Traveling Salesman Problem (TSP) has been seen in diverse applications, which is proven to be NP-complete in most cases. Even though there are multiple heuristic techniques, the problem is still a complex combinatorial optimization problem. The candidate solutions are chosen by considering only a set of high values of the objective function which may not lead to the best solutions. Hence, this paper develops a hybrid optimization algorithm, named Earthworm-based DHOA (EW-DHOA) to solve the TSP problem by finding an optimal solution. The proposed EW-DHOA is developed by integrating the two well-performing meta-heuristic algorithms, such as Deer Hunting Optimization Algorithm (DHOA) and Earthworm Optimization Algorithm (EWA). The EW-DHOA intends to optimize the constraint as the number of cities traveled by the salesman in terms of an optimal path. The main process for attaining this objective is to minimize the distance traveled by the salesman concerning the entire cities. The effectiveness of the proposed hybrid meta-heuristic algorithm is validated over the benchmark dataset. Finally, the experimental results show that the convergence of the proposed hybrid optimization will be better while solving TSP with less computational complexity, and improved significantly in attaining optimal results.

旅行商问题 (TSP) 已出现在各种应用中，在大多数情况下被证明是 NP 完全的。即使有多种启发式技术，该问题仍然是一个复杂的组合优化问题。通过仅考虑可能不会导致最佳解决方案的目标函数的一组高值来选择候选解决方案。因此，本文开发了一种混合优化算法，称为基于蚯蚓的 DHOA (EW-DHOA)，通过寻找最优解来解决 TSP 问题。所提出的 EW-DHOA 是通过集成两种性能良好的元启发式算法而开发的，例如猎鹿优化算法 (DHOA) 和蚯蚓优化算法 (EWA)。EW-DHOA 打算根据最佳路径优化销售员经过的城市数量的约束。实现这一目标的主要过程是最小化销售员在整个城市中所走的距离。在基准数据集上验证了所提出的混合元启发式算法的有效性。最后，实验结果表明，所提出的混合优化在求解TSP时收敛性更好，计算复杂度更低，在获得最优结果方面有显着提高。