Multi-objective Multidisciplinary Optimization Research Articles

Multi-objective, Multidisciplinary Optimization of Low-Boom Supersonic Transports Using Multifidelity Models

A multidisciplinary optimization (MDO) method has been developed to design a computational fluid dynamics (CFD)-based low-boom configuration that can be obtained from a Pareto solution of a low-fidelity multi-objective MDO problem with mission constraints. This paper refines the developed MDO method by using multifidelity models for CFD-based multi-objective MDO and a better method for the system-level trade between the target low-boom ground noise level and the overland range. The refined MDO method can generate a low-boom configuration that satisfies the mission requirements, has the lowest takeoff gross weight and the longest range for the low-boom mission, trims the low-boom cruise flight with fuel redistributions, and has a reversed equivalent area distribution closely matching a low-boom target with ground noise level below 70 perceived level in decibels. The validity of the refined MDO method is demonstrated by a design study of a low-boom supersonic transport that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.7 and range of 3500 n mile, and cruises overwater at Mach 1.8 with range of 3882 n mile. Moreover, the refined MDO method eliminates the difference between the assumed cruise weight for CFD-based low-boom inverse design optimization and the estimated cruise weight of the optimal inverse design solution with respect to the mission requirements.

Comparison of structural parameterization methods for the multidisciplinary optimization of active morphing wing sections

Morphing wings promise to increase the aerodynamic efficiency of future aircraft. A challenging task is to find structures that enable the active deformation of morphing wings leading to an increased aerodynamic efficiency and being lightweight at the same time. For the development of suitable optimization methods, choosing an efficient topology parameterization method is a crucial point. Contrary demands are a small number of design variables and a wide description of valid structures. The present work compares three different parameterization methods for their applicability in the multidisciplinary multi-objective optimization of active morphing wing sections. Namely, these parameterization methods are Lindenmayer cellular systems, Voronoi diagrams and the bijective graph representation. It is shown that all three parameterization methods are basically suitable for the optimization problem addressed but have individual characteristics and benefits.

Pareto front spacing with differential geometry in multidisciplinary systems

Multidisciplinary Design Optimization, also known as MDO, deals with the optimization of complex but typically single-objective design problems. As such, it would be valuable to combine it with Multi-Objective Optimization (MOO). Within MOO, Weighted Sums (WS) is a standard solution method, but it may not produce a good spacing of solution points along the Pareto Front (PF). Using our differential geometry MDO framework, we present a technique for intelligently spacing out Pareto solutions produced with WS in a multidisciplinary MOO formulation. Following an initial demonstration, we present modifications to our method to handle ill-conditioning better, to produce fewer dominated points in PF refinement, and to use MOO solution methods other than WS.

Multi-disciplinary multi-objective design optimization of sounding rocket fins

In this study we carry out multi-disciplinary multi-objective optimization of a solid fin for sounding rocket by considering its (i) aerodynamic performance in terms of static aerodynamic stability and drag, (ii) structural performance in terms of torsional deflection and factor of safety (FOS), and (iii) flight performance in terms of peak altitude (PA) and maximum payload capability for given propulsion system characteristics. Four different fin design optimization problems have been studied:(i) maximize PA of the sounding rocket and maximize aerodynamic static margin, (ii) maximize PA and maximize payload mass, (iii) maximize PA and minimize tip torsion angle of the fin, (iv) maximize PA and maximize FOS. In all of these optimization problems, essential aerodynamic and structural constraints have been satisfied. Multi-objective optimization has been used to get the Pareto-optimal front of the conflicting objectives. It is seen that all the four design problems have conflicting objectives. The study gives insight into the optimal fin configuration variables and effect of active constraints.

Multidisciplinary Multi-objective Optimization Method for Vehicle Crashworthiness Design

This paper proposes a multidisciplinary multi-objective optimization method for vehicle Crashworthiness design. Multi-objective optimization methods are discussed. Considering the objective functions with difference dimensions, we improve -method based on normalizes objective function. As the numerical example, the vehicle crashworthiness design problem is calculated, and we compare the results with SO method, interior point method and active-set method, where interior point method and active-set method are based the improved -method. Examples indicate that this algorithm has less number of iteration than the others. DOI : http://dx.doi.org/10.11591/telkomnika.v12i2.3832

An Aerothermodynamic and Mass-Model Integrated Optimization Framework for Highly-Integrated Forebody-Inlet Configurations

A framework methodology for multidisciplinary multiobjective optimization and analysis is proposed. It is based on analytical aerothermodynamics and mass-modeling parameters of highly-integrated forebody-inlet configuration and representative hypersonic flight vehicle respectively. A complex configuration for a highly-integrated waverider forebody attached to planar compression ramps and planar sidewalled-inlet system is studied. Optimization and analytical solutions are obtained using SHWAMIDOF-FI design tool. Results show substantial improvement in geometric, performance and flow parameters as compared to baseline configuration.

New Approximation Assisted Multi-objective collaborative Robust Optimization (new AA-McRO) under interval uncertainty

Existing collaborative optimization techniques with multiple coupled subsystems are predominantly focused on single-objective deterministic optimization. However, many engineering optimization problems have system and subsystems that can each be multi-objective, constrained and with uncertainty. The literature reports on a few deterministic Multi-objective Multi-Disciplinary Optimization (MMDO) techniques. However, these techniques in general require a large number of function calls and their computational cost can be exacerbated when uncertainty is present. In this paper, a new Approximation-Assisted Multi-objective collaborative Robust Optimization (New AA-McRO) under interval uncertainty is presented. This new AA-McRO approach uses a single-objective optimization problem to coordinate all system and subsystem multi-objective optimization problems in a Collaborative Optimization (CO) framework. The approach converts the consistency constraints of CO into penalty terms which are integrated into the system and subsystem objective functions. The new AA-McRO is able to explore the design space better and obtain optimum design solutions more efficiently. Also, the new AA-McRO obtains an estimate of Pareto optimum solutions for MMDO problems whose system-level objective and constraint functions are relatively insensitive (or robust) to input uncertainties. Another characteristic of the new AA-McRO is the use of online approximation for objective and constraint functions to perform system robustness evaluation and subsystem-level optimization. Based on the results obtained from a numerical and an engineering example, it is concluded that the new AA-McRO performs better than previously reported MMDO methods.

