Improved Solution Search Performance of Constrained MOEA/D Hybridizing Directional Mating and Local Mating

In this study, we propose an improvement to the direct mating method, a constraint handling approach for multi-objective evolutionary algorithms, by hybridizing it with local mating. Local mating selects another parent from the feasible solution space around the initially selected parent. The direct mating method selects the other parent along the optimal direction in the objective space after the first parent is selected, even if it is infeasible. It shows better exploration performance for constraint optimization problems with coupling NSGA-II, but requires several individuals along the optimal direction. Due to the lack of better solutions dominated by the optimal direction from the first parent, direct mating becomes difficult as the generation proceeds. To address this issue, we propose a hybrid method that uses local mating to select another parent from the neighborhood of the first selected parent, maintaining diversity around good solutions and helping the direct mating process. We evaluate the proposed method on three mathematical problems with unique Pareto fronts and two real-world applications. We use the generation histories of the averages and standard deviations of the hypervolumes as the performance evaluation criteria. Our investigation results show that the proposed method can solve constraint multi-objective problems better than existing methods while maintaining high diversity.Comment: Revised paper presented at ISMSI2023, 9pages, 8 figures (Online

Efficient Global Optimization Applied to Design and Knowledge Discovery of Supersonic Wing

Efficient global optimization (EGO) was applied to the multi-objective design and knowledge discovery of a supersonic transport (SST) wing. The objective functions considered here are employed to maximize the lift–to-drag ratio at supersonic cruise, to minimize the sonic boom intensity and to minimize wing structural weight, simultaneously. The EGO process is based on Kriging surrogate models, which were constructed using several sample designs. Subsequently, the solution space could be explored through the maximization of expected improvement (EI) values that corresponded to the objective function of each Kriging model because the surrogate models provide an estimate of the uncertainty at the predicted point. Once a number of solutions have been obtained for the EI maximization problem by means of a multi-objective genetic algorithm (MOGA), the sample designs could be used to improve the models\u27 accuracy and identify the optimum solutions at the same time. In this paper, 108 sample points are evaluated for the constructions of the Kriging models. In order to obtain further information about the design space, two knowledge discovery techniques are applied once the sampling process is completed. First, through functional analysis of variance (ANOVA), quantitative information is gathered and then, self-organizing maps (SOMs) are created to qualitatively evaluate the aircraft design. The proposed design process provides valuable information for the efficient design of an SST wing

Initial Design and Evaluation of a Novel Concept Regional Aircraft

A type of blended-wing-body (BWB) aircraft is expected to be next generation airliner. While many studies for BWB has been performed for a large scale aircraft, an aircraft which is for regional jet is also expected. Such aircraft would be small (about 100-300 seats). In the development of such aircraft, BWB should be also discussed because it has aerodynamic advantage compared with conventional aircrafts. Therefore, the aerodynamic design optimization for a small size BWB is required for conceptual design. In this study, an initial BWB which has 150 seats configuration is designed using genetic algorithm (GA). Three cross sections are optimized under constraint of elliptic span loading. Three dimensional unstructured Navier-Stokes solver is applied to evaluate the aerodynamic performance of BWB initial design

Data mining based multipoint design of next generation transonic wing with small sweep back

Multi-point aerodynamic optimization of a transonic wing using data mining is discussed. Design problem has two objectives which are minimization of drag coefficient at Mach number 0.6 and 0.8 respectively. Here, Mach number 0.6 is considered as a subsonic condition, and Mach number 0.8 is considered as a transonic condition with the local shock. To reduce the local shock that causes wave drag, the sweep back angle is required in transonic condition. On the other hand, the sweep back angle reduces lift to drag ratio in subsonic condition. Thus, a complex high lift device like a flap is required. Moreover, the torsion at wing root becomes stronger with high sweep back angle. As a result, the wing structure weight becomes heavy. To design high efficient new generation civil aircraft, the design knowledge which implements a subsonic and a transonic aerodynamic performance simultaneously with few structure penalty is expected. In this study, tapered wing geometry is defined with two cross sections. 31 sample designs are calculated by the unstructured Euler solver and Kriging surrogate models for the resulting drag coefficient of subsonic and transonic condition are constructed. Using these models, non-dominated solutions are obtained by genetic algorithm (GA). Analysis of variance (ANOVA) and Self-organized map (SOM), which are data mining techniques, are also applied to obtain the relationship between design space and solution space. According to this result, there is trade-off between two objective functions and compromised design can be considered. According to data mining result, there is possible to find the design which achieve low drag with low sweep back angle and contrived cross sections

