Hybrid-Game Strategies for multi-objective design optimization in engineering

A number of game strategies have been developed in past decades and used in the fields of economics, engineering, computer science, and biology due to their efficiency in solving design optimization problems. In addition, research in multiobjective and multidisciplinary design optimization has focused on developing a robust and efficient optimization method so it can produce a set of high quality solutions with less computational time. In this paper, two optimization techniques are considered; the first optimization method uses multifidelity hierarchical Pareto-optimality. The second optimization method uses the combination of game strategies Nash-equilibrium and Pareto-optimality. This paper shows how game strategies can be coupled to multiobjective evolutionary algorithms and robust design techniques to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid and non-Hybrid-Game strategies are demonstrated.

The optimal design of multidisciplinary systems under uncertainty involves three types of iterative analyses- multidisciplinary analyses, reliability analyses, and optimization. If these processes are carried out in a nested manner in reliability based multidisciplinary design optimization (RBMDO), the computational expense can be enormous. Computationally efficient simultaneous analysis and design (SAND) or All-AtOnce methods have been developed earlier for deterministic MDO. Single loop RBDO methods have also been developed to integrate reliability analysis and optimization in a single loop. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints. The formulation allows for solution with a single design optimization loop by using the KKT optimality conditions of the first-order reliability method (FORM) as constraints in the design optimization along with disciplinary consistency constraints. Alternative solution processes which remove the FORM MPP’s from the decision space and many constraints from the problem are developed. The alternative solution methods are more efficient and more robust than using nonlinear programming to solve the single loop formulation. A numerical example is solved with the two proposed solution algorithms. I. Introduction In the design of multidisciplinary systems it is often necessary to make decisions under uncertainty. This requires that multidisciplinary systems modeling be integrated with uncertainty analysis and optimization. A common example of such an engineering design application would be the design of an aircraft wing under uncertain aerodynamic loading conditions, with multiple structural components with uncertain capacities, such that the entire structural system achieves a prescribed level of reliability. The problem has coupled physics, in that the pressure distribution is dependent upon the deflection, and the deflection is dependent on the pressure distribution. Such designs have been performed using multidisciplinary optimization (MDO). Other examples where MDO may be applied include electronics packaging, in which the disciplines of heat transfer and circuit analysis are coupled, the design of new types of aircraft and integrating them into an existing fleet of aircraft, and even the management of interconnected homeland infrastructures. While MDO has matured with the development of different types of algorithms for various types of problems and design organizations, there has been little work to incorporate reliability analysis into MDO. However, system and component reliabilities are often a major concern in the design of multidisciplinary systems. MDO can be computationally expensive due to the need to achieve consistency across multiple disciplinary analysis codes; each disciplinary analysis code may be computationally expensive to run. Further, the optimal design of multidisciplinary systems under uncertainty involves three types of iterative procedures- multidisciplinary analyses, reliability analyses, and optimization. The integration of these three procedures is referred to in this paper as reliability based multidisciplinary design optimization (RBMDO). If these processes are carried out simultaneously, the computational expense can be enormous. Computational savings can often be achieved with simultaneous analysis and design (SAND) or All-At-Once methods, which allow for the solution of the multidisciplinary analyses and the optimization in one single loop. Single loop RBDO methods allow for the integration of reliability analysis and optimization in a single loop. Applying SAND and single-loop RBDO together may allow for large computational savings when applied to problems in RBMDO. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints based on the SAND method for MDO and by use of the KKT conditions of the first order reliability method (FORM). The resulting formulation may be solved as a standard nonlinear programming problem. While the single loop formulation presented in this paper is a solution of the RBMDO problem, robustness and efficiency are improved through two improved algorithms which can remove the MPP’s from the decision space, thereby significantly reducing the optimizer’s workload.

