A major goal of computational astrophysics is to simulate the Milky Way Galaxy with sufficient resolution down to individual stars. However, the scaling fails due to some small-scale, short-timescale phenomena, such as supernova explosions. We have developed a novel integration scheme of N-body/hydrodynamics simulations working with machine learning. This approach bypasses the short timesteps caused by supernova explosions using a surrogate model, thereby improving scalability. With this method, we reached 300 billion particles using 148,900 nodes, equivalent to 7,147,200 CPU cores, breaking through the billion-particle barrier currently faced by state-of-the-art simulations. This resolution allows us to perform the first star-by-star galaxy simulation, which resolves individual stars in the Milky Way Galaxy. The performance scales over 104 CPU cores, an upper limit in the current state-of-the-art simulations using both A64FX and X86-64 processors and NVIDIA CUDA GPUs.

The visualization of the Pareto optimal solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto optimal solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto optimal solution representation capability. One is that the maps have incorrect points that represent non-Pareto optimal solutions. The other is that the coverage of the maps for the edge region of the Pareto optimal solution set is not good. This study proposes a Pareto optimal solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.

In the multi-objective optimization problem that appears naturally in the decision making process for the complex system, the visualization of the innumerable solutions called Pareto optimal solutions is important issue. This study focuses on the Pareto optimal solution visualization method using the self-organizing maps which is one of promising visualization methods. The method has advantages in grasping the overall structure of the solutions and comparing the objective functions simultaneously. However, this method has shortcomings in its solution representation capability. This study proposes a new Pareto optimal solution visualization method using MIGSOM. The MIGSOM is one of the self-organizing algorithms inspired by the neuronal migration. In the MIGSOM algorithm, all input data directly migrate in the projection map space so as to form a suitable map. This direct migration is expected to contribute to the improvements of the solution representation capability. Three improvements are introduced for the application of MIGSOM to the visualization. The effectiveness of the proposed method is confirmed through comparisons to the visualization method using conventional MIGSOM.

The selfish routing problem is a mathematical model to represent the behavior of the selfish players who select a path in a congested network. In the selfish routing problem, Braess's paradox shows that there exists a case that more network resources may cause worse traffic performance contrary to expectations. In the previous studies of the selfish routing problem, the traffic network with a pair or multiple pairs of source sink vertex and the independent normalization constraints has been investigated. This paper introduces a multi-constraint type selfish routing problem. In this problem, a traffic network with multiple source vertices and multiple sink vertices is considered. The total flow from each source vertex is constrained to be constant. The total flow to each sink vertex is also constrained to be constant. This study formulates an optimization problem to obtain the equilibrium solution of the multi-constraint type selfish routing problem. Then, this study considers the meaning of the equilibrium solution through the derivation of the optimality condition. In order to solve the formulated problem, the variable metric gradient projection method is applied. In the numerical experiments, the optimality of the equilibrium solution obtained by the variable metric gradient projection method is verified. Then, the incidence of Braess's paradox in the multi-constraint type selfish routing problem is confirmed.

This study proposes a new global constrained optimization method for nonlinear constrained optimization problems that utilises the chaotic search trajectory generated by using the sequential quadratic approximation type Lagrange quasi-Newton search model, which is equivalent to the Lagrange quasi-Newton dynamics. Specifically, the chaotic search trajectory that can be utilized for the global search is generated through destabilization of the search trajectory of the sequential quadratic approximation type Lagrange quasi-Newton model based on the scenario similar to the scenario appearing in the chaotic optimization method for the unconstrained optimization problem. Then, a multi-point type search method in which the chaotic search trajectory is utilized is proposed. The effectiveness of the proposed method is confirmed through applications to several benchmark problems.

In this study, we transform an optimization problem into a game problem by multiple decision makers. This transformation is called gamification of the optimization problem. Then, we discuss correspondence of the dynamics to search the rational solution of the game problem with the multi-point type optimization method to search the optimal solution of the original problem. Specifically, we propose a condition to compose objective functions of multiple decision makers who interfere with each other from the objective function of the original problem so that equivalence of the Nash equilibrium solution of the game problem to the optimal solution of the original problem is guaranteed. Then, correspondence of the gradient dynamics to solve the game problem with the multi-point type optimization method is discussed. We also show some numerical examples in order to explain the gamification of the optimization problem.

