Eitaro Aiyoshi

A solution method for the static constrained Stackelberg problem via penalty method

This note presents a new solution method for the static constrained Stackelberg problem. Through our approach, the Stackelberg problem is completely transformed into a one-level unconstrained problem such that the newly introduced overall augmented objective function is minimized with repect to the leaders and the followers variables jointly. It can be proved that a sequence of solutions to the transformed problems converges to the solution of the original problem, when the penalty parameters are updated.

Necessary conditions for min-max problems and algorithms by a relaxation procedure

For decision making under uncertainty, a rational optimality criterion is min-max. Min-max problems such that the minimizer makes an optimal decision against the worst case that might be chosen by the maximizer are studied. This paper presents necessary conditions and computational methods for a min-max solution (not a saddle point solution). Those conditions are stated in a form like Kuhn-Tucker theorem. The computational methods are based on the relaxation procedure. A min-max problem such that the minimizer and the maximizer are subject to separate constraints is primarily studied. But it is shown that the obtained results can be applied for the unseparate constraint case by use of duality theory.

A new computational method for Stackelberg and min-max problems by use of a penalty method

This paper is concerned with the Stackelberg problem and the min-max problem in competitive systems. The Stackelberg approach is applied to the optimization of two-level systems where the higher level determines the optimal value of its decision variables (parameters for the lower level) so as to minimize its objective, while the lower level minimizes its own objective with respect to the lower level decision variables under the given parameters. Meanwhile, the min-max problem is to determine a min-max solution such that a function maximized with respect to the maximizers variables is minimized with respect to the minimizers variables. This problem is also characterized by a parametric approach in a two-level scheme. New computational methods are proposed here; that is, a series of nonlinear programming problems approximating the original two-level problem by application of a penalty method to a constrained parametric problem in the lower level are solved iteratively. It is proved that a sequence of approximated solutions converges to the correct Stackelberg solution, or the min-max solution. Some numerical examples are presented to illustrate the algorithms.

Double penalty method for bilevel optimization problems

A penalty function method approach for solving a constrained bilevel optimization problem is proposed. In the algorithm, both the upper level and the lower level problems are approximated by minimization problems of augmented objective functions. A convergence theorem is presented. The method is applicable to the non-singleton lower-level reaction set case. Constraint qualifications which imply the assumptions of the general convergence theorem are given.

A distributed model of the saccade system: simulations of temporally perturbed saccades using position and velocity feedback

Interrupted saccades, movements that are perturbed in mid-flight by pulsatile electrical stimulation in the omnipause neuron region, are known to achieve final eye displacements with accuracies that are similar to normal saccades even in the absence of visual input following the perturbation. In an attempt to explain the neurophysiological basis for this phenomenon, the present paper describes a model of the saccadic system that represents the superior colliculus as a dynamic two-dimensional, topographically arranged array of laterally interconnected units. A distributed feedback pathway to the colliculus from downstream elements, providing both eye position and velocity signals is incorporated in the model. With the help of a training procedure based on a genetic algorithm and gradient descent, the model is optimized to produce both the normal as well as slow saccades with similar accuracy. The slow movements are included in the training set to mimic the accurate saccades that occur despite alterations in alertness, as well as following various degenerative oculomotor diseases. Although interrupted saccades were not included in the training set, the model is able to produce accurate movement of this type as an emergent property for a wide range of perturbed eye velocity trajectories. Our model demonstrates for the first time, that by means of an appropriate feedback mechanism, a single-layered dynamic network can be made to retain a distributed memory of the remaining ocular displacement error even for interrupted and slow saccades. These results support the hypothesis that saccades are controlled by error feedback of signals that code efference copies of eye motion, and further, suggest a possible answer to a long standing question about the kind of the feedback signal, if any, that is received by the superior colliculus during saccadic eye movements.

Optimization of boiling water reactor loading pattern using two-stage genetic algorithm

Abstract A new two-stage optimization method based on genetic algorithms (GAs) using an if-then heuristic rule was developed to generate optimized boiling water reactor (BWR) loading patterns (LPs). In the first stage, the LP is optimized using an improved GA operator. In the second stage, an exposure-dependent control rod pattern (CRP) is sought using GA with an if-then heuristic rule. The procedure of the improved GA is based on deterministic operators that consist of crossover, mutation, and selection. The handling of the encoding technique and constraint conditions by that GA reflects the peculiar characteristics of the BWR. In addition, strategies such as elitism and self-reproduction are effectively used in order to improve the search speed. The LP evaluations were performed with a three-dimensional diffusion code that coupled neutronic and thermal-hydraulic models. Strong axial heterogeneities and constraints dependent on three dimensions have always necessitated the use of three-dimensional core simulators for BWRs, so that optimization of computational efficiency is required. The proposed algorithm is demonstrated by successfully generating LPs for an actual BWR plant in two phases. One phase is only LP optimization applying the Haling technique. The other phase is an LP optimization that considers the CRP during reactor operation. In test calculations, candidates that shuffled fresh and burned fuel assemblies within a reasonable computation time were obtained.

Optimization of a boiling water reactor loading pattern using an improved genetic algorithm

Abstract A search method based on genetic algorithms (GA) using deterministic operators has been developed to generate optimized boiling water reactor (BWR) loading patterns (LPs). The search method uses an Improved GA operator, that is, crossover, mutation, and selection. The handling of the encoding technique and constraint conditions is designed so that the GA reflects the peculiar characteristics of the BWR. In addition, some strategies such as elitism and self-reproduction are effectively used to improve the search speed. LP evaluations were performed with a three-dimensional diffusion code that coupled neutronic and thermal-hydraulic models. Strong axial heterogeneities and three-dimensional-dependent constraints have always necessitated the use of three-dimensional core simulators for BWRs, so that an optimization method is required for computational efficiency. The proposed algorithm is demonstrated by successfully generating LPs for an actual BWR plant applying the Haling technique. In test calculations, candidates that shuffled fresh and burned fuel assemblies within a reasonable computation time were obtained.

Parameter optimization of model predictive control using PSO

Among various control methods, model predictive control (MPC) becomes one of the major control strategies and has many successful applications. This paper presents an automatic tuning method of MPC using particle swarm optimization (PSO). One of the challenges in MPC is how the control parameters can be tuned for various target plants, and usage of PSO for automatic tuning is one of the solutions. The tuning problem of MPC is formulated as an optimization problem and PSO is applied as the optimization techniques. PSO is one of meta-heuristic methods which are known to search a global optimum at a relatively high ratio and with no use of a gradient. The numerical results for simple examples show the effectiveness of the proposed PSO-based automatic tuning method.

Solution to combinatorial problems by using chaotic global optimization method on a simplex

The discretized maps of gradient models with Eulers method generate chaos, which can be used for global optimization by applying the chaotic annealing. In this paper, we apply this approach to solve the traveling salesman problem. We formulate it as continuous optimization problems with particular constraints, and newly derive. gradient projection dynamics whose discretized maps generate chaos on a simplex.

Automatic Tuning of Model Predictive Control Using Particle Swarm Optimization

This paper presents an automatic tuning method of model predictive control (MPC) using particle swarm optimization (PSO). Although conventional PID is difficult to treat constraints and future plant dynamics, MPC can treat this issues and practical control can be realized in various industrial problems. One of the challenges in MPC is how control parameters can be tuned for various target plants and usage of PSO for automatic tuning is one of the solutions. The numerical results show the effectiveness of the proposed PSO-based automatic tuning method