An Adaptive Layered Clustering Framework with Improved Genetic Algorithm for Solving Large-Scale Traveling Salesman Problems

Abstract

Traveling salesman problems (TSPs) are well-known combinatorial optimization problems, and most existing algorithms are challenging for solving TSPs when their scale is large. To improve the efficiency of solving large-scale TSPs, this work presents a novel adaptive layered clustering framework with improved genetic algorithm (ALC_IGA). The primary idea behind ALC_IGA is to break down a large-scale problem into a series of small-scale problems. First, the k-means and improved genetic algorithm are used to segment the large-scale TSPs layer by layer and generate the initial solution. Then, the developed two phases simplified 2-opt algorithm is applied to further improve the quality of the initial solution. The analysis reveals that the computational complexity of the ALC_IGA is between O(nlogn) and O(n2). The results of numerical experiments on various TSP instances indicate that, in most situations, the ALC_IGA surpasses the compared two-layered and three-layered algorithms in convergence speed, stability, and solution quality. Specifically, with parallelization, the ALC_IGA can solve instances with 2×105 nodes within 0.15 h, 1.4×106 nodes within 1 h, and 2×106 nodes in three dimensions within 1.5 h.

An Active Distribution Grid Exceedance Testing and Risk-Planning Simulation Based on Carbon Capture and Multisource Data from the Power Internet of Things

“…Developing optimal AC currents is relevant to nonlinear planning because of the nonlinear characteristics of its constraints. The earliest validation of its effectiveness when used to optimize distribution network power flow was given in relation to the use of evolutionary algorithms, such as the genetic algorithm [26,27] or particle swarm algorithm [28][29][30]. However, evolutionary algorithms also carry obvious defects, such as their inability to guarantee global optimization when used to solve nonlinear models.…”