Design engineers and decision-makers across various fields are constantly working to make optimal design decisions for multidisciplinary engineering systems in an effort to improve performance and reduce costs. The multiple disciplines that decision-makers are forced to consider can range from different physical components of a system, to competing physical phenomena influencing a component (e.g. flow forces and structural strength), to completely separate models of interest to a system (e.g. engineering performance and lifecycle cost). The common element that all these decision-making scenarios share is the presence of couplings between the considered disciplines (or subsystems). How the values for these coupling parameters are determined within a decision-making or optimization framework is the subject of countless research efforts. At present the multidisciplinary design optimization (MDO) community has settled on a few proven techniques such Collaborative Optimization (CO) and Analytic Target Cascading (ATC). However, current MDO techniques have issues that limit their effectiveness in solving various MDO problems. Many of these strategies require close coordination between subsystem optimization solvers, require significant effort by decision-makers to pose their problems in a suitable format, and/or can have large computational efficiency problems due to the fact that they involve solving nested optimization problems. In an effort to alleviate some of these issues and make MDO easier to implement and more computationally efficient, a new sequential MDO algorithm called Cooperative Design Optimization (CDO) is proposed. The CDO approach functions through a series of subsystem optimizations using a successively smaller cooperation space. The cooperation space is analogous to the design space of a traditional optimization problem, but includes only the coupling parameters that are a factor in multiple subsystems. A single iteration of the approach can be thought of as a negotiation between all of the subsystems regarding the boundaries of the cooperation space. To facilitate this cooperation, each subsystem optimization problem is restructured as a multi-objective optimization problem so that a Pareto set of optimal solutions, or agreeable design alternatives, are produced. As a result, after all subsystem optimizations are accomplished, each subsystem’s obtained Pareto optimal solution sets are compared with respect to the coupling parameters and new bounds in the cooperation space are determined for the next iteration. This process allows each subsystem to be optimized completely independently within the boundaries of the agreed upon cooperation space while coordination is achieved through an analysis of obtained optimal solutions for each subsystem. Iterations, or negotiations, are repeated until an acceptable solution or set of solutions is obtained for all included subsystems through this cooperative process.

The design of multidiscipli nary systems (such as aircraft, automobiles, and others) often requires an iterative cycle that includes a design initialization, a system analysis, a sensitivity analysis, and design optimization. This design cycle is standard in the field of Multidisciplinary Optimization (MDO) and has often been referred to in literature as the Multiple Discipline-Feasible (MDF) approach. The name stems from the fact that complete multidisciplinary feasibility is maintained each and every design cycle. The drawback of MDF is that it can be a timely and a costly procedure. Numerous researchers have developed alternate means for posing and subsequently solving the multidisciplinary design problem. One such solution procedure has been referred to both as Simultaneous Analysis and Design (SAND) and All-at-Once (AAO), and treats the entire multidisciplinary design cycle as one large optimization problem. Another alternate solution procedure lias been referred to as Individual-Discipline-Feasible (DDF); this procedure exhibits characteristics which lie in between the two extremes exemplified by MDF and AAO. IDF assures that each individual discipline is feasible on every design cycle, while driving the entire system (all disciplines) towards multidisciplinary feasibility. The present work will present a rigorous numerical comparison of these solution strategies over a wide variety of problem sizes and complexities. The multidisciplinary design test problems that are used for these comparisons are generated by a robust simulation tool called CASCADE. * Research Assistant, Student member, AIAA | Associate Professor, Member AIAA Background and Motivation Concurrent engineering is a systematic approach to the integrated, simultaneous design of products and their related processes. Many of the recently developed capabilities to address concurrent engineering have stemmed from the emerging area of Multidiscipli nary Optimization, or MDO. The origins of MDO can be traced back to the early 1980's, where Sobieski14 used a linear decomposition approach to subdivide the design of a large engineering system into a grouping of related and more manageable subsystems. However, such a decomposition often results in a grouping of subsystems which cannot be placed into a definitive top-down hierarchy. The resultant decomposition grouping is typically hybrid-hierarchic in nature as shown in the example decomposition of Figure 1.

