Travelling Salesman Problem - Science topic

Hypergraphs extend traditional graphs by allowing edges (known as hyperedges) to connect more than two vertices, rather than just pairs. This paper explores fundamental problems and algorithms in the context of SuperHypergraphs, an advanced extension of hypergraphs enabling modeling of hierarchical and complex relationships. Topics covered include...

Wireless sensor networks (WSNs) consist of small, low-cost, low-power sensors deployed to monitor environmental changes and transmit data to a static base station. A major challenge in WSNs is energy consumption, particularly in nodes near the static sink, leading to the "hotspot" or "energy hole" problem, which disrupts data transmission and reduc...

Adding mobile sinks (MSs) to wireless sensor networks (WSNs) has proven to increase network longevity and improve data delivery services. We accomplish this goal by reducing routing expenses and preventing the emergence of any hotspot zones inside the network. On the other hand, path determination and MS visiting point selection in WSNs are difficu...

In this paper, we examine the use of quantum annealing for the Traveling Salesman Problem (TSP) using the D-Wave Advantage quantum annealer and its "Pegasus" architecture. We introduce a refined Quadratic Unconstrained Binary Optimization (QUBO) formulation that simplifies the problem by eliminating the first node and reallocating its effect, there...

The quantum ant colony algorithm (QACO) is explored as a solution to the traveling salesman problem (TSP), targeting inefficiencies such as slow convergence and local optima entrapment found in traditional ant colony optimization (ACO) methods. By integrating quantum computing elements, specifically quantum rotation gates and qubits, into the ACO f...

Due to its NP-Hard property, the Travelling Salesman Problem (TSP) has long been a prominent research topic in path planning. The goal is to design the algorithm with the fastest execution speed in order to find the path with the lowest travelling cost. In particular, new generative AI technology is continually emerging. The question of how to expl...

Optimization challenges necessitate the development of strategies to address computational complexity, aiming to increase efficiency, reduce expenses, or improve the allocation and management of resources. Decomposition, notably clustering, offers streamlined solutions. K-means, Affinity Propagation, and Density Peaks are foundational for clusterin...

The Traveling Salesman Problem (TSP) is a classic problem in combinatorial optimization, aiming to find the shortest path that traverses all cities and eventually returns to the starting point. The ant colony optimization algorithm has achieved significant results, but when the number of cities increases, the ant colony algorithm is prone to fall i...

In this paper, we present the development of a new version of the BrkgaCuda, called BrkgaCuda 2.0, to support the design and execution of Biased Random-Key Genetic Algorithms (BRKGA) on CUDA/GPU-enabled computing platforms, employing new techniques to accelerate the execution. We compare the performance of our implementation against the standard CP...

In contemporary lifestyles, a common challenge is the urgent requirement to purchase a specific item without knowing its location, often due to time constraints. While online ordering is an alternative, the associated waiting period poses a drawback. To address this, a purpose-built application has been developed to efficiently locate products in n...

In this paper, we conducted a study on multi-UAV-assisted Wireless Sensor Networks (WSNs) data collection. First, to address the challenges of network construction and data transmission timeliness, we introduced the concepts of data collection UAV (UAV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \use...

This paper presents a novel Genetic Algorithm (GA) designed to tackle the Travelling Salesman Problem (TSP) with remarkable efficacy. It integrates group theory into population initialization, employs Partially Matched Crossover (PMX), and adopts a 2-optimal mutation strategy. The pioneering approach harnesses algebraic structures in constructing g...

The integration of Augmented Reality (AR) into mobile devices has sparked a trend in the development of mobile AR applications across diverse sectors. Nevertheless, the execution of AR tasks necessitates substantial computational, memory, and storage resources, which poses a challenge for mobile terminals with limited hardware capabilities to run A...

This study introduces a hybrid methodology that integrates the ant colony optimization (ACO) with genetic algorithm (GA) techniques. ACO is employed first to create an initial population and to derive a sub-optimal solution for the TSP using a newly designed inver-over (IO) operator. The Proposed IO operator is utilized to improve the solution deri...

This paper considers the application of Model Predictive Control (MPC) to a weighted coverage path planning (WCPP) problem. The problem appears in a wide range of practical applications, such as search and rescue (SAR) missions. The basic setup is that one (or multiple) agents can move around a given search space and collect rewards from a given sp...

