Related papers: Matrix method for the multi salesmen problem (TSP)…

We present novel path-slicing strategies integrated with quantum local search to optimize solutions for the Traveling Salesman Problem (TSP), addressing the limitations of current Noisy Intermediate-Scale Quantum (NISQ) technologies. Our…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

We introduce a new approach to tackle the mobile manipulator task sequencing problem. We leverage computational geometry, graph theory and combinatorial optimization to yield a principled method to segment the task-space targets into…

We study the fair capacitated vehicle routing problem, in which a fleet of vehicles must serve a set of customers such that the difference between the longest and shortest route, the range, is minimized. A key challenge is that the range…

Given a set $P$ of $n$ points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance…

Multimodal Large Language Models (MLLMs) harness comprehensive knowledge spanning text, images, and audio to adeptly tackle complex problems, including zero-shot in-context learning scenarios. This study explores the ability of MLLMs in…

There has been a growing number of machine learning methods for approximately solving the travelling salesman problem. However, these methods often require solved instances for training or use complex reinforcement learning approaches that…

The Generalized Traveling Salesman Problem (GTSP) is one of the NP-hard combinatorial optimization problems. A variant of GTSP is E-GTSP where E, meaning equality, has the constraint: exactly one node from a cluster of a graph partition is…

In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We…

The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible…

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or…

We consider the bicriteria asymmetric traveling salesman problem (bi-ATSP). Optimal solution to a multicriteria problem is usually supposed to be the Pareto set, which is rather wide in real-world problems. We apply to the bi-ATSP the…

In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the…

In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.

In this paper, we propose a framework for solving a single-agent task by using multiple agents, each focusing on different aspects of the task. This approach has two main advantages: 1) it allows for training specialized agents on different…

Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational…

We consider the NP-hard 2-period balanced travelling salesman problem. In this problem the salesman needs to visit a set of customers in two time periods. A given subset of the customers has to be visited in both periods while the rest of…

The Clustered Traveling Salesman Problem with a Prespecified Order on the Clusters, a variant of the well-known traveling salesman problem is studied in literature. In this problem, delivery locations are divided into clusters with…

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,…

In many applications, including underwater robotics, the coverage problem requires an autonomous vehicle to systematically explore a defined area while minimizing redundancy and avoiding obstacles. This paper investigates coverage path…