Collaborative Optimization of Container Ship on Static and Dynamic Responses

A new improved collaborative optimization (CO) model is used to optimize a container ship structure on static and dynamic responses. The new CO model provides solution capabilities for multiobjective multidisciplinary optimization problems. The system level objective function is advised to minimize relative value between the global optimal solution and the single disciplinary optimal solution. The subsystem level objective function is advised that includes the disciplinary objective function and the modified consistency constraint. The discrete design variable sets including the thickness of plate and the model number of beam are depicted with matrix. The objective functions are how to get the minimum structural mass in the static analysis and how to minimize the maximum acceleration of structure in the dynamic analysis. The proposed model was demonstrated with an optimization problem of stiffness plate under static and seismic loading. Then the model was used to optimize a container ship structure. The optimal design obtained indicates the great potential of decreasing structural mass and vibration level and increasing natural frequency reserve under the strength and stiffness requirements. The analysis progress and results show that the model is feasible and well-suited for using in actual optimization problems of ship design

Efficiency for multiobjective multidisciplinary optimization problems with quasiseparable subproblems

Multidisciplinary optimization (MDO) has proved to be a useful tool for engineering design problems. Multiobjective optimization has been introduced to strengthen MDO techniques and deal with non-comparable and conflicting design objectives. A large majority of papers on multiobjective MDO have been applied in nature. This paper develops theory of multiobjective MDO and examines relationships between efficient solutions of a quasi-separable multiobjective multidisciplinary optimization problem and efficient solutions of its separable counterpart. Equivalence of the original and separable problems in the context of the Kuhn-Tucker constraint qualification and efficiency conditions are proved. Two decomposition approaches are proposed and offer a possibility of finding efficient solutions of the original problem by only finding efficient solutions of the subproblems. The presented results are related to algorithms published in the engineering literature on multiobjective MDO.

Improvement of collaborative optimization

This paper presents a new improved collaborative optimization (CO) model that provides solution capabilities for multiobjective multidisciplinary optimization problems. Reasons that cause computational difficulties in CO algorithm are firstly analyzed. Then a new system level objective function is advised to minimize relative value between the collaborative objective function and single disciplinary objective function. And it eliminates the effect of dimensions and magnitude orders among objectives. A new subsystem level objective function is developed that includes the disciplinary objective function and the consistency constraint. A new CO framework which is more suitable for multilevel distributed design is advised. In this CO framework, the system level optimizer does not only independently invoke the subdisciplinary analysis tools, but also invoke its subdiscipline optimizer. The improved CO model proposed in this work is demonstrated with two examples. The results of examples show the improved CO is not only feasible, reliable and efficient, but also well suitable to solve the multiobjective optimization problems in multidisciplinary design environment.

Genetic Algorithm-Based Multiobjective Optimization for Building Design

Large-scale building design is a constantly evolving process where design managers are always trying to identify means of producing a ‘better’ product in a ‘shorter’ period of time. Hence there is a need for design tools that can help designers better manage collaborative design development. It is becoming difficult to improve the performance of building design based only on improvements in individual disciplines. For this reason, better, system-orientated, holistic, multidisciplinary approaches to building design are needed. This article investigates the applicability of a multidisciplinary design optimization (MDO) methodology in building design. MDO methods divide a single system into a group of smaller subsystems to effectively manage interactions between them. In the context of building design, the system refers to building design as a whole, whereas subsystems represent the various design disciplines or parts of the building, for example spatial zones. Such an approach could reduce the time and cost associated with the multidisciplinary design cycle. As an outcome of this research, a Pareto genetic algorithm-based collaborative optimization (PGACO) framework is developed to support interactions between multiple disciplinary tasks and to coordinate conflicting design objectives. The article demonstrates how the PGACO framework can be applied to a multiobjective multidisciplinary optimization problem. The framework is also tested on a simple mathematical example.

Quality-Assisted Multi-Objective Multidisciplinary Genetic Algorithms

A new method is presented to solve multi-objective multidisciplinary optimization (M-MDO) problems. This M-MDO method is applicable to multi-objective optimization problems that can be decomposed hierarchically into multi-objective subproblems and whose objective functions are either separable or additively separable. In the decomposition, the subproblems may have both common and unique objectives. The method uses a multiobjective genetic algorithm (MOGA) to optimize the multi-objective subproblems; hence, it is referred to as a multi-objective multidisciplinary genetic algorithm (M-MGA). It is shown that for any Pareto point of the original (single-level) problem, M-MGA generates at least one point that is noninferior with respect to that Pareto point. Also a comparison is shown between the computational complexity of M-MGA and a single-level MOGA in terms of number of functions calls. The M-MGA is demonstrated by two engineering examples: the design of a speed reducer and the design of a payload for an undersea autonomous vehicle. In both examples, the generated solutions are similar to solutions generated by solving the examples as single-level problems. M-MGA produces relatively the same solutions from one M-MGA run to another.