Salp Swarm Algorithm (SSA) is a novel swarm intelligent algorithm with good performance. However, like other swarm-based algorithms, it has insufficiencies of low convergence precision and slow convergence speed when dealing with high-dimensional complex optimisation problems. In response to this concerning issue, in this paper, we propose an improved SSA named as WASSA. First of all, dynamic weight factor is added to the update formula of population position, aiming to balance global exploration and local exploitation. In addition, in order to avoid premature convergence and evolution stagnation, an adaptive mutation strategy is introduced during the evolution process. Disturbance to the global extremum promotes the population to jump out of local extremum and continue to search for an optimal solution. The experiments conducted on a set of 28 benchmark functions show that the improved algorithm presented in this paper displays obvious superiority in convergence performance, robustness as well as the ability to escape local optimum when compared with SSA.

As one of the most popular combinatorial optimization problems, Traveling Salesman Problem (TSP) has attracted lots of attention from academia since it was proposed. Numerous meta-heuristics and heuristics have been proposed and used to solve the TSP. Although Ant Colony Optimization (ACO) is a natural TSP solving algorithm, in the process of solving it, there are also some shortcomings such as slow convergence speed and prone to fall into local optimum. Therefore, this paper proposes an improved ant colony optimization based on graph convolutional network: Graph Convolutional Network Improved Ant Colony Optimization (GCNIACO). The graph convolutional network is introduced to generate a better solution, and the better solution is converted into the pheromone on the initial path of the ACO. Thereby, the guiding effect of the pheromone concentration for the ants at the beginning of the algorithm is enhanced. In the meantime, through adaptive dynamic adjustment of the pheromone volatility factor and the introduction of the 3-opt algorithm, the algorithm's ability to jump out of the local optimum is enhanced. Finally, GCNIACO is simulated on TSP datasets and engineering application example. Comparing the optimization results with other classical algorithms, it is verified that the graph convolutional network improved ant colony optimization has better performance in obtaining the optimal solution.

Backtracking search algorithm (BSA) is a relatively new evolutionary algorithm, which has a good optimization performance just like other population‐based algorithms. However, there is also an insufficiency in BSA regarding its convergence speed and convergence precision. For solving the problem shown in BSA, this article proposes an improved BSA named COBSA. Enlightened by particle swarm optimization (PSO) algorithm, population control factor is added to the variation equation aiming to improve the convergence speed of BSA, so as to make algorithm have a better ability of escaping the local optimum. In addition, enlightened by differential evolution (DE) algorithm, this article proposes a novel evolutionary equation based on the fact that the disadvantaged group will search just around the best individual chosen from previous iteration to enhance the ability of local search. Simulation experiments based on a set of 18 benchmark functions show that, in general, COBSA displays obvious superiority in convergence speed and convergence precision when compared with BSA and the comparison algorithms.