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For NP-hard combinatorial optimization problems, it is usually challenging to find high-quality solutions in polynomial time. Designing either an exact algorithm or an approximate algorithm for these problems often requires significantly specialized knowledge. Recently, deep learning methods have provided new directions to solve such problems. In this paper, an end-to-end deep reinforcement learning framework is proposed to solve this type of combinatorial optimization problems. This framework can be applied to different problems with only slight changes of input, masks, and decoder context vectors. The proposed framework aims to improve the models in literacy in terms of the neural network model and the training algorithm. The solution quality of TSP and the CVRP up to 100 nodes are significantly improved via our framework. Compared with the best results of the state-of-the-art methods, the average optimality gap is reduced from 4.53% to 3.67% for TSP with 100 nodes and from 7.34% to 6.68% for CVRP with 100 nodes when using the greedy decoding strategy. Besides, the proposed framework can be used to solve a multi-depot CVRP case without any structural modification. Furthermore, our framework uses about 1/3 ∼ 3/4 training samples compared with other existing learning methods while achieving better results. The results performed on randomly generated instances, and the benchmark instances from TSPLIB and CVRPLIB confirm that our framework has a linear running time on the problem size (number of nodes) during training and testing phases and has a good generalization performance from random instance training to real-world instance testing. [ABSTRACT FROM AUTHOR]

Highlights • Genetic algorithms (GAs) are used to find optimal assignment of tasks to teams of collaborating agents, where performance of a team is based on the collaboration of its members. • We show the shortcoming of standard crossover operators to efficiently solve large instances of the problem. • We suggest extension (shuffled list) to standard crossover operators and introduce two more operators (team-based and team-based shuffled list), which all are capable to efficiently solve the problem. • The position-based crossover operator with a shuffled list is singled out to have the best performance. • Performance of the GAs is further enhanced by using chaotic sequences and the results are significant as compared with PSO and DE. Abstract The problem of optimally assigning agents (resources) to a given set of tasks is known as the assignment problem (AP). The classical AP and many of its variations have been extensively discussed in the literature. In this paper, we examine a specific class of the problem, in which each task is assigned to a group of collaborating agents. APs in this class cannot be solved using the Hungarian or other known polynomial time algorithms. We employ the genetic algorithm (GA) to solve the problem. However, we show that if the size of the problem is large, then standard crossover operators cannot efficiently find near-optimal solutions within a reasonable time. In general, the efficiency of the GA depends on the choice of genetic operators (selection, crossover, and mutation) and the associated parameters. In order to design an efficient GA for determining the near-optimal assignment of tasks to collaborative agents, we focus on the construction of crossover operators. We analyze why a naive implementation with standard crossover operators is not capable of sufficiently solving the problem. Furthermore, we suggest modifications to these operators by adding a shuffled list and introduce two new operators (team-based and team-based shuffled list). We demonstrate that the modified and new operators with shuffled lists perform significantly better than all operators without shuffled lists and solve the presented AP more efficiently. The performance of the GA can be further enhanced by using chaotic sequences. Moreover, the GA is also compared with the particle swarm optimization (PSO) and differential evolution (DE) algorithms, demonstrating the superiority of the GA over these search algorithms. [ABSTRACT FROM AUTHOR]

Abstract Feed-forward neural networks are efficient at solving various types of problems. However, finding efficient training algorithms for feed-forward neural networks is challenging. The dynamic group optimisation (DGO) algorithm is a recently proposed half-swarm half-evolutionary algorithm, which exhibits a rapid convergence rate and good performance in searching and avoiding local optima. In this paper, we propose a new hybrid algorithm, FNNDGO that integrates the DGO algorithm into a feed-forward neural network. DGO plays an optimisation role in training the neural network, by tuning parameters to their optimal values and configuring the structure of feed-forward neural networks. The performance of the proposed algorithm was determined by comparing its performance with those of other training methods in solving two types of problems. The experimental results show that our proposed algorithm exhibits promising performance for solving real-world problems. [ABSTRACT FROM AUTHOR]