Related papers: Improved Space-Time Tradeoffs for Permutation Prob…
The Traveling Salesman Problem (TSP) is a prototypical combinatorial optimization problem, but its quantum implementation is limited by the O(n^2)-qubit overhead of standard one-hot encodings. Here, we propose a resource-efficient…
We propose a non-autoregressive framework for the Travelling Salesman Problem where solutions emerge directly from learned permutations, without requiring explicit search. By applying a similarity transformation to Hamiltonian cycles, the…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of $m$ linear inequalities on $n$ real variables with at most two…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate…
We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space…
Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…
The Analyst's Traveling Salesman Problem asks for conditions under which a (finite or infinite) subset of $\mathbb{R}^N$ is contained on a curve of finite length. We show that for finite sets, the algorithm constructed by Schul (2007)and…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
In order to deal with the high development time of exact and approximation algorithms for NP-hard combinatorial optimisation problems and the high running time of exact solvers, deep learning techniques have been used in recent years as an…
Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to…
The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to…
Computing diverse sets of high-quality solutions has gained increasing attention among the evolutionary computation community in recent years. It allows practitioners to choose from a set of high-quality alternatives. In this paper, we…
Evolutionary algorithms have been shown to obtain good solutions for complex optimization problems in static and dynamic environments. It is important to understand the behaviour of evolutionary algorithms for complex optimization problems…
This paper presents a novel and efficient heuristic framework for approximating the solutions to the multiple traveling salesmen problem (m-TSP) and other variants on the TSP. The approach adopted in this paper is an extension of the…
We propose the Steiner Traveling Salesman Problem with Time Windows and Pickup and Delivery, an advanced and practical extension of classical routing models. This variant integrates the characteristics of the Steiner Traveling Salesman…
The traveling salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing…
This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once…
We propose a simple and exact method for the Traveling Salesman Problem with Time Windows and Makespan objective (\TSPTW-M) that solves all instances of the classical benchmark with $50$ or more customers in less than ten seconds each.…