The Transformer model is widely employed to address the traveling salesman problem due to its robust global information acquisition, learning, and generalization capabilities. However, its high computational complexity and limited accuracy require further refinement. To overcome these shortcomings, a novel model is proposed, integrating a lightweig...

As cities expand and the global push for zero pollution intensifies, sustainable last-mile delivery (LMD) systems are essential to minimizing environmental and health impacts. This study addresses the need for more sustainable LMD by examining the integration of wind conditions into drone-assisted deliveries, focusing on their effects on air and no...

The decision of whether to collaborate with one or multiple sources is a crucial challenge in the supply chain. This decision involves considering various criteria, including price and transportation cost. The traveling purchaser problem (TPP) is an extension of the well-known traveling salesman problem (TSP). While the TSP focuses on product distr...

This work aims to compare two distinct approaches for solving a Travelling Salesman Problem with time window constraints. Given an environment with a fixed number of cities (points of interest), a robot must determine a route such that each city is visited in an imposed time interval. Both of the examined techniques have the objective of identifyin...

In this paper, we address a biomass feedstock logistics problem to supply biomass from production fields to satellite storage locations (SSLs) and from there to bioenergy plants (BePs) and then to a biorefinery. It entails a new problem feature of routing load-out equipment sets among the SSLs to perform loading/unloading of biomass and/or its pre-...

A Dubin's Travelling Salesman Problem (DTSP) of finding a minimum-length tour through a given set of points is considered. DTSP has a Dubins vehicle, which is capable of moving only forward with constant speed. This paper first discusses the Angle Bisector Algorithm (ABA) to address DTSP. In ABA, the Euclidean Travelling Salesman Problem (ETSP) tou...

This paper investigates what properties a neighbourhood requires to support beneficial local search. We show that neighbourhood locality, and a reduction in cost probability towards the optimum, support a proof that search among neighbours is more likely to find an improving solution in a single search step than blind search. This is the first pape...

We consider polynomial time approximation for the minimum cost cycle cover problem of an edge-weighted digraph, where feasible covers are restricted to have at most k disjoint cycles. In the literature this problem is referred to as Min-k-SCCP. The problem is closely related to classic Traveling Salesman Problem (TSP) and Vehicle Routing Problem (V...

This paper considers a patrol inspection scenario where multiple unmanned aerial vehicles (UAVs) are adopted to traverse multiple predetermined cruise points for data collection. The UAVs are connected to cellular networks and they would offload the collected data to the ground base stations (GBSs) for data processing within the constrained duratio...

The Traveling Salesman Problem (TSP) in the two-dimensional Euclidean plane is among the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J. ACM 1998] and Mitchell [SICOMP 1999] gave the first polynomial time approximation schemes. The running time of their approximation schemes was improved by Rao and Smith [STOC...

Phylogenetic networks model the evolutionary history of taxa while allowing for reticulate events such as hybridization and horizontal gene transfer. As is the case for phylogenetic trees, it is often not possible to infer the root location of such a network directly from biological data for several evolutionary models. Hence, we consider semi-dire...

The Traveling Salesman Problem (TSP) is a well-known optimization problem. Its objective is to find the shortest path for a salesman to visit each city on a list and then return to the initial city. A number of approaches have been developed to solve the TSP, including dynamic programming, branch and bound, the nearest neighbour algorithm, genetic...

The emergence of 2.5D chiplet platforms provides a new avenue for compact scale-out implementations of deep learning (DL) workloads (WLs). Integrating multiple small chiplets using a network-on-interposer (NoI) offers not only significant cost reduction and higher manufacturing yield than 2-D ICs but also better energy efficiency and performance. H...

Cyclic routing problems are a well-researched category of combinatorial problems in Operations Research (OR). They involve finding an optimal cycle (route), starting from an initial point (e.g., depot), visiting some nodes (e.g., customer or demand points), and returning to the starting point while adhering to constraints and optimizing a specific...

The Travelling Salesman Problem - TSP is one of the most explored problems in the scientific literature to solve real problems regarding the economy, transportation, and logistics, to cite a few cases. Adapting TSP to solve different problems has originated several variants of the optimization problem with more complex objectives and different rest...