GIScience 2016 Short Paper Proceedings A Multistart Heuristic Approach to Spatial Aggregation Problems Ningchuan Xiao 1 , Peixuan Jiang 2 , Myung Jin Kim 3 , Anuj Gadhave 4 Department of Geography, Ohio State University, Columbus, OH 43210 Email: xiao.37@osu.edu 2 Esri, Redlands, CA, 92373 3 Gyeonggi Institute of Science and Technology Promotion, Suwon, Gyeonggi, Korea 4 Department of Computer Science and Engineering, Ohio State University, Columbus, OH 43210 Abstract In this paper, we present a heuristic method that can be used to search for a diverse set of solutions to spatial aggregation problems. The algorithm is developed using a multistart strategy. Computational experiments are conducted to test the effectiveness of the algorithm. Spatial data are often aggregated for different purposes. The census data in the United States, for example, are aggregated into levels such as blocks, block groups, and tracts. In another example, political redistricting requires the aggregation of spatial units into districts such that some objectives can be optimized. Though aggregation is a common exercise in the use of spatial data, it has been noted that many of the aggregations are arbitrary and may not provide effective spatial units for applications (Martin, 1998; Cockings and Martin, 2005), which often leads to the modifiable areal unit problem (Openshaw, 1983). Equally important is the multiplicity of spatial aggregations: given an aggregation of spatial units, many equivalent schemes may also exist. For example, there often exist many perfect political redistricting plans when population equality is the only objective (Kim and Xiao, 2016). Subsequently, it is important to explore a diverse set of aggregation schemes in order to fully understand the complexity of aggregation. Researchers have developed a wide range of methods that can be used to solve aggregation problems (Openshaw and Rao, 1995; Xiao, 2008). However these methods are designed for specific purposes and they generally do not aim to explore the complexity of aggregation. The purpose of this paper is to develop a heuristic method that can be used to find, not one, but a diverse set of high quality solutions to an aggregation problem. This method first uses a search algorithm to find a set of good solutions. These solutions are stored in a pool and another algorithm is developed to improve the solutions in the pool by recombining them into new solutions. This method is heuristic, meaning it cannot guarantee optimal solutions be found, and we test its effectiveness using a set of benchmark problems. We have tested the multistart algorithm with a wide range of data. Due to the page limit of this abstract, we discuss the first data set of Iowa congressional redistricting for year 2000. The Iowa Constitution dictates that the counties shall not be split for political redistricting purposes, which make it a problem of aggregating 99 spatial units into 5 regions. The official 2000 plan has an objective function value of 0.0080, and the literature has documented a number of redistricting

Model-Based Systems Engineering (MBSE) supports the system-level design of complex products effectively. Currently, system design and optimization for complex products are two distinct processes that must be executed using different software or platforms, involving intricate data conversion processes. Applying multidisciplinary optimization to validate system optimization often necessitates remodeling the optimization objects, which is time-consuming, labor-intensive, and highly error-prone. A critical activity in systems engineering is identifying the optimal design solution for the entire system. Multidisciplinary Design Optimization (MDO) and reliability analysis are essential methods for achieving this. This paper proposes a SysML-based multidisciplinary reliability design optimization modeling method. First, by analyzing the definitions and mathematical models of multidisciplinary reliability design optimization, the SysML extension mechanism is employed to represent the optimization model based on SysML. Next, model transformation techniques are used to convert the SysML optimization model generated in the first stage into an XML description model readable by optimization solvers. Finally, the proposed method’s effectiveness is validated through an engineering case study of an in-vehicle environmental control integration system. The results demonstrate that this method fully utilizes SysML to express MDO problems, enhancing the efficiency of design optimization for complex systems. Engineers and system designers working on complex, multidisciplinary projects can particularly benefit from these advancements, as they simplify the integration of design and optimization processes, facilitating more reliable and efficient product development.

