Memetic algorithms outperform evolutionary algorithms in multimodal optimisation

Memetic algorithms integrate local search into an evolutionary algorithm to combine the advantages of rapid exploitation and global optimisation. We provide a rigorous runtime analysis of memetic algorithms on the Hurdle problem, a landscape class of tunable difficulty with a “big valley structure”, a characteristic feature of many hard combinatorial optimisation problems. A parameter called hurdle width describes the length of fitness valleys that need to be overcome. We show that the expected runtime of plain evolutionary algorithms like the (1+1) EA increases steeply with the hurdle width, yielding superpolynomial times to find the optimum, whereas a simple memetic algorithm, (1+1) MA, only needs polynomial expected time. Surprisingly, while increasing the hurdle width makes the problem harder for evolutionary algorithms, it becomes easier for memetic algorithms. We further give the first rigorous proof that crossover can decrease the expected runtime in memetic algorithms. A (2+1) MA using mutation, crossover and local search outperforms any other combination of these operators. Our results demonstrate the power of memetic algorithms for problems with big valley structures and the benefits of hybridising multiple search operators

Memetic Algorithms Beat Evolutionary Algorithms on the Class of Hurdle Problems

Memetic algorithms are popular hybrid search heuristics that integrate local search into the search process of an evolutionary algorithm in order to combine the advantages of rapid exploitation and global optimisation. However, these algorithms are not well understood and the field is lacking a solid theoretical foundation that explains when and why memetic algorithms are effective. We provide a rigorous runtime analysis of a simple memetic algorithm, the (1+1) MA, on the Hurdle problem class, a landscape class of tuneable difficulty that shows a “big valley structure”, a characteristic feature of many hard problems from combinatorial optimisation. The only parameter of this class is the hurdle width w, which describes the length of fitness valleys that have to be overcome. We show that the (1+1) EA requires Θ(n w) expected function evaluations to find the optimum, whereas the (1+1) MA with best-improvement and first-improvement local search can find the optimum in Θ(n 2 +n 3/w2 ) and Θ(n 3/w2 ) function evaluations, respectively. Surprisingly, while increasing the hurdle width makes the problem harder for evolutionary algorithms, the problem becomes easier for memetic algorithms. We discuss how these findings can explain and illustrate the success of memetic algorithms for problems with big valley structures

Submodular memetic approximation for multiobjective parallel test paper generation

Parallel test paper generation is a biobjective distributed resource optimization problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified assessment criteria. Generating high-quality parallel test papers is challenging due to its NP-hardness in both of the collective objective functions. In this paper, we propose a submodular memetic approximation algorithm for solving this problem. The proposed algorithm is an adaptive memetic algorithm (MA), which exploits the submodular property of the collective objective functions to design greedy-based approximation algorithms for enhancing steps of the multiobjective MA. Synergizing the intensification of submodular local search mechanism with the diversification of the population-based submodular crossover operator, our algorithm can jointly optimize the total quality maximization objective and the fairness quality maximization objective. Our MA can achieve provable near-optimal solutions in a huge search space of large datasets in efficient polynomial runtime. Performance results on various datasets have shown that our algorithm has drastically outperformed the current techniques in terms of paper quality and runtime efficiency

A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Copyright @ Springer-Verlag 2008Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.This work was supported by the National Nature Science Foundation of China (NSFC) under Grant Nos. 70431003 and 70671020, the National Innovation Research Community Science Foundation of China under Grant No. 60521003, and the National Support Plan of China under Grant No. 2006BAH02A09 and the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/01