Abstract: Multiple traveling salesman problems (MTSP) are a typical computationally complex combinatorial optimization problem, which is an extension of the famous traveling salesman problem (TSP). The MTSP can be generalized to a wide variety of routing and scheduling problems. The paper makes the attempt to show how Genetic Algorithm (GA) can be applied to the MTSP with ability constraint. In...

Multiple Travelling Salesman Problem (mTSP) is one of the most popular and widely used combinatorial optimization problems in the operational research. Many complex problems can be modeled and solved by the mTSP. To solve the mTSP, deterministic algorithms cannot be used as the mTSP is an NP-hard optimization problem. Hence, heuristics approaches are usually applied. In this paper, the Gravitat...

The multiple traveling salesmen problem (MTSP) is an extension of the traveling salesman problem with many production and scheduling applications. The TSP has been well studied including methods of solving the problem with genetic algorithms. The MTSP has also been studied and solved with GAs in the form of the vehicle-scheduling problem. This work presents a new modeling methodology for settin...

This paper presents a variation of the Euclidean Traveling Salesman Problem (TSP), the Multiple Traveling Salesman Problem (MTSP), and compares a variety of evolutionary computation algorithms and paradigms for solving it. Techniques implemented, analyzed, and discussed herein with regard to MTSP include use of a neighborhood attractor schema (a variation on k-means clustering), the "shrink-wra...

This paper studies an optimization problem: multi-traveling salesman problem (MTSP), which is an extension of the well known TSP. A columnar competitive model (CCM) of neural networks incorporates with a winner-take-all learning rule is employed to solve the MTSP. Stability conditions of CCM for MTSP is exploited by mathematical analysis. Parameters settings of the network for guaranteeing the ...

The Multiple Traveling Salesman problem (mTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where more than one salesman is allowed to be used in order to visit some cities just once. Furthermore, the formulation of the mTSP applies to a wide range of reallife applications, and can be extended to a wide variety of Vehicle Routing Problems (VRPs) by incorporating some addi...

Abstract: The Lin and Kernighan’s algorithm (LK) for the single objective Traveling Salesman Problem (TSP) is one of the most efficient heuristics for the symmetric case. Although many algorithms for the TSP were extended to the multi-objective version of the problem (MTSP), the LK was still not fully explored. Works that applied the LK for the MTSP were driven to weighted sum versions of the p...

The aim of this paper is to introduce a hybrid two-phase algorithm called SW+ ASelite for solving the MTSP which can be explained as the problem of designing collection of routes from one depot to a number of customers subject to side constraints. At the first stage, the MTSP is solved by the sweep algorithm, and at the second stage, the Elite Ant Colony Optimization ( ASelite ) and 3-opt local...

A hybrid particle swarm optimization (PSO) for multi-machine time scheduling problem (MTSP) with multicycles is proposed in this paper to choose the best starting time for each machine in each cycle under pre-described time window and a set of precedence machines for each machine; to minimize the total penalty cost. We developed hybrid algorithm by using a combination between PSO and Genetic Al...

The minimization of tool switches problem (MTSP) seeks a sequence to process a set of jobs so that the number of tool switches required is minimized. The MTSP is well known to be NP-hard. This paper presents a new hybrid heuristic based on the Biased Random Key Genetic Algorithm (BRKGA) and the Clustering Search (CS). The main idea of CS is to identify promising regions of the search space by g...