This paper proposes a novel evolution strategy for noisy function optimization. We consider minimization of the expectation of a continuous domain function with stochastic parameters. The proposed method is an extended variant of distance-weighted exponential evolution strategy (DX-NES), which is a state-of-the-art algorithm for deterministic function optimization. We name it DX-NES for uncertain environments (DX-NES-UE). DX-NES-UE estimates the objective function by a quadratic surrogate function. In order to make a balance between speed and accuracy, DX-NES-UE uses surrogate function values when the noise is strong; otherwise it uses observed objective function values. We conduct numerical experiments on 20-dimensional benchmark problems to compare the performance of DX-NES-UE and that of uncertainty handling covariance matrix adaptation evolution strategy (UH-CMA-ES). UH-CMA-ES is one of the most promising methods for noisy function optimization. Benchmark problems include a multimodal function, ill-scaled functions and a non-C² function with additive noise and decision variable perturbation (sometime called actuator noise). The experiments show that DX-NES-UE requires about 1/100 times as many observations as UH-CMA-ES does on well-scaled functions. The performance difference is greater on ill-scaled functions.

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In this paper, we propose an estimation of distribution algorithm (EDA) for finding a good individual in getetic network programming (GNP). Our EDA is an extension of Li et al.(2009)'s probabilistic model building genetic network programming (PMBGNP). Each individual in GNP has a directed graph structure composed of a start node, judgment nodes, processing nodes and arcs between nodes. While Li et al.'s PMBGNP builds probabilistic distributions of terminal points of arcs, our PMBGNP also builds probabilistic distributions of function assignments to nodes as well as distributions of terminal points of arcs. Our PMBGNP searchs over the space of possible combinations of function assignments to nodes and terminal points of arcs, and so dispenses with any breakdown of the number of nodes. Two maze problems and the 11-multiplexer problem are used to evaluate the performance of the proposed search method. The experimental results show that our PMBGNP finds the optimum solutions of the tested problems in some moderate probability.

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A lot of researches on MOGA (Multi-Objective Genetic Algorithm), in which Genetic Algorithm is applied to MOPs (Multi-objective Optimization Problems), have been actively reported. MOGA has been also applied to engineering design fields, then it is important not only to obtain nondominated solutions having high performance but also to analyze the acquired nondominated solutions and extract the knowledge of the problem for the designers. The authors have proposed some analysis methods of acquired solutions by evolutionary computation based on “visualization”. However, these approaches in the analyses aim to analyze them and that is the goal. Designers often need better solutions than the acquired ones or better fitness value on a certain objective function keeping the other fitness values. This paper proposes a search method to user's preference direction based on the reference lines which is originally proposed by Deb et al. In the proposed method, a user selects the preference area in the visualized space plotting the acquired solutions, and reference points are generated in the selected area. Reference lines are defined by connecting between the reference points and the original point. Moreover, a user can move the original point based on his/her desired feature of solutions in the proposed method. This paper carried out three experiments. In the first experiment, we compared the proposed method with NSGA-III and showed that NSGA-III could not search well in the preference area when the optimal direction was quite different from the direction of reference lines and the proposed method could. In the second experiment, we examined the effectiveness of the change of the original point. The result showed that the solutions having the desired features could be acquired by moving the original point. In the third experiment, we examined the effectiveness of focusing one specific objective function by moving original point. The result showed that it was possible to adjust the focus degree of the specific objective function. The second and third experiments were also done in MaOPs, and the results showed that the proposed method could search user's preference directions and change the feature of solutions by moving the original point.

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Differential Evolution (DE) is an Evolutionary Algorithm (EA) that was primarily designed for real parameter optimization problems. Despite its relative simplicity, DE has been shown to be competitive with more complex optimization algorithms, and has been applied to many practical problems. The two most common type of crossover in DE are binomial crossover, analogous to uniform crossover in GA's, and exponential crossover, analogous to 1 or 2 point crossover in GA's. Although binomial crossover appears to be more frequently used in state-of-the-art DEs, a number of recent papers have reported successful usage of exponential crossover. In this paper, we demonstrate that exponential crossover exploits an unnatural feature of some widely used synthetic benchmarks such as the Rosenbrock function - dependencies between adjacent variables. However, there is no particular reason that adjacent variables should have such dependencies in real-world, black-box optimization problems, and such dependencies are an artifact of synthetic benchmarks. We show that this unnatural problem structure can be easily eliminated using the randomization procedure and exponential crossover performs quite poorly on benchmarks without this artificial feature for standard DE as well as state-of-the-art adaptive DE. We also show that shuffled exponential crossover, which removes this kind of search bias, significantly outperforms exponential crossover.

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