Generalized partition crossover for the traveling salesman problem

2011 Spring.Includes bibliographical references.The Traveling Salesman Problem (TSP) is a well-studied combinatorial optimization problem with a wide spectrum of applications and theoretical value. We have designed a new recombination operator known as Generalized Partition Crossover (GPX) for the TSP. GPX is unique among other recombination operators for the TSP in that recombining two local optima produces new local optima with a high probability. Thus the operator can 'tunnel' between local optima without the need for intermediary solutions. The operator is respectful, meaning that any edges common between the two parent solutions are present in the offspring, and transmits alleles, meaning that offspring are comprised only of edges found in the parent solutions. We design a hybrid genetic algorithm, which uses local search in addition to recombination and selection, specifically for GPX. We show that this algorithm outperforms Chained Lin-Kernighan, a state-of-the-art approximation algorithm for the TSP. We next analyze these algorithms to determine why the algorithms are not capable of consistently finding a globally optimal solution. Our results reveal a search space structure which we call 'funnels' because they are analogous to the funnels found in continuous optimization. Funnels are clusters of tours in the search space that are separated from one another by a non-trivial distance. We find that funnels can trap Chained Lin-Kernighan, preventing the search from finding an optimal solution. Our data indicate that, under certain conditions, GPX can tunnel between funnels, explaining the higher frequency of optimal solutions produced by our hybrid genetic algorithm using GPX

MODIFICATION OF CROSSOVER OPERATOR ON GA APPLICATION FOR TSP

Genetic Algorithm (GA) has been widely used in many fields of optimization; one of them is Traveling Salesman Problem (TSP). GA in the TSP is primarily used in cases involving a lot of vertices, which is not possible to enumerate the shortest route. One of stages in GA is crossover operation to generate offspring’s chromosome based on parent’s. Example of some crossover operators in GA for TSP are Partially Mapped Crossover (PMX), Order Crossover (OX), Cycle Crossover (CX), and some others. However on constructing the route, they are not considering length of the route to maximize its fitness. The use of random numbers on constructing the route likely produces offspring (a new route) that is not better than its parent. Sequence of nodes in the route affects the length of the route. To minimize uncertainty, then the crossover operation should consider a method to arrange the chromosomes. This article studied incorporating two methods into crossover stage, in order to ensure the offspring has good fitness. Methods to be combined with algorithms are commonly used in the route searching; those are Nearest Neighbor algorithm, and Sequential Insertion. Operators used are CSI (Crossover combined with Sequential Insertion) and CNN (Crossover combined with Nearest Neighbor), named after the method used. Those operators are compared with PMX operator on test using benchmark data from TSPLIB on some independent executions. The tests showed that CSI are better than two other and length of its route was relatively equal to optimal length recorded. Keywords: Genetic Algorithm, Traveling Salesman Problem, Crossover operato

Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination problem is solved within crossover operator. (ii) A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. (iii) Greedy constructive heuristic of W.Zhang and 3-opt local search heuristic are used to generate the initial population. A computational experiment on TSPLIB instances shows that the proposed algorithm yields competitive results to other well-known memetic algorithms for asymmetric travelling salesman problem.Comment: Proc. of The 11th International Conference on Large-Scale Scientific Computations (LSSC-17), June 5 - 9, 2017, Sozopol, Bulgari

A new genetic algorithm for traveling salesman problem and its application.

by Lee, Ka-wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 61-67).Chapter 1 --- Introduction --- p.6Chapter 1.1 --- Traveling Salesman Problem --- p.6Chapter 1.2 --- Genetic Algorithms --- p.8Chapter 1.3 --- Solving TSP using Genetic Algorithms --- p.10Chapter 1.4 --- Outline of Work --- p.12Chapter Part I --- Algorithm Development --- p.14Chapter 2 --- A Local DP Crossover Operator 一 LDPX --- p.15Chapter 2.1 --- Review of DP for Solving TSP --- p.15Chapter 2.2 --- On the Original LDPX --- p.18Chapter 2.2.1 --- Gene Representation --- p.18Chapter 2.2.2 --- The Original Crossover Procedure --- p.19Chapter 2.3 --- Analysis --- p.21Chapter 2.3.1 --- Ring TSP --- p.21Chapter 2.3.2 --- Computational Results of Solving Ring TSP and Other TSP using LDPX --- p.22Chapter 2.4 --- Augmentation of the Gene Set Representation --- p.24Chapter 2.5 --- Enhancement of Crossover Procedure --- p.25Chapter 2.6 --- Computational Comparison of the new proposed LDPX with the orig- inal LDPX --- p.26Chapter 2.7 --- SPIR ´ؤ An Operator for Single Parent Improved Reproduction --- p.26Chapter 3 --- A New TSP Solver --- p.29Chapter 4 --- Performance Analysis of the TSP Solver --- p.33Chapter 4.1 --- Computational results --- p.34Chapter 4.2 --- "Comparison between SPIR/LDPX, PMX and ER" --- p.35Chapter 4.3 --- Convergence Test of SPIR/LDPX --- p.37Chapter Part II --- Application --- p.43Chapter 5 --- Flowshop Scheduling Problem --- p.44Chapter 5.1 --- Brief Review of the Flowshop Scheduling Problem --- p.44Chapter 5.2 --- Flowshop Scheduling with travel times between machines --- p.45Chapter 6 --- A New Approach to Solve FSTTBM --- p.47Chapter 7 --- Computational Results of the New Algorithm for CPFSTTBM --- p.53Chapter 7.1 --- Comparison with Global Optimum --- p.54Chapter 7.2 --- The Algorithm of SPIRIT --- p.55Chapter 7.3 --- Comparison with SPIRIT --- p.57Chapter 8 --- Conclusion --- p.59Bibliography --- p.61Chapter A --- Random CPFSTTBM problem Generation Algorithm --- p.6

A hybrid genetic algorithm and inver over approach for the travelling salesman problem

This article posted here with permission of the IEEE - Copyright @ 2010 IEEEThis paper proposes a two-phase hybrid approach for the travelling salesman problem (TSP). The first phase is based on a sequence based genetic algorithm (SBGA) with an embedded local search scheme. Within the SBGA, a memory is introduced to store good sequences (sub-tours) extracted from previous good solutions and the stored sequences are used to guide the generation of offspring via local search during the evolution of the population. Additionally, we also apply some techniques to adapt the key parameters based on whether the best individual of the population improves or not and maintain the diversity. After SBGA finishes, the hybrid approach enters the second phase, where the inver over (IO) operator, which is a state-of-the-art algorithm for the TSP, is used to further improve the solution quality of the population. Experiments are carried out to investigate the performance of the proposed hybrid approach in comparison with several relevant algorithms on a set of benchmark TSP instances. The experimental results show that the proposed hybrid approach is efficient in finding good quality solutions for the test TSPs.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/E060722/1