To help improve the situation at this stage of the illegal wildlife trade, this article takes a comprehensive look at global data on Illegal Wildlife Trade (IWT) based on the background that illegal wildlife trade is still rampant at this stage. Through data-driven as well as mathematical modeling, feasible and effective measures are proposed. Firs...

Vehicle Routing Problems (VRPs) can model many real-world scenarios and often involve complex constraints. While recent neural methods excel in constructing solutions based on feasibility masking, they struggle with handling complex constraints, especially when obtaining the masking itself is NP-hard. In this paper, we propose a novel Proactive Inf...

In this paper we address the optimal planification of general purpose tasks that includes a wide spectrum of situations: from project management of human teams to the coordination of an automated assembly line or the automated inspection of power grids. There exists many methods for planification. However, the vast majority of such methods are conc...

Multirotor unmanned aerial vehicle is a prevailing type of aerial robots with wide real-world applications. The energy efficiency of the robot is a critical aspect of its performance, determining the range and duration of the missions that can be performed. This paper studies the energy-optimal planning of the multirotor, which aims at finding the...

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, and various other related problems. This work potentially opens up new avenues for algorithm design in neural...

Companies like Amazon and UPS are heavily invested in last-mile delivery problems. Optimizing last-delivery operations not only creates tremendous cost savings for these companies but also generate broader societal and environmental benefits in terms of better delivery service and reduced air pollutants and greenhouse gas emissions. Last-mile deliv...

Probabilistic Bit (P-Bit) device serves as the core hardware for implementing Ising computation. However, the severe intrinsic variations of stochastic P-Bit devices hinder the large-scale expansion of the P-Bit array, significantly limiting the practical usage of Ising computation. In this work, a behavioral model which attributes P-Bit variations...

For citrus trees cultivated by dwarf dense planting, the fruits are randomly distributed in space, which poses difficulties for mechanized picking. To improve picking efficiency, a citrus picking system based on dual robot collaboration is designed and a global scanning picking scheme that scans the entire fruit tree to achieve orderly fruit pickin...

The max-min ant system (MMAS) algorithm has found extensive application in tackling combinatorial optimization challenges such as the traveling salesman problem (TSP), production scheduling, and quadratic assignment. Nevertheless, as the scale of the problem increases, the MMAS algorithm gradually encounters performance limitations. To address the...

Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. The real-world applicability of these problems is dependent on the objectives and constraints considered...

Autonomous exploration in unknown environments is an essential capability for mobile robots. The complexity of autonomous exploration, however, means that existing algorithms struggle to balance efficiency and comprehensiveness, causing low mapping accuracy and redundant path planning. To perform accurate and efficient exploration tasks, we have pr...

The shortest path problem is a fundamental challenge in graph theory, focused on identifying the most efficient routes between nodes in a network. It stands as one of the extensively researched combinatorial optimization problems. In this paper, we explained the fundamental concepts of shortest path algorithms, with a particular emphasis on Floyd W...

The traveling salesman problem (TSP) is an NP-hard problem being studied by many researchers. Metaheuristic algorithms generally depend on nature-inspired phenomena successfully applied to combinatorial optimization, such as routing, scheduling, assignment problems, engineering, optimization, genetics, robotics, nanotechnology, and various fields....

This paper addresses two tasks: (i) fixed-size objects such as hay bales are to be identified in an aerial image for a given reference image of the object, and (ii) variable-size patches such as areas on fields requiring spot spraying or other handling are to be identified in an image for a given small-scale reference image. Both tasks are related....

The purpose of this article is to propose a new approach for finding the guaranteed solution set of minimized assignment problems and maximized assignment problems. Firstly the existence of the minimin and maximax optimization problems are studied with the help of newly defined weakly φ-convex function in φ-convex set. Next the assignment problems...

Recent advancements in learning-based combinatorial optimization (CO) methods have shown promising results in solving NP-hard problems without the need for expert-crafted heuristics. However, high performance of these approaches often rely on problem-specific human-expertise-based search after generating candidate solutions, limiting their applicab...

Monitoring and surveillance using autonomous vehicles offer a low-cost and efficient solution compared to conventional methods that require manual surveys. Monitoring water bodies typically involves comprehensive coverage of a specific area of interest. This study investigates a path planning approach for environmental monitoring using an unmanned...