It is necessary to employ the Multidisciplinary Design Optimization (MDO) method in the design process of automatic weapon, because the process in itself is related to many disciplines and their couplings. The knowledge structure of MDO is analyzed, which includes mathematic modeling, system decomposition, optimization framework, approximation model, sensitivity analysis, optimization method, software integration, and etc.. The idea of using MDO in the design process of individual soldier automatic weapon is also explored. Based on the software package of iSIGHT, the primary multidisciplinary integration is carried out. Current research work will be helpful for further research on integrating MDO into the design of automatic weapon.

During the last decade, energy use in the transportation and distribution sector has been greatly changed by remarkable growth in delivery drones in the direction of sustainable development. In this respect, this paper introduces a novel reconfigurable drone called “SMPCOPTER” by considering reliability and sustainability as paramount goals. The SMPCOPTER is a hybrid helicopter with puller-pusher rotors comprising a 2DOF tilting mechanism, a folding wing system covered with solar panels, and subsystems modularity enabling it to fly in three configurations an airplane, helicopter, and gyrocopter. The conceptual design of this novel configuration is performed by providing a bridge between model-based systems engineering (MBSE) and multidisciplinary design optimization (MDO) using MATLAB System Composer and doing co-simulation between considered disciplines such as propulsion, weight and balance, OpenVSP, and performance. A multi-objective MDO is executed to propose optimal feasible configurations by maximizing range, minimizing gross weight, and fulfilling stability constraints. The proposed configuration improves the reliability of delivery drones as well as the sustainability pillars by applying systems thinking within the design process.

A blowout preventer (BOP) is a large valve that encases an oil well on the surface. The valve may be closed while drilling if overpressure from a reservoir causes formation fluids such as oil and natural gas to back up within the wellbore and endanger the rig. A pipe ram is one of the critical components in the BOP system, which is designed to seal around a drill pipe, restricting the flow in the annulus between the outside of the drill pipe and the wellbore. The pipe ram design family, which contains hundreds of pipe ram designs, intends to cover different configurations to suit a variety of dill pipe sizes. To assure their structural integrity under service loads, these pipe rams need to be designed to meet the stress requirements per the American Petroleum Institute (API) Specification 16A and ASME (American Society of Mechanical Engineers) Boiler and Pressure Vessel Code Section VIII, Division 2. With a conventional manual design workflow, it would take a significant amount of time and effort to complete all the designs for the product family with code compliance. Therefore, a scalable solution is highly desirable for delivery of customer-needed ram blocks with much shorter lead time. MDO (Multi-Disciplinary Optimization) involves multi-code integration, CAE (Computer-Aided Engineering) workflow automation, design space exploration, and optimization. MDO-enabled, automated design optimization is becoming increasingly popular in both scientific and engineering communities. In this paper, a methodology for integration of CAD (Computer Aided Design), FEA (Finite Element Analysis), cost, and optimization packages to enable FEA automation and design optimization is presented. A BOP pipe ram is adopted as the use case. The ram block geometry was parameterized before being imported into an FEA package. The FEA workflow was automated such that once a set of geometric parameters are given, the preprocessing, solving, and postprocessing steps can be automatically completed. As part of the FEA postprocessing, stress linearization analysis per the API and ASME BPVC codes has also been automated, which had never been done in the past. A manufacturing cost analysis package can also be used to consume the parameterized geometry for automatic manufacturability assessment and cost predictions. The stress analysis and cost analysis workflows are conducted separately but also orchestrated by an MDO package. Reports that contain the analysis results are sequentially generated for various design permutations. The MDO-enabled automated design and cost analysis approach could substantially enhance efficiency and consistency in performing FEA and cost studies and producing analysis reports. It is also the backbone for automated design optimization, which could significantly improve the product performance and reliability and, meanwhile, minimize the development and product cost.