The chaotic optimization method is a global optimization method to solve unconstrained optimization problems. Its superior search capability has been confirmed through applications to optimization problems which have high dimensional and multi-peaked objective functions. However, the chaotic optimization method has a drawback in that a parameter called initial sampling parameter has to be tuned on each optimization problem. In this study, we consider two approaches to perform the chaotic optimization method without the initial sampling parameter tuning. One is the initial sampling estimation method based on the characteristics of the chaotic optimization method. In this method, the sampling parameter at which the search trajectory bifurcates from the fixed point convergence to the two periodic solution trajectory, which is called the first bifurcating parameter, is computed from the approximation matrix to Hessian obtained by the quasi-Newton method. Then, suitable initial sampling parameter is estimated using this information. The other is the descent sign vector method. In this method, a descent sign vector extracted from a gradient vector is used as a search direction of a search point. Then, its moving distance is determined so that its search process shifts from the global search to the local search. We compare two methods and their hybrid method through numerical experiments for various optimization problems.

In this study, we propose a new constrained optimization method using the quasi-chaotic optimization method (Q-COM) with the exact penalty function and the Sequential Quadratic Programming (SQP). The Q-COM, which has been proposed recently, is a global optimization method to solve unconstrained optimization problems in which the simultaneous perturbation gradient approximation is introduced into the chaotic optimization method to apply to a class of problems whose objective function values only can be computed. The SQP is well known and powerful constrained optimization method to find local optimal solution. In the proposed method, the Q-COM with the exact penalty function is used as the global search method and the SQP is used as the local search method. We confirm the effectiveness of the proposed method through applications to various types of benchmark problems that include the coil spring design problem and the benchmark problems used in the special session on constrained real parameter optimization in CEC2006.

In this study, we propose a new global optimization method in which the simultaneous perturbation gradient approximation is introduced into a multi-point type chaotic optimization method. The multi-point type chaotic optimization method, which has been proposed recently, is a global optimization method to solve unconstrained optimization problems in which multiple search points which implement global search driven by a chaotic gradient dynamic model are synchronized to their elite search points. The chaotic optimization method uses gradient as a driving force for search points. Hence, its application is confined to a class of problems in which gradient of the objective function can be computed. In this study, we introduce the simultaneous perturbation gradient approximation into the multi-point type chaotic optimization method in order to compute gradient approximately so that the chaotic optimization method can be applied to a class of problems whose objective function values only can be computed. Then, we confirm effectiveness of the proposed method through applications to several unconstrained multi-peaked optimization problems with 100 variables comparing to other major meta-heuristics.

In this study, we propose a new chaotic global optimization method using the Lagrangian method to solve a nonlinear constrained optimization problem. Firstly, we explain the convergence behavior of the first order method regarding convexity of the Lagrangian with respect to decision variables in terms of linear stability theory. Further, we propose a new optimization method in which the convergence behavior of the first order method is improved by two techniques. One is the introduction of a coupling structure. The second is the introduction of objective function weighting. Then, we apply a multipoint type chaotic optimization method so that global search is implemented to find feasible global minima. We then confirm the effectiveness of the proposed method through applications to the coil spring design problem and benchmark problems used in the special session on constrained real parameter optimization in CEC2006.

Many techniques for rendering natural objects such as the sea, terrains, and trees have been developed; they are indispensable for flight simulators. In this paper, techniques for rendering road surfaces under various conditions are discussed. Rendering road surfaces is quite useful for the evaluation of driving safety, and it will play an important part in the development of drive simulators. Light sources with high intensity often disturb drivers especially under wet road surface conditions.This paper proposes two models, a reflection model for road surfaces taking into account weather conditions, and a model on streaks of light taking into account both refraction and diffraction of light. Some examples demonstrate the possibility of applications for drive simulators in the future.