This paper presents a robust Real-coded evolutionary algorithm. Real-coded evolutionary algorithms (RCEAs), such as real-coded genetic algorithms and evolution strategies, are known as effective methods for function optimization. However, they often fail to find the optimum in case the objective function is multimodal, discrete or high-dimensional. It is also reported that most crossover (or recombination) operators for RCEAs has sampling bias that prevents to find the optimum near the boundary of search space. They like to search the center of search space much more than the other. Therefore, they will not work on functions that have their optima near the boundary of search space. In this paper, we apply two methods, genetic algorithm with search area adaptation (GSA) and toroidal search space conversion (TSC), to the function optimization for improving the robustness of RCEAs. The former method searches adaptively and the latter one removes the sampling bias. Through several experiments, we have confirmed that GSA works adaptively and it shows higher performance, and RCEAs with TSC show effectiveness to find the optima near the boundary of search space.

The consecutive meals planning is a combinatorial optimization problem that determines the meals plan on one period consisting of consecutive days. This paper designs two evaluation functions for the planning and applies a permutation GA to optimize it. The evaluation function measures the variation of appearance order of meals or meal's characteristics on the plan. In the numerical experiments, we show that our meals plan has a large variation of appearance order of meal's characteristics.

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SummaryThis paper discusses DNA-based stochastic optimizations under the constraint that the search starts from a given point in a search space. Generally speaking, a stochastic optimization method explores a search space and finds out the optimum or a sub-optimum after many cycles of trials and errors. This search process could be implemented efficiently by "molecular computing", which processes DNA molecules by the techniques of molecular biology to generate and evaluate a vast number of solution candidates at a time. We assume the exploration starting from a single point, and propose a method to embody DNA-based optimization under this constraint, because this method has a promising application in the research field of protein engineering.In this application, a string of nucleotide bases (a base sequence) encodes a protein possessing a specific activity, which could be given as a value of an objective function. Thus, a problem of obtaining a protein with the optimum or a sub-optimum about the desired activity corresponds to a combinatorial problem of obtaining a base sequence giving the optimum or a sub-optimum in the sequence space. Biologists usually modify a base sequence corresponding to a naturally occurring protein into another sequence giving a desired activity. In other words, they explore the space in the proximity of a natural protein as a start point.We first examined if the optimization methods that involve a single start point, such as simulated annealing, Gibbs sampler, and MH algorithms, can be implemented by DNA-based operations. Then, we proposed an application of genetic algorithm, and examined the performance of this application on a model fitness landscape by computer experiments. These experiments gave helpful guidelines in the embodiments of DNA-based stochastic optimization, including a better design of crossover operator.