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

Genetic algorithms

Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology

A Perturbed Self-organizing Multiobjective Evolutionary Algorithm to solve Multiobjective TSP

Travelling Salesman Problem (TSP) is a very important NP-Hard problem getting focused more on these days. Having improvement on TSP, right now consider the multi-objective TSP (MOTSP), broadened occurrence of travelling salesman problem. Since TSP is NP-hard issue MOTSP is additionally a NP-hard issue. There are a lot of algorithms and methods to solve the MOTSP among which Multiobjective evolutionary algorithm based on decomposition is appropriate to solve it nowadays. This work presents a new algorithm which combines the Data Perturbation, Self-Organizing Map (SOM) and MOEA/D to solve the problem of MOTSP, named Perturbed Self-Organizing multiobjective Evolutionary Algorithm (P-SMEA). In P-SMEA Self-Organizing Map (SOM) is used extract neighborhood relationship information and with MOEA/D subproblems are generated and solved simultaneously to obtain the optimal solution. Data Perturbation is applied to avoid the local optima. So by using the P-SMEA, MOTSP can be handled efficiently. The experimental results show that P-SMEA outperforms MOEA/D and SMEA on a set of test instances

Balanced task allocation by partitioning the multiple traveling salesperson problem

Task assignment and routing are tightly coupled problems for teams of mobile agents. To fairly balance the workload, each agent should be assigned a set of tasks which take a similar amount of time to complete. The completion time depends on the time needed to travel between tasks which depends on the order of tasks. We formulate the task assignment problem as the minimum Hamiltonian partition problem (MHPP) form agents, which is equivalent to the minmax multiple traveling salesperson problem (m-TSP). While the MHPP’s cost function depends on the order of tasks, its solutions are similar to solutions of the average Hamiltonian partition problem (AHPP) whose cost function is order-invariant. We prove that the AHPP is NP-hard and present an effective heuristic, AHP, for solving it. AHP improves a partitions of a graph using a series of transfer and swap operations which are guaranteed to improve the solution’s quality. The solution generated by AHP is used as an initial partition for an algorithm, AHP-mTSP, which solves the combined task assignment and routing problems to near optimality. For n tasks and m agents, each iteration of AHP is O(n2) and AHP-mTSP has an average run-time that scales with n2.11m0.33. Compared to state-of-the-art approaches, our approach found approximately 10% better solutions for large problems in a similar run-time