Treffer: Multi-objective brainstorm optimization algorithm based on Bayesian inference learning automaton for solving CVRP with time windows.

This paper proposes a new Bayesian inference-based learning automaton with a multi-objective brainstorm algorithm to find the best solutions for combinatorial optimization problems such as vehicle routing problems. Initially, a robust deep k-means algorithm is used to solve the consumer allocation problem to various clusters. Then, a multi-objective brainstorm optimization algorithm is used to determine non-dominated solutions and thereby, the Pareto front of the solution space can be formed. The proposed method uses an external archive to store the attained non-dominated solutions. In addition, a reinforcement learning algorithm is used for improving the overall convergence of the brainstorm optimization algorithm, and it can be used to discover good designs for the parameters of the brainstorm algorithm and ensure the best transition decisions by balancing the exploration and exploitation phases. Here, the control of two phases can be handled by Q-table in reinforcement learning. Subsequently, the Bayesian inference-based learning automaton is employed to learn the optimal actions by placing the agent in a complex environment. The proposed method is implemented in the Python working platform, and the performance of the proposed approach is validated based on Solomon's benchmark problems. Additionally, the effectiveness of the proposed method can be validated by comparing it with other algorithms in terms of Pareto optimal results, hypervolume, generational distance, inverted generation distance, space and spread. As a result, the proposed method has obtained better generational distance and inverted generation distance of 0.0669 and 0.0004 than other competitive methods, and it is superior for solving vehicle routing problems. ● Integrate the machine learning techniques into meta-heuristics for solving CVRP with Time Windows. ● Formulate a MOP for Vehicle Routing based on the constraints of total route distance and total customer waiting time. ● Modify the CRLA using learning automaton to improve the overall meta-heuristics convergence by learning the actions optimally. ● Validate the performance of the proposed algorithm on VRP benchmarks. [ABSTRACT FROM AUTHOR]