Robust Constrained Multi-Objective Guidance of Supersonic Transport Landing Using Evolutionary Algorithm and Polynomial Chaos

Landing of supersonic transport (SST) suffers from a large uncertainty due to its highly sensitive aerodynamic properties in the subsonic domain, as well as the wind gusts around runways. At the vehicle design stage, a landing trajectory optimization under wind uncertainty in a multi-objective solution space is desired to explore the possible trade-off in its key flight performance metrics. The proposed algorithm solves this robust constrained multi-objective optimal control problem by integrating non-intrusive polynomial chaos expansion into a constrained evolutionary algorithm. The computationally tractable optimization is made possible through the conversion of a probabilistic problem into an equivalent deterministic representation while maintaining a form of the multi-objective problem. The generated guidance trajectories achieve a significant reduction of the uncertainty in their terminal states with a marginal modification in the control history of the deterministic solutions, validating the importance of the consideration of robustness in trajectory optimization

Aerodynamic design optimization of new conceptual civil aircraft

Blended-Wing-Body (BWB) aircraft is expected to be next generation airliner. While many studies for BWB has been performed for a large scale aircraft, an aircraft which is for regional jet is also expected. Such aircraft would be small (about 100-300 seats). In the development of such aircraft, BWB should be also discussed because it has aerodynamic advantage compared with conventional aircrafts. Therefore, the aerodynamic design optimization for a small size BWB is required for conceptual design. In this study, an initial BWB which has 150 seats configuration is designed using genetic algorithm (GA). Because BWB\u27s fuselage has similar geometry to a conventional airfoil, two types of airfoil optimizations are preformed to decide the fuselage and outboard wing section, separately. Unstructured Euler analysis is applied to evaluate the aerodynamic performance of BWB initial design

Characteristics of Vortices around Forward Swept Wing at Low Speeds/High Angles of Attack

The forward-swept wing (FSW), one of the wing planforms used in aircraft, is known for its high performance in reducing wave drag. Additionally, a study has shown that this wing planform can mitigate sonic booms, which pose a significant challenge to achieving supersonic transport (SST). Therefore, FSW is expected to find applications in future SST aircraft owing to aerodynamic advantages at high speeds. However, there is a lack of sufficient knowledge and systematization to improve aerodynamic performance at low speeds and high angles of attack during takeoff and landing. These are crucial for practical implementation. Although the aerodynamic benefits of an FSW in high-speed flight can be harnessed using advanced structural and control technologies, the realization of SST using an FSW is challenging without enhanced research on low-speed aerodynamics. This study explores the practical aerodynamic knowledge of FSWs. We utilized a numerical simulation based on the Navier–Stokes equation and focused on investigating wake vortex phenomena. Our simulation included various wing planforms, including backward-swept wings (BSWs). The results revealed the presence of vortices with lateral axes emanating from the FSW, while longitudinal vortices were observed in the BSW. Based on these results, we developed a theoretical hypothesis for the vortex structure around an FSW

Multi-Fidelity Multi-Objective Efficient Global Optimization Applied to Airfoil Design Problems

In this study, efficient global optimization (EGO) with a multi-fidelity hybrid surrogate model for multi-objective optimization is proposed to solve multi-objective real-world design problems. In the proposed approach, a design exploration is carried out assisted by surrogate models, which are constructed by adding a local deviation estimated by the kriging method and a global model approximated by a radial basis function. An expected hypervolume improvement is then computed on the basis of the model uncertainty to determine additional samples that could improve the model accuracy. In the investigation, the proposed approach is applied to two-objective and three-objective optimization test functions. Then, it is applied to aerodynamic airfoil design optimization with two objective functions, namely minimization of aerodynamic drag and maximization of airfoil thickness at the trailing edge. Finally, the proposed method is applied to aerodynamic airfoil design optimization with three objective functions, namely minimization of aerodynamic drag at cruising speed, maximization of airfoil thickness at the trialing edge and maximization of lift at low speed assuming a landing attitude. XFOILis used to investigate the low-fidelity aerodynamic force, and a Reynolds-averaged Navier–Stokes simulation is applied for high-fidelity aerodynamics in conjunction with a high-cost approach. For comparison, multi-objective optimization is carried out using a kriging model only with a high-fidelity solver (single fidelity). The design results indicate that the non-dominated solutions of the proposed method achieve greater data diversity than the optimal solutions of the kriging method. Moreover, the proposed method gives a smaller error than the kriging method