Genetic algorithm for the one-commodity pickup-and-delivery traveling salesman problem

Performing a local search around solutions found by an evolutionary algorithm is a common practice. Local search is well known to significantly improve the solutions, in particular in the case of combinatorial problems. In this paper a new local search procedure is proposed that uses a locally established utopia point. In the tests in which several instances of the Travelling Salesman Problem (TSP) were solved using an evolutionary algorithm the proposed local search procedure outperformed a local search procedure based on Pareto dominance. Because the local search is focused on improving individual solutions and the multiobjective evolutionary algorithm can improve diversity, various strategies of sharing computational resources between the evolutionary algorithm and the local search are used in this paper. The results attained by the tested methods are compared with respect to computation time, which allows a fair comparison between strategies that distribute computational resources between the evolutionary optimization and the local search in various proportions.

Genetic local search for multi-objective combinatorial optimization

Optimization problem like Travelling Salesman Problem (TSP) can be solved by applying Genetic Algorithm (GA) to obtain perfect approximation in time. In addition, TSP is considered as a NP-hard problem as well as an optimal minimization problem. Selection, crossover and mutation are the three main operators of GA. The algorithm is usually employed to find the optimal minimum total distance to visit all the nodes in a TSP. Therefore, the research presents a new crossover operator for TSP, allowing the further minimization of the total distance. The proposed crossover operator consists of two crossover point selection and new offspring creation by performing cost comparison. The computational results as well as the comparison with available well-developed crossover operators are also presented. It has been found that the new crossover operator produces better results than that of other cross-over operators.

New Formulations for the Orienteering Problem

Genetic algorithms (GAs) are search algorithms based on population genetics and natural selection concepts. Maintaining population variety in GAs is critical for ensuring global exploration and mitigating the risks of premature convergence. Rapid convergence to local optima is one such challenge in the application of genetic algorithms. To address this issue, we provide Cave-Surface GA (CSGA), an alternative method based on the Dual Population Genetic Algorithm and inspired by the genetic variety observed in Mexican cavefish. Through inter-population crossbreeding, CSGA increases diversity via a secondary population (Cave population) and facilitates the exchange of information between populations, effectively counteracting premature convergence. Several experiments are carried out utilizing benchmark instances of the Traveling Salesman Problem (TSP) obtained from TSPLIB, a well-known TSP problem library. Our experimental results over many TSP instances show that CSGA outperforms both classic GAs and other GAs that use diversity preservation techniques, such as Multipopulation GA (MPGA). CSGA has the potential to give promising solutions to challenging optimization issues like TSP.

The generalization challenges faced by neural methods in solving the Travelling Salesman Problem (TSP) have attracted substantial attention. Current neural approaches predominantly rely on Deep Neural Networks with global receptive fields to capture global features, often overlooking the critical role of local topological information. To address this limitation, we propose a Global & Local Encoder (G&L-Encoder) that efficiently integrates local and global information within the feature space. The G-Encoder, with global receptive field, takes charge of capturing global features and facilitating the fusion of global and local information, while the L-Encoder, with its local neighborhood receptive field, extracts finer-grained features specific to each node's neighborhood, serving as an essential complement to the global one. Furthermore, we propose a simple yet efficient supervised learning framework, leveraging the recursive optimality inherent in optimal solutions to dig into their implicit knowledge. Extensive experiments on the TSP demonstrate that our method significantly improves generalization performance and achieves state-of-the-art results on medium-scale TSP tasks. Our source code is available at https://github.com/bxx-seu/GL-POMO.

In this paper, the authors have explained a time limited travelling salesman problem (TSP) where a time limit is associated with each city. The traveller must reach each city on or before the predetermined time limit (that is fixed for each city) in his/her tour. Travel cost is also a parameter for the proposed model. This time limit indicates the maximum time unit by which the traveller must reach a particular city. Here, travel cost is the objective of the problem. Moreover, total travel time is also fixed for a complete tour. This research recently introduced this time limit for each of the cities. The proposed TSP is solved by using a genetic algorithm-based method. The cyclic crossover and special mutation operations have been adapted to GA for solving the proposed TSP. To show the effectiveness of proposed algorithm, the authors have considered some benchmark instances. Then the authors redefine a few benchmark instances for the proposed TSP. Computational results with different data sets are presented.

