In engineering activities, engineers solve various kinds of problems. Most of these problems are routine problems that are easy to formalize and formalized knowledge is useful for these problems. On the other hand, there are complicated problems that is difficult to formalize all of the problem solving process. One of the useful information to solve such complicated problems is result of the similar problem solving process. In addition, later in such complicated problem solving process, most of the decomposed subproblems are able to handle as routine problems. In this research, we decide to use formalized knowledge and document information that represents the history of problem solving processes to support to solve both types of the problem. For that purpose, we propose a new knowledge management system that supports a user to solve the problem through document processing. In this support process, the system retrieves related documents for user's problems by using formalized knowledge and information retrieval techniques. After retrieving related documents, he/she modifies them to fit his/her problems. Modified information is associated with the formalized knowledge and stored as documents for future reuse.

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In this paper, we study an inverse kinematics problem in which the trajectories of walking robot toes are generated under the condition of minimum walking energy. It is important for a walking robot that motions of legs are determined to achieve a desired body operation. A 4-legged walking robot with two rinks and two motors at joints of waist and knee is assumed in this study. A mathematical optimization method is used for optimization of several parameters which describe the trajectory function of toe. We use a neural network controller to obtain trajectory parameters to control walking robot in real time. Some trained neural network controllers for several obstacle shapes are used by changing for each obstacle.

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Mixed-integer linear programming (MILP) can be used for a variety of optimization problems. However, it is limited to relatively small-scale problems, because its computation time increases dramatically with the number of integer variables. A decomposition method has been proposed to derive good feasible solutions of large-scale MILP problems by the authors. The method is composed of solution of original and reduced MILP master problems, solution of MILP subproblems, and assumption of values of part of integer variables, which are repeated until a suboptimal solution is obtained. The objective of this paper is to propose a strategy to determine appropriately the number of integer variables whose values are assumed by means of multistage use of the decomposition method. A multi-period operational planning problem of a heat supply system is investigated numerically to show the validity and effectiveness of the strategy. It turns out that the strategy can derive a better suboptimal solution and an effective approximate lower bound for the optimal value of the objective function.

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In optimization algorithms, the value of design variables are updated according to some criterion and it is nesessary to evaluate objective functions and constraints repeatedly if design variables are updated. In design problems, performances are often taken as the objective functions or constraints and it needs a time to evaluate the performances. A same situation is observed in the multi-objective optimization problems that can handle several objective function simultaneously and is suitable for the real design. Therefore it is desiable to decrease the number of evaluation count of the objective function and constrains. The response surface methodology is helpful for such a situation and many studies have been done. In real design problems, nonlineality of the objective function and constraints can been seen and this make the objective function or constraints the complex form about the design variables. On the other hand, in the mult-objective optimization problems, we have to calculate the pareto optimal set that could not be defined the inferiority or supriority among the solutions. The pareto optimal set forms the hyper plane in objective function space and the sensitivity of this plane make us to be able to do the trade-off analysis among the objective functions. The difficulty to obtain pareto optimal set could be seen in calculation because of the nonlinearity of the objective function and constraints. That is, it seems to be difficult to fund some part of pareto optimal set in probablistic method. In this study, we will approximate the pareto optimal set using response surface methodology and identify the region that needs evaluation. Through numerical example, we will discuss the fundamental charastaristics of the proposed method

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In many practical engineering design problems, the form of objective function is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the value of objective function is obtained by some analysis such as structural analysis, fluidmechanic analysis, thermodynamic analysis, and so on. Usually, these analyses are considerably time consuming to obtain a value of objective function. In order to make the number of analyses as few as possible, we suggest a method by which optimization is performed in parallel with predicting the form of objective function. Techniques of machine learning can be applied for predicting the form of objective function. In this paper, radial basis function networks (RBFN) are employed in predicting the form of objective function, and genetic algorithms (GA) in searching the optimal value of the predicted objective function. The effectiveness of the suggested method will be shown through some numerical examples.

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Radius Basis Function Network (RBFN) can make up response surface of interpolation quite well even if it has multi-peak. Thus, we can optimize functions that is not explicitly expressed, such as we use in Engineering Analysis. In unconstraint case, it works successively to reduce a number of function calls, to obtain global optimum value and also to obtain over all response surface. On the other hand, when it is constrained, we need a number of function calls onry to find feasible region. In this study, we use RBF to classify feasible region by given data, and give a new data according to the information that is given by RBF classifier.

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For the complicated nonlinear optimization problems or multidisplinary optimization problems, Reponse surface methodology is one of the popular tools. Usually, polynomials are employed as response surfaces. For the creation of the response surfaces, several commertial software tools have been distributed. In the present study, we have developed a simple macro for Microsoft Excel to create response surfaces. The present study shows the effectiveness of the tool and shows the optimization process using Microsoft Excel.

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