Influence of Programming Language on the Execution Time of Ant Colony Optimization Algorithm

Supply chains can be accelerated by route optimization, a computationally intensive process for a large number of instances. Traveling Salesmen Problem, as the representative example of routing problems, is NP-hard combinatorial problem. It means that the time needed for solving the problem with exact methods increases exponentially with the increased dataset. Using metaheuristic methods, like Ant Colony Optimization, reduces the time needed for solving the problem drastically but finding a solution still takes a considerable amount of time for large datasets. In today’s dynamic environment finding the solution as fast as possible is important as finding a quality solution. The programming language used for finding the solution also influences execution time. In this paper, the execution time of Ant Colony Optimization to solve Traveling Salesman Problems of different sizes was measured. The algorithm was programmed in several programming languages, execution time was measured to rank programming languages

Assessment of genetic algorithm based assignment strategies for unmanned systems using the multiple traveling salesman problem with moving targets

Title from PDF of title page, viewed March 1, 2023Thesis advisor: Travis FieldsVitaIncludes bibliographical references (pages 100-106)Thesis (M.S.)--Department of Civil and Mechanical Engineering. University of Missouri--Kansas City, 2021The continuous and rapid advancements in autonomous unmanned systems technologies presents increasingly sophisticated threats to military operations. These threats necessitate the prioritization of improved strategies for military resources and air base defense. In many scenarios, it is necessary to combat hostile unmanned systems before they reach the defensible perimeters of existing fixed-base defense systems. One solution to this problem is weaponizing friendly unmanned systems to hunt and kill hostile unmanned systems. However, the assignment and path planning of these “Hunter-Killer” systems to incoming hostile unmanned systems, in a multiple friendly versus multiple enemy scenario, presents a major challenge and can be represented by the Multiple Traveling Salesmen Problem with Moving Targets (MTSPMT). The MTSPMT is a combinatorial optimization problem and an extension of the classical Traveling Salesman Problem whereby the number of salesmen is increased and targets (cities) move with respect to time. The objective of the MTSPMT, for the application of military defense using a squadron of Hunter-Killer unmanned systems, is to determine a path that minimizes the cost required for multiple Hunter-Killer unmanned systems to successfully intercept all incoming threats. In this study, an assessment of genetic algorithm based assignment strategies for unmanned systems using the MTSPMT is performed. A number of scenarios were constructed using up to 50 hostile unmanned systems and the generated solutions were compared based on their resulting time to converge, solution fitness, and number of generations required. Findings indicate that under certain conditions genetic based algorithms provide better results on average and converge more rapidly than brute force searching and existing assignment and path planning solutions.Introduction -- Literature review -- Problem formulation and model design -- Methodology -- Results and Discussion -- Conclusio

Several approaches for the traveling salesman problem

We characterize both approaches, mldp and k-mldp, with several methodologies; both a linear and a non-linear mathematical formulation are proposed. Additionally, the design and implementation of an exact methodology to solve both linear formulations is implemented and with it we obtained exact results. Due to the large computation time these formulations take to be solved with the exact methodology proposed, we analyse the complexity each of these approaches and show that both problems are NP-hard. As both problems are NP-hard, we propose three metaheuristic methods to obtain solutions in shorter computation time. Our solution methods are population based metaheuristics which exploit the structure of both problems and give good quality solutions by introducing novel local search procedures which are able to explore more efficiently their search space and to obtain good quality solutions in shorter computation time. Our main contribution is the study and characterization of a bi-objective problematic involving the minimization of two objectives: an economic one which aims to minimize the total travel distance, and a service-quality objective which aims to minimize of the waiting time of the clients to be visited. With this combination of objectives, we aim to characterize the inclusion of the client in the decision-making process to introduce service-quality decisions alongside a classic routing objective.This doctoral dissertation studies and characterizes of a combination of objectives with several logistic applications. This combination aims to pursue not only a company benefit but a benefit to the clients waiting to obtain a service or a product. In classic routing theory, an economic approach is widely studied: the minimization of traveled distance and cost spent to perform the visiting is an economic objective. This dissertation aims to the inclusion of the client in the decision-making process to bring out a certain level of satisfaction in the client set when performing an action. We part from having a set of clients demanding a service to a certain company. Several assumptions are made: when visiting a client, an agent must leave from a known depot and come back to it at the end of the tour assigned to it. All travel times among the clients and the depot are known, as well as all service times on each client. This is to say, the agent knows how long it will take to reach a client and to perform the requested service in the client location. The company is interested in improving two characteristics: an economic objective as well as a servicequality objective by minimizing the total travel distance of the agent while also minimizing the total waiting time of the clients. We study two main approaches: the first one is to fulfill the visits assuming there is a single uncapacitated vehicle, this is to say that such vehicle has infinite capacity to attend all clients. The second one is to fulfill the visits with a fleet of k-uncapacitated vehicles, all of them restricted to an strict constraint of being active and having at least one client to visit. We denominate the single-vehicle approach the minimum latency-distance problem (mldp), and the k-sized fleet the k-minimum latency-distance problem (k-mldp). As previously stated, this company has two options: to fulfil the visits with a single-vehicle or with a fixed-size fleet of k agents to perform the visits

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations

This paper introduces a new mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. Of particular interest is the monitoring of transient events that can not be easily forecast. Application areas range from natural phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano using a ground robot) to urban activities ({\em e.g.}, monitoring early formations of traffic congestion using an aerial robot). Motivated by those and many other examples, this paper focuses on problems in which the precise occurrence times of the events are unknown {\em a priori}, but statistics for their inter-arrival times are available. The robot's task is to monitor the events to optimize the following two objectives: {\em (i)} maximize the number of events observed and {\em (ii)} minimize the delay between two consecutive observations of events occurring at the same location. The paper considers the case when a robot is tasked with optimizing the event observations in a balanced manner, following a cyclic patrolling route. First, assuming the cyclic ordering of stations is known, we prove the existence and uniqueness of the optimal solution, and show that the optimal solution has desirable convergence and robustness properties. Our constructive proof also produces an efficient algorithm for computing the unique optimal solution with $O(n)$ time complexity, in which $n$ is the number of stations, with $O(\log n)$ time complexity for incrementally adding or removing stations. Except for the algorithm, most of the analysis remains valid when the cyclic order is unknown. We then provide a polynomial-time approximation scheme that gives a $(1+\epsilon)$-optimal solution for this more general, NP-hard problem