Meta-heuristics Genetic Algorithms (GA) and Ant Colony Optimisation (ACO) have both shown success when applied to permutation problems such as the Traveling Salesman Problem (TSP). Therefore, combining the approaches could prove beneficial. This paper presents an ACO inspired mutation operator for use in a GA based on Partial-ACO. Applied to a range of TSP instances the ACO mutation operator demonstrates considerable improvements over standard GA mutation operators finding solutions within a few percent of optimal for TSP instances of nearly 4000 cities. In fact, experiments demonstrate performance close to that of local search with standard mutation operators. Moreover, when integrating local search the ACO inspired mutation operator continues to provide improved results over standard mutation and local search.KeywordsAnt colony optimisationGenetic algorithmMutation

The probabilistic travelling salesman problem (PTSP) is an extension of the well-known travelling salesman problem (TSP), which has been extensively studied in the field of combinatorial optimization. The goal of the TSP is to find the minimum length of a tour to all customers, given the distances between all pairs of customers whereas the objective of the PTSP is to minimize the expected length of the a priori tour where each customer requires a visit only with a given probability (Bertsimas, 1988; Bertsimas et al., 1990; Jaillet, 1985). The main difference between the PTSP and the TSP is that in the PTSP the probability of each node being visited is between 0.0 and 1.0 while in TSP the probability of each node being visited is 1.0. Due to the fact that the element of uncertainty not only exists, but also significantly affects the system performance in many real-world transportation and logistics applications, the results from the PTSP can provide insights into research in other probabilistic combinatorial optimization problems. Moreover, the PTSP can also be used to model many real-world applications in logistical and transportation planning, such as daily pickup-delivery services with stochastic demand, job sequencing involving changeover cost, design of retrieval sequences in a warehouse or in a cargo terminal operations, meals on wheels in senior citizen services, trip-chaining activities, vehicle routing problem with stochastic demand, and home delivery service under e-commerce (Bartholdi et al., 1983; Bertsimas et al., 1995; Campbell, 2006; Jaillet, 1988; Tang & Miller-Hooks, 2004). Early PTSP computational studies, dating from 1985, adopted heuristic approaches that were modified from the TSP (e.g., nearest neighbor, savings approach, spacefilling curve, radial sorting, 1-shift, and 2-opt exchanges) (Bartholdi & Platzman, 1988; Bertsimas, 1988; Bertsimas & Howell, 1993; Jaillet, 1985, 1987; Rossi & Gavioli, 1987). With its less than satisfactory performance in yielding solution quality, researchers in the recent years switch to metaheuristic methods, such as ant colony optimization (Bianchi, 2006; Branke & Guntsch, 2004), evolutionary algorithm (Liu et al., 2007), simulated annealing (Bowler et al., 2003), threshold accepting (Tang & Miller-Hooks, 2004) and scatter search (Liu, 2006, 2007, 2008). Because the genetic algorithm (GA), a conceptual framework of the population-based metaheuristic method, has been shown to yield promising outcomes for solving various complicated optimization problems in the past three decades (Back et al., 1997; Davis, 1991; O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Traveling salesman problem (TSP) is a problem of determining the shortest path for a salesman to take to visit all cities. Although a small number of cities is easy to solve, as the number of cities increases, it’s not possible to solve in polynomial time as it was a combinatorial nondeterministic polynomial (NP-hard) problem. Hence, this project is implementing a genetic algorithm (GA) to solve TSP using Python programming. The focus of this paper is to analyze the GA using order crossover (OX) and random crossover (RX) and propose a combination mechanism, direct combination (OX-RX) and Dynamic Linear combination (OXRX-Linear) to optimize TSP. We test GA for OX and RX in a random set of cities, up to 75 total cities. Then compare the result of the proposed combination OX-RX and OX-RXLinear. The result shows that both proposed combined mechanisms OX-RX and OX-RX-Linear improve the performance of GA in solving TSP.

This research report introduces two new hybrid genetic algorithms and compares them to solve the traveling salesman problem (TSP). The new algorithms are a combination of a genetic algorithm (GA) with a nearest neighbor algorithm (NNA). The NNA is used to influence the population of the GA and the selection of the parents in the GA. The results of the conducted experiments, performed in MATLAB environment, have shown that the new algorithms can be successfully used to solve the TSP. Depending on the size of the TSP, the new algorithms achieve better results than the initial GA, which is also used. However, in terms of selecting the best algorithm, no conclusive results were obtained and the best choice depends on the particular TSP.

