Abstract
This paper presents a new metaheuristic named Dhouib-Matrix-3 (DM3) inspired by our recently developed constructive stochastic heuristic Dhouib-Matrix-TSP2 (DM-TSP2) and characterized by only one parameter: the number of iterations. The proposed metaheuristic DM3 is an iterative algorithm in which every iteration is based on two relay hybridization techniques. At first, the constructive stochastic heuristic DM-TSP2 starts by generating a different initial basic feasible solution and then each solution is intensified by the novel procedure Far-to-Near which exchanges far cities by closer ones using three perturbation techniques: insertion, exchange, and 2-opt. Experimental results carried out on the classical travelling salesman problem using the well-known TSP-LIB benchmark instances demonstrate that our approach DM3 outclasses the simulated annealing algorithm, the genetic algorithm, and the cellular genetic algorithm. Furthermore, the proposed DM3 is statistically concurrent to the hybrid simulated annealing cellular genetic algorithm. Nevertheless, DM3 is easier to implement and needs only one parameter to identify (the maximum number of iterations).
Highlights
In real-world industry, decision makers are daily confronted with several complicated combinatorial optimization problems such as the scheduling problem, the transportation problem, the knapsack problem, the travelling salesman problem (TSP), and so on
The approximative methods gather heuristics as well as metaheuristics. e heuristics are dedicated to specific optimization problems, whereas the metaheuristics are more flexible in a way that they can solve several complex optimization problems
Tremendous research works are developed in order to prove the efficiency of metaheuristics in the resolution of NP-hard problems. e majority of metaheuristics are stimulated from the collective behavior of creatures in nature. e genetic algorithm (GA) was designed in [1] and was proven as a very successful optimization technique especially with its various variants such as those in [2, 3]. e harmony search (HS) algorithm is based on the search of the best of harmonics, which was firstly introduced in [4]. e artificial bee colony (ABC) is inspired by honey bee mating, which was proposed in [5]. e firefly algorithm (FA) is an optimization algorithm depicted in [6] and invigorated from lights and radiance of fireflies
Summary
In real-world industry, decision makers are daily confronted with several complicated combinatorial optimization problems such as the scheduling problem, the transportation problem, the knapsack problem, the travelling salesman problem (TSP), and so on. DM3 drives the search space through two steps in an iterated structure (see Figure 2) At first, it rapidly generates a good initial basic feasible solution using the stochastic heuristic DM-TSP2; it intensifies this initial solution using the original procedure, namely, the FtN. To solve this problem, the heuristic DM-TSP2 needs only four simple iterations to generate the optimal or near-optimal solution. DM-TSP2 is a very simple and fast stochastic heuristic It needs only 4 iterations (where 4 represents the number of cities) to generate an initial basic feasible solution. In order to perform DM-TSP2, a guided repetitive structure is needed and for that we design and develop the metaheuristic DM3
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