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We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various…
The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into…
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…
The traveling salesman (or salesperson) problem, short TSP, is a problem of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application…
The Moving-Target Traveling Salesman Problem (MT-TSP) seeks a shortest path for an agent that starts at a stationary depot, visits a set of moving targets exactly once, each within one of their respective time windows, and returns to the…
This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…
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…
We present an application of the tensor network generator-enhanced optimization (TN-GEO) framework to address the traveling salesman problem (TSP), a fundamental combinatorial optimization challenge. Our approach employs a tensor network…
We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we…
Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe an…
The increasing use of drones to perform various tasks has motivated an exponential growth of research aimed at optimizing the use of these means, benefiting both military and civilian applications, including logistics delivery. In this…
Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are…
In this paper we schedule the travel path of a set of drones across a graph where the nodes need to be visited multiple times at pre-defined points in time. This is an extension of the well-known multiple traveling salesman problem. 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…