features (i.e., inputs) to build prediction models. However, there are usually some irrelevant and redundant variables, which increase training difficulty and decrease prediction accuracy. This article proposes a new interaction-based prediction (IP) method, which captures the correlation of variables with prediction targets and selects the most relevant variables to build prediction models using neural networks. In particular, the interaction between variables is detected to remove redundant variables. In addition, a correction procedure is developed to further improve predicted solutions according to the prediction error in past environments. The predicted solutions are used to update the population according to a specifically designed update strategy. Integrating the IP method into the framework of multiobjective evolutionary algorithm based on decomposition (MOEA/D), a new algorithm named IP-DMOEA is put forward. Experimental results on a typical dynamic multiobjective test suite demonstrate the better performance of the proposed IP-DMOEA than state-of-the-art algorithms in terms of convergence speed and solution quality. The proposed IP-DMOEA is also successfully applied to the multirobot task scheduling problem.

Decomposition methods play a critical role in cooperative co-evolutionary algorithms (CCEAs) for solving large-scale optimization problems. Although some well-performing decomposition methods have been designed based on the interactions among variables (IaV), their grouping accuracy is still limited due to the poor performance on the overlapping problems and the computational roundoff errors of IaV in the implementation. To deal with these limitations, a graph-based deep decomposition (GDD) method is proposed to obtain more accurate grouping results, especially for the overlapping problems. On the one hand, the GDD mines the IaV information and obtains the minimum vertex separator of the interaction graph of variables, so as to group variables deeply and recursively. On the other hand, the GDD has the ability of fault tolerance to deal with the computational roundoff errors of IaV and can improve the grouping accuracy. For better experimental studies of overlapping problems, a novel overlapping function generator is designed with the random and complicate overlap type, and two new metrics are proposed to evaluate the grouping accuracy. Comprehensive experiments show that GDD can greatly improve the grouping accuracy and help CCEAs perform better than other existing algorithms, especially on the overlapping problems. In addition, the GDD is highly fault tolerant and can divide problems accurately even on the inaccurate IaV.