Advantages of evolutionary computation with very large population for many-objective optimization problems are investigated. Effects of the population size are investigated up to 1,000,000 while the number of generations is fixed to 100. To overcome difficulty in computational time, we use a many-objective evolutionary algorithm designed for massive parallelization (CHEETAH) and use the supercomputer K. As for unimodal test problems DTLZ2 and DTLZ4, IGD property are improved up to population size 1,000,000 while GD property is saturated at population size of 10,000. Even when the total number of evaluations is fixed, this conclusion stays same. As for multimodal test problems DTLZ1 and DTLZ3, GD and IGD properties are improved up to population size 10,000 while they are not drastically improved with population size larger than that. It is probably due to the difficulty in obtaining good Pareto-optimal solutions of DTLZ1 and DTLZ3 with the current CHEETAH, which bases on NSGA-II.

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With the multi-combustion technology, the combustion in a hybrid rocket engine (HRE) can be temporarily stopped via oxidizer throttling. In this paper, two types of HREs, one with multi-combustion technology and the other without, are compared to investigate the effects of multi-combustion on the flight performance of launch vehicles (LVs). Non-dominated Sorting Genetic Algorithm-II (NSGA-II) which was a multi-objective evolutionary algorithm (MOEA) was applied to solve the design problems using real-number coding and the Pareto ranking method. To investigate the effects of the multi-combustion on flight performance of LV with HRE, three design problems were considered. The first case was the maximization of the flight altitude and the minimization of the gross weight. The second case was the minimization of the maximum acceleration and the minimization of the gross weight. The final case was the maximization of the flight downrange and the minimization of the gross weight. Many non-dominated solutions were obtained by NSGA-II, and a trade-off was observed between the two objective functions in each case. MOEA results were visualized using a parallel coordinate plot. According to the exploration result, it was found that the multi-combustion of HRE was effective to reduce the maximum acceleration. Such ability could be expected to reduce the shock load to payloads carried by the LV with HRE.

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A proposed framework is specialized for large scale vehicle routing problems (VRPs) and based on problem decomposition and gradual restoration mechanisms to perform more efficiently search. First mechanism is used to break a large scale problem into small size sub-problems and second one is to restore these to original state gradually. These mechanisms having contradictory features can be expected to work efficiently in large scale problem having more than hundreds. Firstly, an original large scale problem is divided into some small sub-areas and optimal solutions in each sub-area are derived. When a best incumbent solution remains unchanged for a certain period, sub-problems are gradually integrated and new optimal solutions in a new integrated sub-problem are re-searched through use of the obtained solutions in previous sub problems. This gradual integration and optimization would be iterated until all sub-problems are integrated into the one (the original problem), and the optimal solution of original problem can be obtained in the overall integrated which is same as original problem. Through some typical test problems from Cordeau's instances, it was demonstrated that the proposed framework could derive better results more effectively than conventional one.

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