Evolutionary algorithms (EAs) have received increasing interests both in the academy and industry. One main difficulty in applying EAs to real-world applications is that EAs usually need a large number of fitness evaluations before a satisfying result can be obtained. However, fitness evaluations are not always straightforward in many real-world applications. Either an explicit fitness function does not exist, or the evaluation of the fitness is computationally very expensive. In both cases, it is necessary to estimate the fitness function by constructing an approximate model. In this paper, a comprehensive survey of the research on fitness approximation in evolutionary computation is presented. Main issues like approximation levels, approximate model management schemes, model construction techniques are reviewed. To conclude, open questions and interesting issues in the field are discussed.

The combination of Evolutionary algorithms with local search was named "Memetic Algorithms" (MAs) in [1]. These methods are inspired by models of natural systems that combine the evolutionary adaptation of a population with individual learning within the lifetimes of its members. Additionally, MAs are inspired by Richard Dawkin's concept of a meme, which represents a unit of cultural evolution that can exhibit local refinement [2]. In the case of MAs "memes" refer to the strategies (e.g. local refinement, perturbation or constructive methods, etc) that are employed to improve individuals. In this paper we review some works on the application of MAs to well known combinatorial optimisation problems, and place them in a framework defined by a general syntactic model. This model provides us with a classification scheme based on a computable index D, which facilitates algorithmic comparisons and suggests areas for future research. Also, by having an abstract model for this class of meta-heuristics it is possible to explore their design space and better understand their behaviour from a theoretical standpoint. We illustrate the theoretical and practical relevance of this model and taxonomy for MAs in the context of a discussion of important design issues that must be addressed to produce effective and efficient Memetic Algorithms.

The capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable to small instances, heuristic and metaheuristic methods are widely adopted when solving CARP. In this paper, we propose a memetic algorithm, namely memetic algorithm with extended neighborhood search (MAENS), for CARP. MAENS is distinct from existing approaches in the utilization of a novel local search operator, namely Merge-Split (MS). The MS operator is capable of searching using large step sizes, and thus has the potential to search the solution space more efficiently and is less likely to be trapped in local optima. Experimental results show that MAENS is superior to a number of state-of-the-art algorithms, and the advanced performance of MAENS is mainly due to the MS operator. The application of the MS operator is not limited to MAENS. It can be easily generalized to other approaches.

This paper presents enhancements to a surrogateassisted evolutionary optimization framework proposed earlier in the literature for solving computationally expensive design problems on a limited computational budget [1]. The main idea of our former framework was to couple evolutionary algorithms with a feasible sequential quadratic programming solver in the spirit of Lamarckian learning, including a trustregion approach for interleaving the true fitness function with computationally cheap local surrogate models during gradientbased search. In this paper, we propose a hierarchical surrogateassisted evolutionary optimization framework for accelerating the convergence rate of the original surrogate-assisted evolutionary optimization framework. Instead of using the exact high-fidelity fitness function during evolutionary search, a Kriging global surrogate model is used to screen the population for individuals that will undergo Lamarckian learning. Numerical results are presented for two multi-modal benchmark test functions to show that the proposed approach leads to a further acceleration of the evolutionary search process.

Abstract—For many real-world optimization problems, the robustness of a solution is of great importance in addition to the solution’s quality. By robustness, we mean that small deviations from the original design, e.g., due to manufacturing tolerances, should be tolerated without a severe loss of quality. One way to achieve that goal is to evaluate each solution under a number of different scenarios and use the average solution quality as fitness. However, this approach is often impractical, because the cost for evaluating each individual several times is unacceptable. In this paper, we present a new and efficient approach to estimating a solution’s expected quality and variance. We propose to construct local approximate models of the fitness function and then use these approximate models to estimate expected fitness and variance. Based on a variety of test functions, we demonstrate empirically that our approach significantly outperforms the implicit averaging approach, as well as the explicit averaging approaches using existing estimation techniques reported in the literature. Index Terms—Evolutionary optimization, fitness approximation, robustness, uncertainty. I.

This paper presents a memory-based Reactive Affine Shaker (M-RASH) algorithm for global optimization. The Reactive Affine Shaker is an adaptive search algorithm based only on the function values. M-RASH is an extension of RASH in which good starting points to RASH are suggested online by using Bayesian Locally Weighted Regression (B-LWR). Both techniques use the memory about the previous history of the search to guide the future exploration but in very different ways. RASH compiles the previous experience into a local search area where sample points are drawn, while locally-weighted regression saves the entire previous history to be mined extensively when an additional sample point is generated. Because of the high computational cost related to the B-LWR model, it is applied only to evaluate the potential of an initial point for a local search run. The experimental results, focussed onto the case when the dominant computational cost is the evaluation of the target f function, show that M-RASH is indeed capable of leading to good results for a smaller number of function evaluations.

Abstract. In this paper we present an enhanced evolutionary algorithm (EA) to solve computationally expensive design optimization problems. In this algorithm we integrate a genetic algorithm (GA) with a local search method to expedite convergence of the GA. We first use a GA to generate a population of data by evaluating real functions, then we construct computationally cheap surrogate models based on the available data. Thereafter, we perform gradient-based local searches on the surrogate models in lieu of the real functions. We apply the GA and gradientbased method alternatively until an optimum is reached. To guarantee convergence to the original problem, we use a trust region management to handle surrogate models. We investigate the effects of number of points used to construct the surrogate model, number of surrogate model constructed, and number of local search performed. Our numerical results, based on two single-objective problems and one multi-objective optimization problem, demonstrate the advantages of the hybrid GA over pure GAs. 1

We have developed an algorithm for reduction of search-space, called Domain Optimization Algorithm (DOA), applied to global optimization. This approach can efficiently eliminate search-space regions with low probability of containing a global optimum. DOA basically works using simple models for search-space regions to identify and eliminate non-promising regions. The proposed approach has shown relevant results for tests using hard benchmark functions.

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