Ant Colony Optimization (ACO) is a powerful metaheuristic algorithm widely used to solve complex optimization problems in production and logistics. This paper presents a methodology for enhancing the ACO performance when applied to Traveling Salesman Problems (TSP). By reducing the number of ants in the colony, the algorithm's computational speed i...

A well-studied continuous model of graphs considers each edge as a continuous unit-length interval of points. For $\delta \geq 0$, we introduce the problem $\delta$-Tour, where the objective is to find the shortest tour that comes within a distance of $\delta$ of every point on every edge. It can be observed that 0-Tour is essentially equivalent to...

Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To date, the community has created numerous open-source neural solvers with distinct motivations and inductive biases...

The traveling salesman problem (TSP) is a frequently studied problem by researchers today and belongs to the class of combinatorial optimization problems. It can be used to solve many current world problems such as scheduling, circuit design, layout design of plants in factories, route planning and printed circuit design. Therefore, researchers wor...

The development of advanced quantum-classical algorithms is among the most prominent strategies in quantum computing. Numerous hybrid solvers have been introduced recently. Many of these methods are created ad hoc to address specific use cases. However, several well-established schemes are frequently utilized to address optimization problems. In th...

The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its respective delivery point. The goal is to minimize the total distance traveled. SCP is known to be NP-hard, even o...

Intriguing symmetries are uncovered regarding all magic squares of orders 3, 4, and 5, with 1, 880, and 275,305,224 distinct configurations, respectively. In analogy with the travelling salesman problem, the distributions of the total topological distances of the paths travelled by passing through all the vertices (matrix elements) only once and sp...

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 implementation of their technique, employing an exact TSP solver to locate k-opt moves in the elimination pro...

Quantum ant colony optimization (QACO) has drew much attention since it combines the advantages of quantum computing and ant colony optimization (ACO) algorithm overcoming some limitations of the traditional ACO algorithm. However,due to the hardware resource limitations of currently available quantum computers, the practical application of the QAC...

The embedding of complex networks into metric spaces has become a research topic of high interest with a wide variety of proposed methods. Low dimensional hyperbolic spaces offer a natural co-domain for embeddings allowing a roughly uniform spatial distribution of the nodes even for scale-free networks and the efficient navigability and estimation...

Complexity science studies physical phenomena that cannot be explained by the mere analysis of the single units of a system but requires to account for their interactions. A feature of complexity in connected systems is the emergence of mesoscale patterns in a geometric space, such as groupings in bird flocks. These patterns are formed by groups of...

In recent years, wireless rechargeable sensor networks (WRSNs) have gained significant attention in the research community due to the current advancements in wireless power transfer technology. In mobile charger scheduling, previous works primarily emphasized the survival rate of sensor nodes. However, the primary task of a WRSN is to monitor targe...

A single-celled amoeba can solve the traveling salesman problem through its shape-changing dynamics. In this paper, we examine roles of several elements in a previously proposed computational model of the solution-search process of amoeba and three modifications towards enhancing the solution-search performance. We find that appropriate modificatio...

Multi-objective combinatorial optimization problems (MOCOPs) are designed to identify solution sets that optimally balance multiple competing objectives. Addressing the challenges inherent in applying deep reinforcement learning (DRL) to solve MOCOPs, such as model non-convergence, lengthy training periods, and insufficient diversity of solutions,...

The combinatorial problem in this paper is motivated by a variant of the famous traveling salesman problem where the salesman must return to the starting point after each delivery. The total length of a delivery route is related to a metric known as closeness centrality. The closeness centrality of a vertex v in a graph G was defined in 1950 by Bav...

Ensuring that the outputs of neural networks satisfy specific constraints is crucial for applying neural networks to real-life decision-making problems. In this paper, we consider making a batch of neural network outputs satisfy bounded and general linear constraints. We first reformulate the neural network output projection problem as an entropy-r...

Heuristics are commonly used to tackle diverse search and optimization problems. Design heuristics usually require tedious manual crafting with domain knowledge. Recent works have incorporated large language models (LLMs) into automatic heuristic search leveraging their powerful language and coding capacity. However, existing research focuses on th...