In this paper we focus on the linearly constrained continuous optimization. A one of the state-of-the-art stochastic algorithms for ill-conditioned and nonseparable unconstrained problems, namely the covariance matrix adaptation evolution strategy (CMA-ES) is applied to solve linearly constrained continuous optimization problems. We extend the box constraint handling technique that turns a box constrained optimization problem into an unconstrained optimization problem by introducing an artificial fitness landscape, where a penalty function is added to the function value at the nearest feasible solution. The penalty function is adapted during search so as to create an artificial landscape outside the feasible domain that makes the function as easily solvable by the CMA-ES as possible. Treating a box constraint as a special case of linear constraints, we generalize the box constraint handling to apply the same technique to an arbitrary linear constrained problem. Moreover, the adaptation of the penalty coefficient is accelerated. The resulting linear constraint handling technique exhibits an invariant performance on problems with linear constraints under a linear transformation of the coordinate system, showing that a linearly constrained problem can be essentially as efficiently solvable by the CMA-ES as a box constrained problem.
In recent years, accidents and product recalls caused by product failures have become major problems in many industries worldwide. To predict how changes of a product recall system affects safety in the society and to get valuable suggestions to improve product recall systems, we simulated the recall process in society using social simulation model. This research is important because the current product recall systems are not designed by mathematical and predictive approaches such as a computer simulation, but designed by empirical approaches. As a simulation model, we propose Layered Co-evolution Model with Logic Value Typed Genetic Programming (GP). We evaluated the proposed method by using the multi-agent simulation in an artificial society where producer agents and consumer agents both compete and cooperate with each other. This experiment discovered that the producer agents and the consumer agents are able to co-evolve toward a convergence point in Layered Co-evolution Model through the interactions between both types of agents. From the experiment, it is also understood that Logic Value Typed GP, which uses logic values and logic operators, has the advantages over the existing GP method that uses real number values. The Logic Value Typed GP is more stable in the evolutionary process and more efficient in terms of agents' learning process. In addition, we predicted that making the accident-compensation-level stricter decreases the frequency of product accidents in the whole artificial society. This is the result of the producer agents increasing the frequency of product recalls or raising production costs under such a stricter level. This prediction is useful for realizing a safer society.
In Evolutionary Computation (EC), it is difficult to maintain efficient building blocks and to combine them efficiently. In particular, the control of building blocks in the population of Genetic Programming (GP) is relatively difficult because of tree-shaped individuals and also because of bloat, which is the uncontrolled growth of ineffective code segments in GP. It has been reported that the parameter tuning for solving the above mentioned problems requires a significant amount of efforts. Aimed at utilizing building blocks efficiently, this paper presents a GP algorithm called “Genetic Programming with Multi-Layered Population Structure (MLPS-GP)”. MLPS-GP employs multi-layered population like the pyramid-like population and searches solutions using local search and crossover. The computational experiments were conducted by taking several classical Boolean problems as examples.
The population size, i.e., the number of candidate solutions per iteration, is the only parameter for the covariance matrix adaptation evolution strategy (CMA-ES) that needs to be tuned depending on the ruggedness and the uncertainty of the objective function. The population size has a great impact on the performance of the CMA-ES, however, it is prohibitively expensive in black-box scenario to tune the population size in advance. Moreover, a reasonable population size is not constant during the optimization. In this paper, we propose a novel strategy to adapt the population size. We introduce the evolution path in the parameter space of the Gaussian distribution, which accumulates successive parameter updates. Based on the length of the evolution path with respect to the Fisher metric, we quantify the accuracy of the parameter update. The population size is then updated so that the quantified accuracy is kept in the constant range during search. The proposed strategy is evaluated on test functions including rugged functions and noisy functions where a larger population size is known to help to find a better solution. The experimental results show that the population size is kept as small as the default population size on unimodal functions, and it is increased at the early stage of the optimization of multimodal functions and decreased after the sampling distribution is concentrated in a single valley of a local optimum. On noisy test functions, the proposed strategy start increasing the population size when the noise-to-signal ratio becomes relatively high. The proposed strategy is compared with the CMA-ES and the state-of-the-art uncertainty handling in the CMA-ES, namely UH-CMA-ES, with a hand-tuned population sizes.
In recent years, there has been many examples of applying evolutionary multi-criterion optimization (EMO) to practical problems in many fields. On the other hand, a new problem of how to analyze non-dominated solutions (NDSs) with many design variables and many objectives arises. For this problem, we has provided our original analysis support system using association rules, which is correlation-based information hierarchical structuring method (CIHSM). CIHSM could extract features of NDSs through objective analysis using association rules and visually present result of analyses as a hierarchical tree. However, there remains two problems in our CIHSM; the parameter setting related to association rules and the feature extraction required by user's interest. In this paper, we have proposed a modified CIHSM having two mechanism for dissolving these two problems. We called it ``on-demand CIHSM''. The first mechanism is the feature selection according to user's interest region in objective space. The important point of this mechanism is that user can select his interests region visually. And the second mechanism is to tune the value of minimum support parameter automatically. The setting of this parameter has a strong influence for the number of extracted rules. But this mechanism could provide use's requirement number of rules without tuning the value of this parameter. To investigate the effectiveness of on-demand CIHSM, we applied it to the conceptual design problem of hybrid rocket engine(HRE) problem, which is a real problem provided by JAXA. Through this experiments, it was verified that our on-demand CIHSM is very useful to extract features of NDS according to user's interest.