A Colored Traveling Salesman Problem with Varying City Colors

Abstract

A colored traveling salesman problem (CTSP) is a path optimization problem in which colors are used to characterize diverse matching relationship between cities and salesmen. Namely, each salesman has a single color while every city has one to multiple salesmen’s colors, thus allowing salesmen to visit exactly once the cities of their colors. It is noteworthy that cities’ accessibilities to salesmen may change over time, which usually takes place in the multiwarehouse distribution of online retailers. This work presents a new CTSP with dynamically varying city colors for describing and modeling some scheduling problems with variable city accessibilities. The problem is more complicated than the previously proposed CTSP with varying edge weights. In particular, the solution feasibility changes as the cities change their colors, that is, a feasible original solution path may become no longer feasible after city colors change. A variable neighborhood search (VNS) algorithm is presented to solve the new problem. Specifically, a dynamic environment simulator with an adjustable frequency and amplitude is designed to mimic such color changes. Then, direct-route encoding, greedy initialization, and appropriate population immigrant are proposed to form an enhanced VNS, and then its performance is evaluated. The results of extensive experiments show that the proposed VNS can quickly track the environmental changes and effectively resolve the problem.

Angle constrained Paths

“…This problem represents a variant of the multiple traveling salesman problem, wherein each salesman is associated with a distinct color and is permitted to visit points of the same color, along with shared points that are common to all salesmen. In [6], the colored traveling salesman problem is considered on the points with varying colors. The Labeled Traveling Salesman Problem [7] is defined as the problem of finding a tour on a complete graph with colored edges, aiming to maximize or minimize the number of distinct colors used.…”