The first and foremost aim with this book is to serve as a guide and reference for engineers that want to use surrogate modeling techniques when they design or develop products, systems and components. Additionally, the book constitutes part of the literature for the courses in Design Optimization and Multidisciplinary Design Optimization at Linköping University. It is the intention of the author that the content should serve as an easily understood introduction to surrogate modeling. The more advanced details are briefy mentioned but can be found in the scientifc papers referenced in this book. There exist numerous books and review articles regarding surrogate modeling, e.g. Forrester, Sóbester, and Keane, 2008 and Krawczyk and Arabas, 2025, which means that all methods presented here can be found elsewhere. The two main advantages of this book are Many methods are exemplifed using numerical examples Some practical guidelines recommended by the author are presented

Microelectromechanical systems (MEMS) are a highly multidisciplinary field and this has large implications on their applications and design. Designers are often faced with the task of balancing the modelling, simulation and optimisation that each discipline brings in order to bring about a complete whole system. In order to aid designers, strategies for navigating this multidisciplinary environment are essential, particularly when it comes to automating design synthesis and optimisation. This paper outlines a new multi-objective and multidisciplinary strategy for the application of engineering design problems. It employs a population-based evolutionary approach that looks to overcome the limitations of past work by using a non-hierarchical architecture that allows for interaction across all disciplines during optimisation. Two case studies are presented, the first focusing on a common speed reducer design problem found throughout the literature used to validate the methodology and a more complex example of design optimisation, that of a MEMS bandpass filter. Results show good agreement in terms of performance with past multi-objective multidisciplinary design optimisation methods with respect to the first speed reducer case study, and improved performance for the design of the MEMS bandpass filter case study.

This paper presents a framework for multi-objective and multidisciplinary design optimization using highfidelity analysis tools. In this framework the aerodynamic performance is evaluated based on a Navier‐Stokes equation solver, and the structure dynamics is computed using commercially available finite element software. We employ a genetic algorithm as a robust design optimization tool to facilitate the multi-objective optimization. We also use the response surface approach to tackle the difficulties associated with the organizational complexity and computational burden inherent in the multidisciplinary optimization. The coupling between the fluid solver and structural solver is realized through a thin-plate spline interpolation algorithm. The proposed approach is then used to perform aerostructural optimization of a three-dimensional transonic compressor blade. Our numerical results show that this method can improve the existing design and reduce the required computational time by orders of magnitude.

Purpose – The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design optimization methods. Reliability-Based Design Optimization (RBDO), Possibility-Based Design Optimization (PBDO) and Robust Design Optimization (RDO) methods were developed to handle uncertainties of design optimization. The RBDO method is found suitable for uncertain parameters when sufficient information is available. On the other hand, the PBDO method is proposed when uncertain parameters have insufficient information. The RDO method can apply to both cases. The RBDO, PBDO and RDO methods were considered with the Multidisciplinary Design Optimization (MDO) method to generate conservative design results when low fidelity analysis tools are used. Design/methodology/approach – Methods combining MDO with RBDO, PBDO and RDO were developed and have been applied to a numerical analysis and an aircraft conceptual design. This research eva...

Multivariable optimization techniques have emerged as powerful tools in civil engineering design, enabling engineers to achieve optimal structural, environmental, and economic performance by simultaneously considering multiple conflicting objectives. This paper explores the applications of multivariable optimization methods such as gradient-based algorithms, genetic algorithms, and particle swarm optimization in the design of civil infrastructure. Key areas include structural optimization, resource allocation, cost minimization, and sustainability integration. The study highlights case examples illustrating the improvement in design efficiency, robustness, and sustainability. A comparative analysis of optimization methods is provided alongside a graphical demonstration of cost versus structural safety trade-offs. The paper concludes with a discussion on future trends and challenges in incorporating multivariable optimization for intelligent civil engineering solutions.

High performance computing for multidisciplinary design optimization and robustness of vehicle structures