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This paper investigates the behavior of (¿/¿_I,¿)-¿SA-ES on a class of positive definite quadratic forms. After introducing the fitness environment and the strategy, the self-adaptation mechanism is analyzed with the help of the self-adaptation response function. Afterward, the steady state of the strategy is analyzed. The dynamical equations for the expectation of the mutation strength ¿ and the localization parameter ¿ will be derived. Building on that, the progress rate ¿ is analyzed and tuned by means of the learning parameter ¿. An approximate formula for ¿_opt, yielding locally maximal progress, is presented. Finally, the performance of the ¿SA-rule is compared with the performance of the cumulative step size adaptation rule, and a rough approximation for the expected runtime is presented.

The layout design of complex engineering systems (such as satellite-module layout design) is very difficult to solve in polynomial time. This is not only a complex coupled system design problem but also a special combinatorial problem. The fitness function for this problem is characterized as multimodal because of interference constraints among layout components (objects), etc. This characteristic can easily result in premature convergence when solving this problem using evolutionary algorithms. To deal with the above two problems simultaneously, we propose a dual-system framework based on the cooperative coevolutionary algorithm (CCEA, e.g., cooperative coevolutionary genetic algorithm) like multidisciplinary design optimization. The proposed algorithm has the characteristic of solving the complex coupled system problem, increasing the diversity of population, and decreasing the premature convergence. The basis for the proposed algorithm is as follows. The original coupled system P is decomposed into several subsystems according to its physical structure. The system P is duplicated as systems A and B, respectively. The A system is solved on a global level (all-in-one), whereas the solving of B system is realized through the computation of its subsystems in parallel. The individual migration between A and B is implemented through the individual migration between their corresponding subsystems. To reduce the computational complexity produced additionally by the dual-systems A and B, we employ a variable-grain model of design variables. During the process of optimization, the two systems A and B gradually approximate to the original system P, respectively. The above-proposed algorithm is called the dual-system variable-grain cooperative coevolution algorithm (DVGCCEA) or Oboe-CCEA. The numerical experimental results of a simplified satellite-module layout design case show that the proposed algorithm can obtain better robustness and trade-off between computational prec-
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ision and computational efficiency.

Using surrogate models in evolutionary search provides an efficient means of handling today’s complex applications plagued with increasing high-computational needs. Recent surrogate-assisted evolutionary frameworks have relied on the use of a variety of different modeling approaches to approximate the complex problem landscape. From these recent studies, one main research issue is with the choice of modeling scheme used, which has been found to affect the performance of evolutionary search significantly. Given that theoretical knowledge available for making a decision on an approximation model a priori is very much limited, this paper describes a generalization of surrogate-assisted evolutionary frameworks for optimization of problems with objectives and constraints that are computationally expensive to evaluate. The generalized evolutionary framework unifies diverse surrogate models synergistically in the evolutionary search. In particular, it focuses on attaining reliable search performance in the surrogate-assisted evolutionary framework by working on two major issues: 1) to mitigate the ‘curse of uncertainty’ robustly, and 2) to benefit from the ‘bless of uncertainty.’ The backbone of the generalized framework is a surrogate-assisted memetic algorithm that conducts simultaneous local searches using ensemble and smoothing surrogate models, with the aims of generating reliable fitness prediction and search improvements simultaneously. Empirical study on commonly used optimization benchmark problems indicates that the generalized framework is capable of attaining reliable, high quality, and efficient performance under a limited computational budget.

The discovery of low-energy stable and meta-stable molecular structures remains an important and unsolved problem in search and optimization. In this paper, we contribute two stochastic algorithms, the archiving molecular memetic algorithm (AMMA) and the archiving basin hopping algorithm (ABHA) for sampling low-energy isomers on the landscapes of pure water clusters (H₂O)n. We applied our methods to two sophisticated empirical water cluster models, TTM2.1-F and OSS2, and generated archives of low-energy water isomers (H₂O)n n=3-15. Our algorithms not only reproduced previously-found best minima, but also discovered new global minima candidates for sizes 9-15 on OSS2. Further numerical results show that AMMA and ABHA outperformed a baseline stochastic multistart local search algorithm in terms of convergence and isomer archival. Noting a performance differential between TTM2.1-F and OSS2, we analyzed both model landscapes to reveal that the global and local correlation properties of the empirical models differ significantly. In particular, the OSS2 landscape was less correlated and hence, more difficult to explore and optimize. Guided by our landscape analyses, we proposed and demonstrated the effectiveness of a hybrid local search algorithm, which significantly improved the sampling performance of AMMA on the larger OSS2 landscapes. Although applied to pure water clusters in this paper, AMMA and ABHA can be easily modified for subsequent studies in computational chemistry and biology. Moreover, the landscape analyses conducted in this paper can be replicated for other molecular systems to uncover landscape properties and provide insights to both physical chemists and evolutionary algorithmists.