Random-key cuckoo search for the travelling salesman problem

Combinatorial optimization problems are typically NP-hard, and thus very challenging to solve. In this paper, we present the random key cuckoo search (RKCS) algorithm for solving the famous Travelling Salesman Problem (TSP). We used a simplified random-key encoding scheme to pass from a continuous space (real numbers) to a combinatorial space. We also consider the displacement of a solution in both spaces using L\'evy flights. The performance of the proposed RKCS is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that RKCS is superior to some other metaheuristic algorithms

Random-key cuckoo search for the travelling salesman problem

Combinatorial optimization problems are typically NP-hard, and thus very challenging to solve. In this paper, we present the random key cuckoo search (RKCS) algorithm for solving the famous Travelling Salesman Problem (TSP). We used a simplified random-key encoding scheme to pass from a continuous space (real numbers) to a combinatorial space. We also consider the displacement of a solution in both spaces using L\'evy flights. The performance of the proposed RKCS is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that RKCS is superior to some other metaheuristic algorithms

Effectiveness of Local Search for Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude 1/epsilon^c is an approximation scheme for the following problems in the Euclidean plane: TSP with random inputs, Steiner tree with random inputs, uniform facility location (with worst case inputs), and bicriteria k-median (also with worst case inputs). The randomness assumption is necessary for TSP

Transformations of node-balanced routing problems

This paper describes a polynomial transformation for a class of unit-demand vehicle routing problems, named node-balanced routing problems (BRP), where the number of nodes on each route is restricted to be in an interval such that the workload across the routes is balanced. The transformation is general in that it can be applied to single or multiple depot, homogeneous or heterogeneous fleet BRPs, and any combination thereof. At the heart of the procedure lies transforming the BRP into a generalized traveling salesman problem (GTSP), which can then be transformed into a traveling salesman problem (TSP). The transformed graph exhibits special properties which can be exploited to significantly reduce the number of arcs, and used to construct a formulation for the resulting TSP that amounts to no more than that of a constrained assignment problem. Computational results on a number of instances are presente

Genetic Algorithm Guidance of a Constraint Programming Solver for the Multiple Traveling Salesman Problem

This project developed a metaheuristic approach to the Multiple Traveling Salesman Problem that pairs a custom genetic algorithm with a conventional combinatorial optimization solver. This combined approach was used to build an optimal route for two popular radio show hosts to visit each of the 37 Atlanta area Jersey Mike\u27s Subs in one day. This supported a fundraising eort to send children with chronic and terminal illnesses to Disney World through an organization called Bert\u27s Big Adventure. Atlanta-area Jersey Mike\u27s locations donated 100% of proceeds earned on this Day of Giving to Bert\u27s Big Adventure. With the suggested route developed through our approach, the radio hosts successfully visited all 37 Jersey Mike\u27s in one day, a task Bert\u27s Big Adventure staff members had not been able to complete in previous years

Engineering an Approximation Scheme for Traveling Salesman in Planar Graphs

We present an implementation of a linear-time approximation scheme for the traveling salesman problem on planar graphs with edge weights. We observe that the theoretical algorithm involves constants that are too large for practical use. Our implementation, which is not subject to the theoretical algorithm\u27s guarantee, can quickly find good tours in very large planar graphs

Training software for orthogonal packing problems

An open source architecture for the interactive solution of packing problems in two dimensions is presented. Although primarily developed for helping engineering students to understand the algorithmic approaches to the solution of difficult combinatorial optimization problems, the application can be useful to practitioners and developers thanks to its visual tools. The paper gives intuitive and formal definitions of the problems at hand, discusses two natural heuristic approaches, provides technical information on the application, and reports the results of classroom experimental testings

A Systematic Literature Review of Quantum Computing for Routing Problems

Quantum Computing is drawing a significant attention from the current scientific community. The potential advantages offered by this revolutionary paradigm has led to an upsurge of scientific production in different fields such as economics, industry, or logistics. The main purpose of this paper is to collect, organize and systematically examine the literature published so far on the application of Quantum Computing to routing problems. To do this, we embrace the well-established procedure named as Systematic Literature Review. Specifically, we provide a unified, self-contained, and end-to-end review of 18 years of research (from 2004 to 2021) in the intersection of Quantum Computing and routing problems through the analysis of 53 different papers. Several interesting conclusions have been drawn from this analysis, which has been formulated to give a comprehensive summary of the current state of the art by providing answers related to the most recurrent type of study (practical or theoretical), preferred solving approaches (dedicated or hybrid), detected open challenges or most used Quantum Computing device, among others

The Traveling Salesman Problem

This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances