Meta-RaPS: a simple and effective approach for solving the traveling salesman problem

DePuy, Gail W.; Moraga, Reinaldo J.; Whitehouse, Gary E.

doi:10.1016/j.tre.2004.02.001

Cited by 43 publications

(15 citation statements)

References 29 publications

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“…The average percentage deviations to optimal (or the best known solutions) of the PBM_TSP is 1.09% and it is 15.5% lower than in Meta-RaPS (DePuy, Morga, & Whitehouse, 2005). Comparing execution time of both algorithms we are obtaining in average 119.8 s for PBM_TSP and 944.8 s for Meta-RaPS.…”

Section: Tspmentioning

confidence: 80%

“…In the paper DePuy, Morga, and Whitehouse (2005) there are comparative results of algorithm Meta-RaPS and other 23 algorithms well known in literature. The fastest of these algorithms is Meta-RaPS.…”

Section: Tspmentioning

confidence: 99%

“…The fastest of these algorithms is Meta-RaPS. We have used the same benchmark instances as in the paper DePuy et al (2005). Table 1 includes comparisons of the calculations between PBM_TSP and Meta-RaPS algorithms.…”

Section: Tspmentioning

confidence: 99%

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Solving permutational routing problems by population-based metaheuristics

Boejko

Wodecki

2009

Computers & Industrial Engineering

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Section: Tspmentioning

confidence: 80%

Section: Tspmentioning

confidence: 99%

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Solving permutational routing problems by population-based metaheuristics

Boejko

Wodecki

2009

Computers & Industrial Engineering

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“…For example, one might divide metaheuristics into two categories depending on whether they are pure or hybrid. Examples of pure metaheuristics for the TSP include Simulated Annealing (Kirkpatrick et al, 1983;Malek et al, 1989), Tabu Search (Malek, 1988;Malek et al, 1989;Tsubakitani and Evans, 1998a), Guided Local Search (Voudouris and Tsang, 1999), Jump Search (Tsubakitani and Evans, 1998b), Randomized Priority Search (DePuy, Moraga and Whitehouse, 2005), Greedy Heuristic with Regret (Hassin and Keinan, 2008), Genetic Algorithms (Jayalakshmi et al, 2001;Tsai et al, 2003;Albayrak and Allahverdi, 2011;Nagata and Soler, 2012), Evolutionary Algorithms (Liao et al, 2012), Ant Colony Optimization (Dorigo and Gambardella, 1997), Artificial Neural Networks (Leung et al, 2004;Li et al, 2009), Water Drops Algorithm (Alijla et al, 2014), Discrete Firefly Algorithm (Jati et al, 2013), Invasive Weed Optimization (Zhou et al, 2015), Gravitational Search (Dowlatshahi et al, 2014), and Membrane Algorithms (He et al, 2014). Examples of hybrid metaheuristics include Simulated Annealing with Learning (Lo and Hsu, 1998), Genetic Algorithm with Learning (Liu and Zeng, 2009), SelfOrganizing Neural Networks and Immune System (Masutti and de Castro, 2009), Genetic Algorithm and Local Search (Albayrak and Allahverdi, 2011), Genetic Algorithm and Ant Colony Optimization (Dong at al., 2012), Honey Bees Mating and GRASP (Marinakis et al, 2011), and Particle Swarm Optimization and Ant Colony Optimization (Elloumi et al, 2014).…”

Section: Heuristic Approaches and Methodsmentioning

confidence: 99%

A dual local search framework for combinatorial optimization problems with TSP application

Ouenniche

Ramaswamy

Gendreau

2017

Journal of the Operational Research Society

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Abstract:In practice, solving realistically sized combinatorial optimization problems (COPs) to optimality is often too time-consuming to be affordable; therefore, heuristics are typically implemented within most applications software. A specific category of heuristics has attracted considerable attention, namely, local search methods. Most local search methods are primal in nature; that is, they start the search with a feasible solution and explore the feasible space for better feasible solutions. In this research, we propose a dual local search method and customise it to solve the traveling salesman problem (TSP); that is, a search method that starts with an infeasible solution, explores the dual space -each time reducing infeasibility, and lands in the primal space to deliver a feasible solution. The proposed design aims to replicate the designs of optimal solution methodologies in a heuristic way. To be more specific, we solve a combinatorial relaxation of a TSP formulation, design a neighborhood structure to repair such an infeasible starting solution, and improve components of intermediate dual solutions locally. Sample-based evidence along with statistically significant t-tests support the superiority of this dual design compared to its primal design counterpart.

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“…DePuy et al [14] proposed a metaheuristic called Meta-RaPS to solve combinatorial problems and DePuyet al [15] investigated differences between Meta-RaPS and GRASP. Lan et al [16] applied Meta-RaPS for set covering problem and compared with five best algorithms used by Grossman and Wool [2].…”

Section: Algorithm Gmc(sk)mentioning

confidence: 99%

Big Step Greedy Heuristic for Maximum Coverage Problem

Chandu¹

2015

IJCA

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This paper proposes a greedy heuristic called Big step greedy heuristic and investigates its application to compute approximate solution for maximum coverage problem. Greedy algorithms construct the solution in multiple steps, the classical greedy algorithm for maximum coverage problem, in each step selects one set that contains the greatest number of uncovered elements. The Big step greedy heuristic, in each step selects p (1 <= p <= k) sets such that the union of selected p sets contains the greatest number of uncovered elements by evaluating all the possible p-combinations of given sets. When p=k Big step greedy algorithm behaves like an exact algorithm that computes optimal solution by evaluating all possible k-combinations of the given sets. When p=1 it behaves like the classical greedy algorithm. The Big step greedy heuristic can be combined with local search methods to compute better approximate solution.

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Meta-RaPS: a simple and effective approach for solving the traveling salesman problem

Cited by 43 publications

References 29 publications

Solving permutational routing problems by population-based metaheuristics

Solving permutational routing problems by population-based metaheuristics

A dual local search framework for combinatorial optimization problems with TSP application

Big Step Greedy Heuristic for Maximum Coverage Problem

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