The travelling salesman problem (TSP) is a benchmark problem in which a salesman has to visit all nodes (cities) in a network exactly once except the starting node, come back to the starting node and find the shortest tour. Genetic algorithm (GA) is one of the best algorithms to deal with the travelling salesman problem (TSP). In GA, crossover operator plays a vital role and the sequential constructive crossover (SCX) is one of the best crossover operators for solving the TSP. Several improvements have been proposed for other crossover operators. In this paper we propose four improved genetic algorithms using three local search methods – 2-opt search, a hybrid mutation, and a combined mutation operator, and incorporate them into SCX. The experimental results on some TSPLIB instances show that our improved GAs can significantly improve simple GA using SCX in terms of solution quality.

The traveling salesman problem (TSP), a typical non-deterministic polynomial (NP) hard problem, has been used in many engineering applications. Genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. However, it has some issues for solving TSP, including quickly falling into the local optimum and an insufficient optimization precision. To address TSP effectively, this paper proposes a hybrid Cellular Genetic Algorithm with Simulated Annealing (SA) Algorithm (SCGA). Firstly, SCGA is an improved Genetic Algorithm (GA) based on the Cellular Automata (CA). The selection operation in SCGA is performed according to the state of the cell. Secondly, SCGA, combined with SA, introduces an elitist strategy to improve the speed of the convergence. Finally, the proposed algorithm is tested against 13 standard benchmark instances from the TSPLIB to confirm the performance of the three cellular automata rules. The experimental results show that, in most instances, the results obtained by SCGA using rule 2 are better and more stable than the results of using rule 1 and rule 3. At the same time, we compared the experimental results with GA, SA, and Cellular Genetic Algorithm (CGA) to verify the performance of SCGA. The comparison results show that the distance obtained by the proposed algorithm is shortened by a mean of 7% compared with the other three algorithms, which is closer to the theoretical optimal value and has good robustness.

A new heuristic algorithm is proposed by this paper, on multi-objective optimization using metaheuristics and TSP (travelling salesman problems). Basic thinking behind this algorithm is minimizing the TSP path or tour by dividing the entire tour into blocks that are overlapped to each other and then improve each individual block separately. Although it is unproven that a good solution have small improvement chances if a node moved far way to a position compared to its original solution. By intensively searching each block, further improvement is possible in TSP path or tour that never be supported in various search methods and genetic algorithm. Proposed algorithm and computational experiment performance was tested, and these tests are carried out with support of already present instances of problem. According to the results represented by paper, the computation verifies that proposed algorithm can solve TSPs efficiently. Proposed algorithm is then used for selecting optimal test cases, thousands of those test cases which are selected after confirming that they identify bugs and they itself selected from a repository of test cases; these thousand test cases are those test cases which are selected from several thousand test cases because they detect bugs. Few test cases from repository act as milestones (nodes) and having certain weight associated with each, proposed algorithm based on TSP implemented over selected result and select the optimal result or path or solution. These selected optimal test cases or selected path are further used to perform the regression testing, by applying those test cases selected by proposed algorithm in order to remove most of the faults or bugs effectively, i.e. take less time and identify almost all the bugs with few test cases. Hence this proposed algorithm assures most effective solution for regression testing test case selection.

This study discusses effect of tournament selection on the way individuals compete on the performance of Genetic Algorithms so which one tournament selection is most suitable for the Traveling Salesman Problem (TSP). One algorithm in solving TSP is Genetic Algorithm, which has 3 (three) main operators, namely selection, crossover, and mutation. Selection is one of the main operators in the Genetic Algorithm, where select the best individuals who can survive (the shortest travel route). Tournament selection compares a number of individuals through a match to choose the best individual based on each fitness value, so that the winning individual (the individual going to the next generation) will be chosen. There is two way to compete in an individual in tournament selection is by tournament selection with replacement (TSWR) and without replacement (TSWOR). The final results of the study conducted TSWR gets the best fitness, even though the generation that gets the best fitness is reaching the maximum generation (takes longer to get the best fitness).