A Hybrid Genetic Algorithm for the min-max Multiple Traveling Salesman Problem

This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual, and a dynamic programming algorithm is employed to evaluate the individual and find the optimal mTSP solution for the given sequence of cities. A novel crossover operator is designed to combine similar tours from two parents and offers great diversity for the population. For some of the generated offspring, we detect and remove intersections between tours to obtain a solution with no intersections. This is particularly useful for the min-max mTSP. The generated offspring are also improved by a self-adaptive random local search and a thorough neighborhood search. Our algorithm outperforms all existing algorithms on average, with similar cutoff time thresholds, when tested against multiple benchmark sets found in the literature. Additionally, we improve the best-known solutions for 21 out of 89 instances on four benchmark sets

Applying a Genetic Algorithm to a m-TSP: Case Study of a Decision Support System for Optimizing a Beverage Logistics Vehicles Routing Problem

Route optimization has become an increasing problem in the transportation and logistics sector within the development of smart cities. This article aims to demonstrate the implementation of a genetic algorithm adapted to a Vehicle Route Problem (VRP) in a company based in the city of Covilhã (Portugal). Basing the entire approach to this problem on the characteristic assumptions of the Multiple Traveling Salesman Problem (m-TSP) approach, an optimization of the daily routes for the workers assigned to distribution, divided into three zones: North, South and Central, was performed. A critical approach to the returned routes based on the adaptation to the geography of the Zones was performed. From a comparison with the data provided by the company, it is predicted by the application of a genetic algorithm to the m-TSP, that there will be a reduction of 618 km per week of the total distance traveled. This result has a huge impact in several forms: clients are visited in time, promoting provider-client relations; reduction of the fixed costs with fuel; promotion of environmental sustainability by the reduction of logistic routes. All these improvements and optimizations can be thought of as contributions to foster smart cities.Fundação para a Ciência e a Tecnologia (FCT—MCTES) for its financial support via the project UIDB/00151/2020 (C-MAST).info:eu-repo/semantics/publishedVersio

Hybrid Spatial-Artificial Intelligence Approach for Renewable Energy Sources Sites Identification and Integration in Sarawak State

As many new power infrastructures are planned under Sarawak State, the energy demand is expected to grow exponentially in these coming years. Besides, the minority of the rural villages are still not electrified yet. Fortunately, Sarawak State is blessed with indigenous Renewable Energy such as solar, hydro and wind power but they are scattered in the interior of the Sarawak State. Thus, the first phase is to develop a criteria scheme data for potential Renewable Energy Sources (RES) sites. It is followed by identifying RES sites using spatial data and Multi-Criteria Decision Making-Analytical Hierarchy Process (MCDM-AHP) algorithm. Accordingly, Spatial-Artificial Intelligence (AI) approach is utilised to integrate a high number of RES sites with minimum total distance. The research also proposed a hybrid Spatial-AI approach to integrate a high number of RES sites with minimum total distance and minimum total elevation difference. Initially, the Geographic Information System (GIS) tool is utilised to perform the assessments on current geographical conditions. From this, the spatial criteria scheme data is produced. The MCDM-AHP algorithm is applied to the criteria scheme data to identify the number of RES sites. Four cases were developed for RES sites integration, representing four different arrangements of RES sites. In each case, the Traveling Salesman Problem-Genetic Algorithm (TSP-GA) algorithm is applied to determine a minimum total distance of RES sites integration. Furthermore, a hybrid Spatial-Artificial Intelligence (AI) algorithm is proposed to integrate RES sites with minimum total distance and minimum total elevation difference. This research successfully identifies 55 solar energy sites and 15 wind energy sites. Meanwhile, 155 hydro energy sites were identified using the spatial map from Sarawak Energy Berhad (SEB). The second phase of the research work is to integrate the RES sites. TSP-GA algorithm is applied to generate the transmission line routing among the RES sites with minimum total distance. The minimum total distances in all four cases are acquired and validated as both the TSP-GA algorithm and the Traveling Salesman Problem-Mixed Integer Linear Programming (TSP-MILP) algorithm produced the same routing pattern. In the end, the proposed algorithm is successfully minimized the total distance and total elevation difference. The improved Spatial-AI algorithm showed approximately 15% better compared to ordinary TSP-GA in all four cases

