This paper presents a parallel memetic algorithm for solving the vehicle routing problem with time windows (VRPTW). The VRPTW is a well-known NP-hard discrete optimization problem with two objectives. The main objective is to minimize the number of vehicles serving customers scattered on the map, and the second one is to minimize the total distance traveled by the vehicles. Here, the fleet size is minimized in the first phase of the proposed method using the parallel heuristic algorithm (PHA), and the traveled distance is minimized in the second phase by the parallel memetic algorithm (PMA). In both parallel algorithms, the parallel components co-operate periodically in order to exchange the best solutions found so far. An extensive experimental study performed on the Gehring and Homberger's benchmark proves the high convergence capabilities and robustness of both PHA and PMA. Also, we present the speedup analysis of the PMA.
Evolutionary algorithms have attracted the scientific attention to solve the VRPTW due to their high search capabilities. Genetic algorithms were applied by Cheng and Wang @cite_9 , @cite_0 and @cite_8 . The evolution strategies were proposed by Gehring and Homberger @cite_30 , @cite_31 and @cite_17 . The sequential and parallel memetic algorithms (MAs), combining the evolutionary algorithms for more distant search with the local optimization and refinements algorithms for local exploitation, were described by Berger and Barkaoui @cite_3 , @cite_24 and Nagata and Br " a ysy @cite_2 . The MA based on the edge-assembly crossover operator (EAX) has been proposed by Nagata and Br " a ysy @cite_2 .
@cite_30 @cite_8 @cite_9 @cite_3 @cite_0 @cite_24 @cite_2 @cite_31 @cite_17
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This article deals with the vehicle routing problem with time windows (VRPTW). This problem consists in determining a least-cost set of trips to serve customers during specific time windows. The proposed solution method is a memetic algorithm (MA), a genetic algorithm hybridised with a local search. Contrary to most papers on the VRPTW, which minimize first the number of vehicles, our method is also able to minimize the total distance travelled. The results on 56 classical instances are compared to those of the best metaheuristics. The efficiency of the MA is similar for the classical criterion, but it becomes the best algorithm available for the total distance, being much faster and improving 20 best-known solutions. In this paper, we present an effective memetic algorithm for the vehicle routing problem with time windows (VRPTW). The paper builds upon an existing edge assembly crossover (EAX) developed for the capacitated VRP. The adjustments of the EAX operator and the introduction of a novel penalty function to eliminate violations of the time window constraint as well as the capacity constraint from offspring solutions generated by the EAX operator have proven essential to the heuristic's performance. Experimental results on Solomon's and Gehring and Homberger benchmarks demonstrate that our algorithm outperforms previous approaches and is able to improve 184 best-known solutions out of 356 instances. Many different algorithms have been developed in the last few decades for solving complex real-world search and optimization problems. The main focus in this research has been on the development of a single universal genetic operator for population evolution that is always efficient for a diverse set of optimization problems. In this paper, we argue that significant advances to the field of evolutionary computation can be made if we embrace a concept of self-adaptive multimethod optimization in which multiple different search algorithms are run concurrently, and learn from each other through information exchange using a common population of points. We present an evolutionary algorithm, entitled A Multialgorithm Genetically Adaptive Method for Single Objective Optimization (AMALGAM-SO), that implements this concept of self adaptive multimethod search. This method simultaneously merges the strengths of the covariance matrix adaptation (CMA) evolution strategy, genetic algorithm (GA), and particle swarm optimizer (PSO) for population evolution and implements a self-adaptive learning strategy to automatically tune the number of offspring these three individual algorithms are allowed to contribute during each generation. Benchmark results in 10, 30, and 50 dimensions using synthetic functions from the special session on real-parameter optimization of CEC 2005 show that AMALGAM-SO obtains similar efficiencies as existing algorithms on relatively simple unimodal problems, but is superior for more complex higher dimensional multimodal optimization problems. The new search method scales well with increasing number of dimensions, converges in the close proximity of the global minimum for functions with noise induced multimodality, and is designed to take full advantage of the power of distributed computer networks. A key search mechanism in Evolutionary Algorithms is the mixing or juxtaposing of partial solutions present in the parent solutions. In this paper we look at the efficiency of mixing in genetic algorithms (GAs) and estimation-of-distribution algorithms (EDAs). We compute the mixing probabilities of two partial solutions and discuss the effect of the covariance build-up in GAs and EDas. Moreover, we propose two new Evolutionary Algorithms that maximize the juxtaposing of the partial solutions present in the parents: the Recombinative Optimal Mixing Evolutionary Algorithm (ROMEA) and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA).