In this paper, we present an efficient sampling method for a multimodal and high-dimensional distribution. For sampling from a high-dimensional distribution, DE-MC, which is based on the Markov chain Monte Carlo(MCMC) methods, has been proposed. It showed good performance in sampling from any probability distribution based on constructing a Markov chain that has the desired distribution. However, DE-MC has inherent difficulties in sampling from a multimodal distribution. To overcome this problem, we incorporate a replica exchange method into DE-MC and propose a replica exchange resampling DE-MC method (reRDE-MC) based on sampling importance resampling to improve its performance. The proposed method is evaluated by using three types of distributions with multimodal and high dimensions as artificial data. We verified that the proposed method can sample from a multimodal and highdimensional distribution more effectively than by a conventional method. We then evaluated the proposed method by using financial data as actual data, and confirmed that the proposed method can capture the behavior of financial data.
We propose a sensitivity analysis technique for the class of mathematical programming problems. So far, there are no concrete methodologies of sensitivity analysis for the mathematical programming problems especially with integer constraints in general. Quantifier elimination is a concept of simplification used in mathematical logic and enables problems to be analyzed of their sensitivities to the objective functions. In this paper, we applied the quantifier elimination to a class of job shop scheduling problems as a case of mixed integer programming problems in order to demonstrate the evaluation of the sensitivities of the processing time to both of the makespan and the due date tardiness. In order to cope with computational complexities of quantifier elimination, we propose the problem decomposition and the sequential application of the quantifier elimination techniques based on the decomposition.
MOEA/D decomposes a multiobjective optimization problem into a set of single objective subproblems. When there are a few differences in difficulty of each objective function, it can obtain widely-spread and uniformly-distributed solutions. However, in real-world problems, the complexities of the objective functions are often heterogeneous. In this case, each subproblem of the MOEA/D has different difficulty so that the spread and uniformity of the population is deteriorated because the search direction in the objective space tends to be biased into the feasible region which is easily explored. To overcome this issue, an adaptive weight assignment strategy for MOEA/D is proposed in this paper. In the proposed method, the subproblems are divided into some groups and the convergence speed is estimated for each group and utilized as the metric of the difficulty of the subproblems. Moreover, the weight vectors of easy subproblem groups are modified to bias their search into the subproblem group with higher difficulty. Our proposed method is validated on the region-of-interests determination problem in brain network analysis whose objective functions have heterogeneous difficulties. The experimental results showed that our method worked better than the conventional weight assignment strategy in MOEA/D.
This paper proposes an effective algorithm for the recently proposed simultaneous design optimization problem of multiple car structures. In recent years, evolutionary algorithms typified by genetic algorithms have been extensively studied to solve single- and multi-objective real-world optimization problems. Mazda Motor Corporation developed the simultaneous design optimization benchmark problem that is based on a real car structures design and consists of many design variables and severe constraints. In this benchmark, three models of cars are simultaneously optimized and it is difficult to acquire optimal solutions with the limited number of evaluations with existing methods. This paper aims at proposing an algorithm based on NSGA-II, one of the most typical multi-objective evolutionary algorithm, and introduces several modifications considering the characteristics of the Mazda's benchmark problem. Specifically, we propose a method to effectively generate parent individuals using the characteristic that design variables of three cars are independent and genetic manipulation taking into consideration the characteristics of the objective function. In order to verify the effectiveness of the proposed method, we conduct experiments using the Mazda's benchmark problem. In the experiment, we compare NSGA-II with the proposed modifications with the original NSGA-II. The experimental result reveals that the proposed method can acquire extremely better solution set compared with the existing method.
Linear aerospike engine is a rocket engine that is composed of arrays of small cell engines and a large spike nozzle whose one side is open to atmosphere. It is one of the promising propulsion systems for future space transportation since it can realize high performance for a wide range of ambient pressure conditions. Despite this advantage of the aerospike engine, previous design studies on aerospike nozzle shape are only devoted to maximizing the performance at a single design point. In order to explore the design of the aerospike engine considering performance at multiple operating altitudes, multi-objective design optimization is conducted in this paper. Design variables define cell engine parameters and the shape of the spike nozzle whose parameterization is carried out using monotonic cubic spline. An engineering-level performance analysis model of the engine is developed by combining 1) chemical equilibrium calculation for cell engines, 2) Riemann solver for spike wall flow, and 3) theoretical model for spike base flow. Five objective functions are considered for the maximization of specific impulse at three operating altitudes, the minimization of spike nozzle arc length, and the minimization of total engine height. The formulated many-objective problem is solved via MOEA/D with dynamic control of aggregate functions, and well-converged and widely-spread nondominated solutions are obtained. In these solutions, spike nozzle shapes that are different from shapes designed by previous methods are observed. After representative solutions are inspected in detail, the relations between objective functions and design variables in superior solutions are revealed using parallel coordinates plots.
Evolutionary computation competition 2017 was held in December 9, 2017 in conjunction with evolutionary computation symposium 2017. It was confirmed that evolutionary algorithms can discover good designs of the design optimization problem of vehicle structures provided by Mazda motor company. Nine teams participated in the single-objective optimization division and eleven teams in the multiobjective optimization division. Prof. Shinya Watanabe's team from Muroran Institute of Technology won in the single-objective optimization division, Prof. Isao Ono's team from Tokyo Institute of Technology won in the multi-objective optimization division. The industrial use special prize was awarded to Dr. Tomohiro Harada's team from Ritsumeikan University. In the single-objective design optimization division, the groups using evolution strategies found good Pareto-optimal solutions. In the multiobjective optimization division, the groups who found good Pareto-optimal designs studied characteristics of the benchmark problem very much and implemented the most suitable optimization algorithm. Mazda benchmark problem has many severe constraints and thus feasible design space is strictly limited. Some teams used special techniques such as ε constraint method. Current result indicated that balance between search in feasible region and infeasible region may be important for constrained design optimization problems.