Application of Genetic Algorithms to Solve MTSP Problems with Priority (Case Study at the Jakarta Street Lighting Service)

Transportation is one thing that is very important and is the highest cost in the supply chain. One way to reduce these costs is to optimize vehicle routes. The Multiple Traveling Salesman Problem (MTSP) and Capacitated Vehicle Routing Problem (CVRP) are models that have been extensively researched to optimize vehicle routes. In its development based on actual events in the real world, some priorities must be visited first in optimizing vehicle routes. Several studies on MTSP and CVRP models have been conducted with exact solutions and algorithms. In a real case in the Jakarta City Street Lighting Section, the problem of determining the route in three shifts is a crucial problem that must be resolved to increase worker productivity to improve services. Services in MCB (Miniature Circuit Breaker) installation and maintenance activities for general street lights and priority is given to light points that require replacement. Because, in this case, the delivery capacity is not taken into account, the priority of the lights visited is random, and the number of street light points is enormous, in this study, we use the MTSP method with priority and solve by a genetic algorithm assisted by the nearest neighbor algorithm. From the resolution of this problem, it was found that the travel time reduction was 32 % for shift 1, 24 % for shift 2, and 23 % for shift 3. Of course, this time reduction will impact worker productivity so that MCB installation can be done faster for all lights and replace a dead lamp

Review of Multiple Traveling Salesman Model and Its Application

As a generalization of the classical traveling salesman problem (TSP), the multiple traveling salesman problem (MTSP) is one of the well-known combinatorial optimization problems. However, as a classical NP hard problem, the problem scale and computational complexity of the multiple traveling salesman problem have very high requirements for the solution method. This paper focuses on the multiple traveling salesman problem. Firstly, several characteristics, objective functions, problem constraints and variants of MTSP model are subdivided. Secondly, it classifies and sorts out the specific methods of several common heuristic algorithms in solving MTSP, and compares the similarities and differences of optimization objectives and solutions under different algorithms, so as to understand the general methods of solving multiple traveling salesman problems among different algorithms more intuitively. With the continuous development of multiple traveling salesman problem, scholars are not satisfied with simply solving mathematical problems, and try to regard many practical problems that meet conditions as multiple traveling salesman problems. This paper summarizes the specific construction methods of MTSP model in the context of practical applications such as logistics distribution, wireless sensor network, emergency rescue and UAV collaborative task planning. From the perspective of application results, using MTSP model to solve practical problems can not only reduce enterprise and individual costs, improve revenue, but also promote the development of this field towards a more efficient and intelligent direction. This paper mainly studies the multiple traveling salesman model and its application, which fills the gap in this research field

Evolutionary Diversity Optimisation for Combinatorial Problems

Diversity optimisation explores a variety of solutions for the intended problem and is rapidly growing and getting more popular within the evolutionary computation community as a result. There can be found several studies that introduce and examine evolutionary approaches to compute a diverse set of solutions for optimisation problems in the continuous domain. To the best of our knowledge, the discrete problems are yet to be studied in the context of diversity optimisation. Thus, this thesis focuses on combinatorial optimisation problems with discrete solution spaces. Here, we compute and explore such solution sets for several noticeable combinatorial problems. We aim to introduce and design evolutionary algorithms capable of computing a diverse set of solutions for the given combinatorial optimisation problem. First, we begin with a comprehensive literature review of the recent developments and then dig deep into two prominent diverse paradigms in evolutionary computation: evolutionary diversity optimisation and quality diversity. These concepts have gained a considerable amount of attention in recent years. Quality diversity aims to achieve diversity in behavioural spaces, while evolutionary diversity optimisation sees diversity in the structural properties of solutions. We study the evolutionary algorithms for the travelling salesperson problem, the travelling thief program, the knapsack problem, and finally, the Boolean satisfiability problem. The prospective results demonstrate the capability of the introduced algorithms to achieve diverse and high-quality solutions.Thesis (Ph.D.) -- University of Adelaide, School of Computer and Mathematical Sciences, 202