A Binary Programming Solution to the Min-Max Multiple-Depots, Multiple Traveling Salesman Problem (original) (raw)
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A Market-based Solution to the Multiple Traveling Salesmen Problem
Journal of Intelligent & Robotic Systems, 2013
This paper describes a market-based solution to the problem of assigning mobile agents to tasks. The problem is formulated as the multiple depots, multiple traveling salesmen problem (MTSP), where agents and tasks operate in a market to achieve near-optimal solutions. We consider both the classical MTSP, in which the sum of all tour lengths is minimized, and the Min-Max MTSP, in which the longest tour is minimized. We compare the market-based solution with direct enumeration in small scenarios, and show that the results are nearly optimal. For the classical MTSP, we compare our results to linear programming, and show that the results are within 1% of the best cost found by linear programming in more than 90% of the runs, with a significant reduction in runtime. For the Min-Max case, we compare our method with Carlsson's algorithm and show an improvement of 5% to 40% in cost, albeit at an increase in runtime. Finally, we demonstrate the ability of the market-based solution to deal with changes in the scenario, e.g., agents leaving and entering the market. We show that the market paradigm is ideal for dealing with these changes during runtime, without the need to restart the algorithm, and that the solution reacts to the new scenarios in a quick and near-optimal way.
An open close multiple travelling salesman problem with single depot
Decision Science Letters
This paper introduces a novel practical variant, namely an open close multiple travelling salesmen problem with single depot (OCMTSP) that concerns the generalization of classical travelling salesman problem (TSP). In OCMTSP, the overall salesmen can be categorized into internal/permanent and external/outsourcing ones, where all the salesmen are positioned at the depot city. The primary objective of this problem is to design the optimal route such that all salesmen start from the depot/base city, and then visit a given set of cities. Each city is to be visited precisely once by exactly one salesman, and only the internal salesmen have to return to the depot city whereas the external ones need not return. To find optimal solutions, an exact pattern recognition technique based Lexi-search algorithm (LSA) is developed which has been subjected in Matlab. Comparative computational results of the LSA have been made with the existing methods for general multiple travelling salesman problem (MTSP). Further, to test the performance of LSA, computational experiments have been carried out on some benchmark as well as randomly generated test instances for OCMTSP, and results are reported. The overall computational results demonstrate that the proposed LSA is efficient in providing optimal and sub-optimal solutions within the considerable CPU times. .
International Journal of Services and Operations Management, 2018
Consider the problem of having a team of cooperative and autonomous vehicles to repeatedly visit a set of target locations and return back to their initial locations. This problem is known as multi-depot multiple travelling salesman problems (MD-MTSP), which applies to several mobile robots applications. The non-fixed destination multi-depot multiple travelling salesmen with time window problem (MmTSPTW) is a generalisation of a well-known MmTSP with considering time window for each node in a tour. The salesmen also are not forced to return to their starting depot. This problem is of great complexity and belongs to NP-complete class of problems. In this paper, a new mathematical model is proposed for MmTSPTW by considering waiting penalties and time window is defined for each depot (city). The salesmen only can service the customers within these time windows and also some penalties are considered for any deviation of start time. The objective function of problem is to minimise the total costs and penalties of the tours.
A multi-depot travelling salesman problem and its iterative and integrated approaches
International Journal of Operational Research, 2006
This paper formulates a logistics distribution problem as the multi-depot travelling salesman problem (MDTSP). The decision makers not only have to determine the travelling sequence of the salesman for delivering finished products from a warehouse or depot to a customer, but also need to determine which depot stores which type of products so that the total travelling distance is minimised. The MDTSP is similar to the combination of the travelling salesman and quadratic assignment problems. In this paper, the two individual hard problems or models are formulated first. Then, the problems are integrated together, that is, the MDTSP. The MDTSP is constructed as both integer nonlinear and linear programming models. After formulating the models, we verify the integrated models using commercial packages, and most importantly, investigate whether an iterative approach, that is, solving the individual models repeatedly, can generate an optimal solution to the MDTSP.
Networks and Spatial Economics, 2015
In this paper we study the one commodity pickup-and-delivery traveling salesman problem with restricted depot (1-PDTSP-RD), which is a generalization of the classical traveling salesman problem (TSP). We first introduce a polynomial size integer programming formulation for the problem and then study the feasibility issue which is shown to be N P-complete by itself. In particular, we prove sufficient conditions for the feasibility of the problem and provide a polynomial algorithm to find a feasible solution. We also develop a bound on the cost of the 1-PDTSP-RD solution in terms of the cost of the TSP solution. Based on this bound, we provide a heuristic algorithm to solve the 1PDTSP-RD. Extensive numerical experiments are performed to evaluate the efficiency of both the exact and approximation algorithms.
The multiple traveling salesman problem: an overview of formulations and solution procedures
The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. Moreover, the characteristics of the mTSP seem more appropriate for real-life applications, and it is also possible to extend the problem to a wide variety of vehicle routing problems (VRPs) by incorporating some additional side constraints. Although there exists a wide body of the literature for the TSP and the VRP, the mTSP has not received the same amount of attention. The purpose of this survey is to review the problem and its practical applications, to highlight some formulations and to describe exact and heuristic solution procedures proposed for this problem.
The traveling salesman problem with delivery and backhauls
Operations Research Letters, 1994
The problem that we consider here deals with a single vehicle of a given capacity that needs to serve N customers: some of the customers require a delivery of stock from the warehouse, whereas others need to deliver stock from their location to the warehouse. The objective is to find a shortest feasible tour visiting all customers, emanating from and ending at the warehouse. We introduce an efficient (O(N2)) heuristic for this problem. The heuristic improves the worst-case bound known in the literature from 2.5 to 2. However, its average performance is shown in our numerical study to be slightly worse than that of a previously published (O(N3)) solution method.
A transformation for a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem
2009 American Control Conference, 2009
Unmanned aerial vehicles (UAVs) are being increasingly used for surveillance missions in civil and military applications. These vehicles can be heterogeneous in the sense that they can differ either in their motion constraints or sensing/attack capabilities. Given a surveillance mission that require a group of heterogeneous UAVs to visit a set of targets, this paper addresses a resource allocation problem of finding the optimal sequence of targets for each vehicle such that 1) each target is visited at least once by some vehicle, and 2) the total cost travelled by all the vehicles is minimized. This problem can be posed as a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP). This paper presents a transformation of a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available for the single salesman problem can be used to solve the HMDMTSP. To show the effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results show that good quality solutions can be obtained for the HMDMTSP relatively fast.
The multi-commodity one-to-one pickup-and-delivery traveling salesman problem
European Journal of Operational Research, 2009
This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commodity one-to-one Pickup-and-Delivery Traveling Salesman Problem (m-PDTSP) in which cities corresponds to customers providing or requiring known amounts of m different objects, and the vehicle has a given upper-limit capacity. Each object has exactly one origin and one destination, and the vehicle must visit each customer exactly once. This justifies the words "one-to-one" and "traveling salesman problem" in the name of the problem, respectively. We introduce a Mixer Integer Linear Programming model for the m-PDTSP, discuss decomposition techniques and describe some strategies to solve the problem based on a branchand-cut procedure. Preliminary computational experiments on randomly generated euclidian instances are shown.