This paper proposes a new framework of real-coded genetic algorithms (RCGAs) for the multi-funnel function optimization. The RCGA is one of the most powerful function optimization methods. Most conventional RCGAs work effectively on the single-funnel function that consists of a single big-valley. However, it is reported that they show poor performance or, sometimes, fail to find the optimum on the multi-funnel function that consists of multiple big-valleys. In order to remedy this deterioration, Innately Split Model (ISM) has been proposed as a framework of RCGAs. ISM initializes an RCGA in a small region and repeats a search with the RCGA as changing the position of the region randomly. ISM outperforms conventional RCGAs on the multi-funnel functions. However, ISM has two problems in terms of the search efficiency and the difficulty of setting parameters. Our proposed method, Big-valley Explorer (BE), is a framework of RCGAs like ISM and it has two novel mechanisms to overcome these problems, the big-valley estimation mechanism and the adaptive initialization mechanism. Once the RCGA finishes a search, the big-valley estimation mechanism estimates a big-valley that the RCGA already explored and removes the region from the search space to prevent the RCGA from searching the same big-valley many times. After that, the adaptive initialization mechanism initializes the RCGA in a wide unexplored region adaptively to find unexplored big-valleys. We evaluate BE through some numerical experiments with both single-funnel and multi-funnel benchmark functions.

抄録全体を表示

This paper proposes a reasonable stopping criterion for Adaptive Weighted Aggregation (AWA), which is a scalarization-based multi-start framework developed in our previous study on continuous multiobjective optimization. Our previous study shows that AWA yields good solutions covering the entire Pareto set and front within a small consumption of running time and function evaluation on 2- to 6-objective benchmark problems. The experimental results also indicate, however, that the number of solutions generated by AWA is multiplied every iteration. The rapid increase of solutions requires a careful choice of the stopping criterion: even one iteration of shortage may deteriorate the coverage of solutions into an unsatisfactory level and one of excess gives rise to a significant waste of computational resources. We therefore discuss the minimum iteration that AWA yields an enough solution set to cover the Pareto set and front in the sense that the set contains at least one interior point of each of their non-empty "faces", that is, boundary submanifolds induced from the Pareto sets of subproblems with the same inclusion relation as faces of the simplex. Then, such an iteration, named the representing iteration, is proposed as a stopping criterion for AWA, and the number of solutions found by the representing iteration, named the representing number, is derived to analyze the space complexity of AWA. We also discuss the time complexity of AWA based on numerical experiments. The distribution of obtained solutions and its coverage measure show the usefulness of the proposed stopping criterion.

抄録全体を表示

Design informatics, which is the efficient design methodology, has three points of view. The first is the efficient exploration in design space using evolutionary-based optimization methods. The second is the structurization and visualization of design space using data mining techniques. The third is the application to practical problems. In the present study, the influence of the difference among the seven pure and hybrid optimization methods for design information has been investigated in order to explain the selection manner of optimization methods for data mining. The practical problem of a single-stage hybrid rocket is picked up as the present design object. A functional analysis of variance and a self-organizing map are employed as data mining techniques in order to acquire the global design information in dasign space. As a result, mining result depends on not the number of generation (i.e. convergence) but the optimization methods (i.e. exploration space). Consequently, the optimization method with diversity performance is the beneficial selection in order to obtain the global design information in design space.

抄録全体を表示

We present an efficient designing process of nano-photonic polarization control elements using Genetic Algorithm (GA). Photonic nanostructures, which have a periodic metallic pattern pitching smaller than light wavelength, can produce unique optical functions such as polarization transformation by the near-field light effect. Because of the complex interaction between the light and metal, it is essentially difficult to optimize the nanostructure, thus no systematic design procedure is currently in operational. To tackle this problem, we utilize the finite-difference time-domain (FDTD) method to simulate and evaluate the polarization transformation efficiency and apply GA to optimize it. To drive the GA optimization procedure, a periodic 2D nanostructure is deformed by mutation. Started from a circular shape, the metallic pattern comes into a specific shape, which has two sharp tips and smooth S-shape outline curve. The optimization procedure takes approximately 20 days to reach a local minimum. Experiment results show efficacy of the proposed design procedure based on FDTD and GA.

抄録全体を表示