In this paper, portfolio optimization using loan is formulated as a chance constrained problem in which the money borrowed from a loan is invested in risk assets. Then the chance constrained problem is transformed into a deterministic optimization problem that has an equality constraint. In order to apply conventional Differential Evolution (DE) algorithms to the constrained optimization problem effectively, two types of Genotype-Phenotype (GP) mappings, namely a conventional GP mapping and a newly proposed GP mapping, are compared. As a result of numerical experiments including a two-way analysis of variance (two-way ANOVA), it is shown that the proposed GP mapping outperforms the conventional one because the former enhances the quality of solutions obtained by DE algorithms. By using historical data of assets, an advantage of the investment using loan is also confirmed.

This study has attained three two-objective optimum designs of constellation orbit with three satellites specialized for regional coverage observation on the Earth's ground. Space transportation is becoming more frequent and less expensive due to actively participating by numerous venture companies. Besides, improvements in manufacturing technology and onboard electronics have rendered it possible to promptly and economically fabricate small satellites. Hence, the market in individual cases by multiple small satellites surges from national projects using a single large satellite. However, the design method of constellation orbit specialized for particular local realm observation, which is the purpose of small-scale projects, has not been established. This study describes the six orbital elements of the satellites as design variables; we express the mission as objective functions coinciding with system performance and operation cost, which we perceive as a multi-/many-objective optimization problem. Consequently, the result indicated the correlation between the objective functions and elucidated the profitable operation principle of the three-satellite constellation quantitatively. Furthermore, we accumulated the improvement perspectives regarding the objective-function definition to represent the mission, which the conclusion would procure the knowledge to conduct sophisticating the next-step problem definition.

This paper proposes a decomposition-based multi-objective evolutionary algorithm that dynamically arranges weight vectors based on a Pareto front estimation. Evolutionary multi-objective optimization generally requires a solution set that uniformly approximates the Pareto front. Decomposition-based algorithms use a weight vector set specifying the target approximation points on the Pareto front. The distribution of solutions depends on the distribution of the weight vector set, and an appropriate weight vector distribution depends on the Pareto front. Conventional algorithms dynamically arranging the weight vector set have employed an archive of non-dominated solutions to estimate the Pareto front. However, the number of non-dominated solutions is limited, even if all of them are archived during the search. The proposed method estimates the Pareto front shape using the response surface methodology and the Pareto front range using the alpha shape based on the limited non-dominated solutions. The proposed method picks a representative set of objective vectors on the estimated Pareto front, converts it to the new weight vector set, and uses it for the search. Experimental results on three objective problems with concave, convex, inverted, and disconnected Pareto fronts show that the radial basis neural network, a response surface methodology, is suited for the Pareto front estimation. Also, results show that the proposed algorithm achieves better search performance than the conventional MOEA/D, S$^3$-CMA-ES, RVEA, MOEA/D-DCWV, -AWA, -URAW, and AR-MOEA.