Noriyasu Hirokawa

Voronoi Diagram Based Blending of Quadratic Response Surfaces for Cumulative Global Optimization

This paper proposes a Voronoi diagram based blending scheme of local response surfaces for cumulative global optimization. In the scheme, after sample points are distributed over the design space and local function expressions are generated as quadratic polynomials for the subspaces around respective sample points, they are blended into the global approximation by using superposable function approximation based on geometric structure that is represented by Voronoi diagram, a technique of computational geometry. Under its superposability, it has an ability of cumulative function approximation, in which sample points are adaptively added based on tentative optimization results and approximation fidelity is cumulatively enhanced. Numerical examples of cumulative global optimization are given to ascertain the effectiveness and validity of the proposed blending scheme.

Mini-Max Type Formulation of Strict Robust Design Optimization Under Correlative Variation

This paper proposes a mini-max type formulation for strict robust design optimization under correlative variation based on design variation hyper sphere and quadratic polynomial approximation. While various types of formulations and techniques have been developed for computational robust design, they confront the compromise among modeling of parameter variation, feasibility assessment, definition of optimality such as sensitivity, and computational cost. The formulation of this paper aims that all points within the distribution region are thoroughly optimized. For this purpose, the design space with correlative variation is diagonalized and isoparameterized into a hyper sphere, and the functions of nominal constraints and the nominal objective are modeled as quadratic polynomials. These transformation and approximation enable the analytical discrimination of inner or boundary type on the worst design and its quantified values with less computation cost under a certain condition, and bring the procedural definition of the strictly robust optimality of a design as a maximization problem. The minimization of this formulation, that is, mini-max type optimization, can find the robust design under the above meaning. Its validity is ascertained through numerical examples.Copyright

DESIGN OPTIMIZATION OF MULTI-LINK SUSPENSION SYSTEM FOR TOTAL VEHICLE HANDLING AND STABILITY

This paper discusses the design problem of vehicles using multi-link suspension system with the aim of totally optimizing vehicle handling and stability. Since this problem includes many evaluation items, and multi-link suspension system has interconnected behavior, the optimization is so complicated. An efficient and computable model is indispensable for compromising the total optimization. This paper investigates a hierarchical structure of objectives, introduces appropriate simulation models for respective items, and formulates a mathematical optimization model based on them. Further, we apply a genetic algorithm based optimization method to this problem. The genetic algorithm is based on Simple GA and introduces several extensions such as fitness function for constrained multi-objective optimization problems, similarity-based selection, direct crossover within side constraints, etc. The result of optimization calculation shows the validity of the optimization model and the optimization algorithm as mathematical computation based design methods.

VORONOI DIAGRAM BASED CUMULATIVE APPROXIMATION FOR ENGINEERING OPTIMIZATION

This paper proposes a function approximation scheme based on Voronoi diagram, a technique of computational geometry, toward optimization cost saving in real engineering applications. The scheme consists of a blending function of local information over spatial structure among sample points that is topologically represented with Voronoi diagram, an estimation method of function gradients through the method of least squares along each Voronoi region, and an associated overall optimization algorithm. The scheme can locally establish and cumulatively update an approximation function based on the nature of Voronoi diagram, and this leads efficient and accurate accumulation of samples toward superior global fidelity in function approximation. Its validity and advantages are demonstrated through its application to a twodimensional example problem and a welded beam structure design problem.

Effectiveness of a Balance Chair for Maintaining a Seating Posture During Light-Duty Work

This study discusses the effectiveness of using a balance chair and adjusting a desk height and working position for maintaining seating posture during light-duty work. It is important for a worker to maintain good posture to improve work efficiency and protect his or her health. However, the worker’s body trunk tends to lean forward unconsciously when he or she is working on an ordinary chair. Meanwhile, a person sitting on a balance chair, which comprises a forward-declined seat and a knee pad, can maintain a posture that resembles that of standing. This study measures the body trunk angles of a subject performing light-duty work while seated on an ordinary chair and a balance chair and discusses the influence of desk height and working position.

Enhancement of Mini-Max Type Robust Optimal Design using Function Regularization

This paper proposes a method for enhancing the quality of mini-max type robust optimal design by using the concept of function regularization. Since robust optimal design considers variations under various noises, the quality of a solution is affected by the intermediate model for considering variations of the objective function and constraints within a distribution region.The mini-max type robust optimal design has been proposed by the authors for considering the bounding points of the objective and constraints within the distribution region as a definition of robust optimality. The function regularization proposed in this paper enhances its accuracy by filtering the functions so as to improve fidelity of quadratic approximation, which is used for obtaining the bounding points. The filter is formulated as the form of Fourier series and is implemented for the mini-max type robust optimal design scheme. Then, numerical experiments, in which second-order Fourier series is used as the filter, are demonstrated with two numerical sample problems; a two-dimensional algebraic problem and a simple structural optimal design problem.

DESIGN OPTIMIZATION BY INTEGRATION OF EVOLUTIONARY SEARCH AND CUMULATIVE APPROXIMATION

This paper proposes a new design optimization framework by integrating evolutionary search and cumulative function approximation. While evolutionary algorithms are robust even under multi-peaks, rugged natures, etc., their computational cost is inferior to ordinary schemes such as gradient-based methods. While response surface techniques such as quadratic approximation can save computational cost for complicated design problems, the fidelity of solution is affected by density of samples. The new framework simultaneously performs evolutionary search and constructs response surfaces. That is, in its early phase the search is performed over roughly but globally approximated surfaces with the relatively small number of samples, and in its later phase the search is performed intensively around promising regions, which are revealed in the preceded phases, over response surfaces enhanced with additional samples. This framework is expected to be able to robustly find the optimal solution with less sampling. An optimization algorithm is implemented by combining a real-coded genetic algorithm and a Voronoi diagram based cumulative approximation, and it is applied to some numerical examples for discussing its potential and promises.Copyright

Total Design Optimization of Multi-Link Suspension System for Vehicle Handling and Stability.

This paper discusses the design problem of vehicles using multi-link suspension system with the aim of totally optimizing vehicle handling and stability. Since this problem includes many evaluation items, and multi-link suspension system has interconnected behavior, the optimization is so complicated. An efficient and computable model is indispensable for compromising the total optimization. This paper investigates a hierarchical structure of objectives, introduces appropriate simulation models for respective items, and formulates a mathematical optimization model based on them. Further, we apply a genetic algorithm based optimization method to this problem. The genetic algorithm is based on Simple GA and introduces several extensions such as fitness function for constrained multi-objective optimization problem, similarity-based selection, direct crossover within side constraints, etc. The result of optimization calculation shows the validity of the optimization model and the optimization algorithm as a mathematical computation based design methodology.