Parameterized Runtime Analyses of Evolutionary Algorithms for the Planar Euclidean Traveling Salesperson Problem

Sutton, Andrew M.; Neumann, Franz‐Josef; Nallaperuma, Samadhi

doi:10.1162/evco_a_00119

Cited by 48 publications

(56 citation statements)

References 38 publications

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“…Even two good solutions might be good for different reasons [25,26]. One solution might have an efficient solution for one graph section while another good solution could have efficiency in another section [27]. The merging and crossing over of the different solutions is the elementary idea to improvement in GAs solution [28][29][30].…”

Section: Experimental Set-upmentioning

confidence: 99%

Construct Linear Polynomial Complementary Transformation for NP-Completeness Using Parallel Genetic Algorithm

Eltaeib

Dichter

2016

Preprint

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This paper examines the correlation between numbers of computer cores in parallel genetic algorithms. The objective to determine the linear polynomial complementary equation in order represent the relation between number of parallel processing and optimum solutions. Model this relation as optimization function (f(x)) which able to produce many simulation results. F(x) performance is outperform genetic algorithms. Compression results between genetic algorithm and optimization function is done. Also the optimization function give model to speed up genetic algorithm. Optimization function is a complementary transformation which maps a TSP given to linear without changing the roots of the polynomials.

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Section: Experimental Set-upmentioning

confidence: 99%

Construct Linear Polynomial Complementary Transformation for NP-Completeness Using Parallel Genetic Algorithm

Eltaeib

Dichter

2016

Preprint

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“…Theorem 1: Let V be a set of points in the plane and π * be a permutation on V that minimizes the cost function defined in Equation (1). Without loss of generality assume π * (1) = p 1 (since tours are equivalent up to cyclic permutation symmetries).…”

Section: Preliminariesmentioning

confidence: 99%

“…This approach allows one to take an additional parameter measuring the hardness of an instance into account. Results have been obtained for vertex cover [3], minimum leaf spanning trees [4], makespan scheduling [5], and the Euclidean Traveling Salesperson problem [1]. The parameterized complexity analysis of bio-inspired computing seems to be very promising for bridging theory and practice in the field of bio-inspired computing.…”

Section: Introductionmentioning

confidence: 99%

Fixed-parameter evolutionary algorithms for the Euclidean Traveling Salesperson problem

Nallaperuma

Sutton

Neumann

2013

2013 IEEE Congress on Evolutionary Computation

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Recently, Sutton and Neumann [1] have studied evolutionary algorithms for the Euclidean traveling salesman problem by parameterized runtime analyses taking into account the number of inner points k and the number of cities n. They have shown that simple evolutionary algorithms are XPalgorithms for the problem, i. e., they obtain an optimal solution in expected time O(n g(k) ) where g(k) is a function only depending on k. We extend these investigations and design two evolutionary algorithms for the Euclidean Traveling Salesperson problem that run in expected time g(k) · poly(n) where k is a parameter denoting the number inner points for the given TSP instance, i. e., they are fixed-parameter tractable evolutionary algorithms for the Euclidean TSP parameterized by the number of inner points. While our first approach is mainly of theoretical interest, our second approach leverages problem structure by directly searching for good orderings of the inner points and provides a novel and highly effective way of tackling this important problem. Our experimental results show that searching for a permutation on the inner points is a significantly powerful practical strategy.

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“…During the past few years theoretical investigations about EAs focused on the runtime or(and) the probability of EAs for finding globally optimal solutions of fundamental optimization problems or their variants. These problems include plateaus of constant fitness [15], linear function problems [16]- [18], minimum cut problems [19], satisfiability problems [20], minimum spanning tree problems [21], Eulerian cycle problems [22], Euclidean traveling salesperson problems [23], etc.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Evolutionary Algorithms for the Minimum Label Spanning Tree Problem

Lai

Zhou

et al. 2014

IEEE Trans. Evol. Computat.

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Some experimental investigations have shown that evolutionary algorithms (EAs) are efficient for the minimum label spanning tree (MLST) problem. However, we know little about that in theory. As one step towards this issue, we theoretically analyze the performances of the (1+1) EA, a simple version of EAs, and a multi-objective evolutionary algorithm called GSEMO on the MLST problem. We reveal that for the MLST b problem the (1+1) EA and GSEMO achieve a b+1 2 -approximation ratio in expected polynomial times of n the number of nodes and k the number of labels. We also show that GSEMO achieves a (2ln(n))-approximation ratio for the MLST problem in expected polynomial time of n and k. At the same time, we show that the (1+1) EA and GSEMO outperform local search algorithms on three instances of the MLST problem. We also construct an instance on which GSEMO outperforms the (1+1) EA. Index TermsEvolutionary algorithm; time complexity; approximation ratio; minimum label spanning tree; multi-objective I. INTRODUCTION The minimum label spanning tree (MLST) problem is an issue arising from practice, which seeks a spanning tree with the minimum number of labels in a connected undirected graph with labeled edges. For example, we want to find a spanning tree that uses the minimum number of types of communication channels in a communication networks connected with different types of channels. The MLST problem, proposed by Chang and Leu, is proved to be NP-hard [1].For this problem, Chang and Leu have proposed two heuristic algorithms. One is the edge replacement algorithm, ERA for short, the other is the maximum vertex covering algorithm, MVCA for short. Their experimental results showed that ERA is not stable, and MVCA is more efficient.The genetic algorithm, belonging to the larger class of EAs, is a general purpose optimization algorithm [2]-[4] with a strong globally searching capacity [5]. So, Xiong, Golden, and Wasil proposed a one-parameter genetic algorithm for the MLST problem. The experimental results on extensive instances generated randomly showed that the genetic algorithm outperforms MVCA [6]. Nummela and Julstrom also proposed an efficient genetic algorithm for solving the MLST problem [7].Besides, many methods recently have been proposed for solving this NP-hard problem. Consoli et al. proposed a hybrid local search combining variable neighborhood search and simulated annealing [8]. Chwatal and Raidl presented exact methods including branch-and-cut and branch-and-cut-and-price [9]. Cerulli et al. utilized several metaheuristic methods for this problem, such as simulated annealing, reactive tabu search, the pilot method, and variable neighborhood search [10]. Consoli et al. still proposed a greedy randomized adaptive search procedure and a variable neighborhood search for solving the MLST problem [11].Since both ERA and MVCA are two original heuristic algorithms for the MLST problem, the worst performance analysis of these two algorithms, especially MVCA, is a hot research topic in recent years. Krumke ...

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Parameterized Runtime Analyses of Evolutionary Algorithms for the Planar Euclidean Traveling Salesperson Problem

Cited by 48 publications

References 38 publications

Construct Linear Polynomial Complementary Transformation for NP-Completeness Using Parallel Genetic Algorithm

Construct Linear Polynomial Complementary Transformation for NP-Completeness Using Parallel Genetic Algorithm

Fixed-parameter evolutionary algorithms for the Euclidean Traveling Salesperson problem

Performance Analysis of Evolutionary Algorithms for the Minimum Label Spanning Tree Problem

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