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The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by…
The $k$-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces $k$ edges of the tour by $k$ other edges, as long as this yields a shorter tour. We…
Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based…
In this paper we study a natural special case of the Traveling Salesman Problem (TSP) with point-locational-uncertainty which we will call the {\em adversarial TSP} problem (ATSP). Given a metric space $(X, d)$ and a set of subsets $R =…
This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformulations that approximate the Euclidean distances and…
The maximum traveling salesman problem (Max TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. This problem is APX-hard in the general metric case but admits…
Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in…
We introduce a fast, quasi-linear-time heuristic for the Close-Enough Traveling Salesman Problem (CETSP), a continuous generalization of the Euclidean TSP in which each target is a disk that must be intersected. The method adapts the…
Multi Expression Programming (MEP) is an evolutionary technique that may be used for solving computationally difficult problems. MEP uses a linear solution representation. Each MEP individual is a string encoding complex expressions…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
NP hard optimization problems like the Traveling Salesman Problem (TSP) defy efficient solutions in the worst case, yet real-world instances often exhibit exploitable patterns. We propose a novel patternaware complexity framework that…
We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between…
The travelling salesman problem (TSP) is one of the well-studied NP-hard problems in the literature. The state-of-the art inexact TSP solvers are the Lin-Kernighan-Helsgaun (LKH) heuristic and Edge Assembly crossover (EAX). A recent study…
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…
The path version of the Traveling Salesman Problem is one of the most well-studied variants of the ubiquitous TSP. Its generalization, the Multi-Path TSP, has recently been used in the best known algorithm for path TSP by Traub and Vygen…
The travelling salesman problem (TSP) of space trajectory design is complicated by its complex structure design space. The graph based tree search and stochastic seeding combinatorial approaches are commonly employed to tackle the…
Deep learning has shown significant potential in solving combinatorial optimization problems such as the Euclidean traveling salesman problem (TSP). However, most training and test instances for existing TSP algorithms are generated…
While there are optimal TSP solvers, as well as recent learning-based approaches, the generalization of the TSP to the Multiple Traveling Salesmen Problem is much less studied. Here, we design a neural network solution that treats the…
We present a black-box reduction from the path version of the Traveling Salesman Problem (Path TSP) to the classical tour version (TSP). More precisely, we show that given an $\alpha$-approximation algorithm for TSP, then, for any $\epsilon…
Among various variants of the traveling salesman problem, the s-t-path graph TSP has the special feature that we know the exact integrality ratio, 3/2, and an approximation algorithm matching this ratio. In this paper, we go below this…