Strategies for Modeling, Approximation, and Decomposition in Genetic Algorithms Based Multidisciplinary Design

Slime mold algorithm (SMA) is a recently developed meta-heuristic algorithm that mimics the ability of a single-cell organism (slime mold) for finding the shortest paths between food centers to search or explore a better solution. It is noticed that entrapment in local minima is the most common problem of these meta-heuristic algorithms. Thus, to further enhance the exploitation phase of SMA, this paper introduces a novel chaotic algorithm in which sinusoidal chaotic function has been combined with the basic SMA. The resultant chaotic slime mold algorithm (CSMA) is applied to 23 extensively used standard test functions and 10 multidisciplinary design problems. To check the validity of the proposed algorithm, results of CSMA has been compared with other recently developed and well-known classical optimizers such as PSO, DE, SSA, MVO, GWO, DE, MFO, SCA, CS, TSA, PSO-DE, GA, HS, Ray and Sain, MBA, ACO, and MMA. Statistical results suggest that chaotic strategy facilitates SMA to provide better performance in terms of solution accuracy. The simulation result shows that the developed chaotic algorithm outperforms on almost all benchmark functions and multidisciplinary engineering design problems with superior convergence.

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions - including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties - is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation - input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.

Uncertainty-based multidisciplinary design optimization (UMDO) often relies on propagation of uncertainties across several disciplines. If the several disciplines cannot be tightly integrated, then it is helpful to use a UMDO method that conducts uncertainty propagation in each discipline and combines their results into a system level uncertainty. Existing methods such as moment-matching collaborative optimization (MM-CO) use this strategy, preserving some disciplinary autonomy in uncertainty propagation. However, they do not capture dependence in coupling variables, which can lead to less accurate results in the system level uncertainty. Covariance-matching collaborative optimization (CMCO) builds on MM-CO by posing target correlations of coupling variables to guide discipline-level uncertainty propagation. The method is demonstrated on an algebraic test problem and a multidisciplinary aircraft conceptual design problem.

This paper describes the formulation and application of a design framework that supports the complex task of multidisciplinary design optimisation of Unmanned Aerial Vehicles (UAVs). The framework includes a Graphical User Interface (GUI), a robust Evolutionary Algorithm optimiser, several design modules, mesh generators and post-processing capabilities in an integrated platform. Traditional deterministic optimisation techniques for MDO are effective when applied to specific problems and within a specified range. A new class of optimisation techniques named Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEAs) have shown to be robust as they require no derivatives or gradients of the objective function, have the capability of finding globally optimum solutions amongst many local optima, can be executed asynchronously in parallel and adapted easily to arbitrary solver codes without major modifications. The application of the methodology is illustrated on multi-criteria and multidisciplinary design problems. Results indicate the practicality and robustness of the method in finding optimal solutions and Pareto trade-offs between the disciplinary analyses and producing a set of non dominated individuals.

Designing turbine wheels for automotive turbochargers one is faced with a multidisciplinary design problem with many input and output parameters. Especially in the automotive industry short development cycles for high quality products in a competitive environment are daily routine. For meeting these requirements optimization algorithms can be a powerful tool in the design process. This paper presents the multidisciplinary optimization of an automotive mixed flow turbine wheel used in a 4 cylinder 1.6 l spark ignition engine. Before describing the optimization workflow in detail, the requirements for turbines operating in an automotive environment under pulsating flow conditions and during an engine load step are discussed. From there objectives for a multidisciplinary optimization are derived. The turbine wheel is optimized with respect to maximizing efficiency in two design points and minimizing its moment of inertia. For the optimization process, an algorithm based on evolution theory is used. As constraints, the operating points are fixed and the natural frequencies are limited to ensure the mechanical strength of the turbine. To speed up the optimization process meta models based on neural networks are applied. Three designs of the Pareto frontier are chosen and their characteristics are discussed. Using statistical methods, the interaction of the input variables and their impact on turbine performance are presented.

The design of space systems is a complex and multidisciplinary process with multiple conflicting objectives, large number of design variables, and constraints that limits application of the existing multidisciplinary design optimization architectures to this class of design problems. This paper presents an enhanced multidisciplinary design optimization architecture to concurrent holistic design optimization of a satellite system. The proposed multidisciplinary design optimization architecture extends concepts of multidiscipline feasible and bi-level integrated system synthesis into a unified architecture using metamodels. The proposed architecture was evaluated and compared with the existing multidisciplinary design optimization architectures that include all-at-once, bi-level integrated system synthesis, and multidisciplinary design optimization using a remote sensing small satellite in low earth orbit. The satellite design optimization problem deals with the minimization of the total mass of the satellite, involving disciplines of mission analysis, payload, structures, attitude determination and control, communication, command and data handling, power and thermal. The computational performance and accuracy of the proposed architecture were compared with multidisciplinary design optimization benchmark problems. Then the proposed architecture is successfully applied to the satellite system design problem. The results obtained show that metamodel-based bi-level integrated system synthesis-multidisciplinary design optimization architecture presented in this paper provides an effective way of solving large-scale design problems.

Modern radio and navigation systems (Fig. 1) for automotive applications are highly complex systems with a large variety of mechanical and electrical components and assemblies: front module, frame brackets, PCBs, drives, fans, connectors, heat sinks or EMC-shieldings. Increased power dissipation and density due to higher demands on the audio power amplifier and functionality such as new multimedia features (video, internet, MP3) require intelligent thermal management strategies. This includes the selection of materials and components as well as their design and placement. The design of such electronic systems requires the interaction of mechanical, electrical and software engineers in order to achieve a system solution, hence a multi-disciplinary design and optimization problem.

Decomposition of multidisciplinary engineering system design problems into smaller subproblems is desirable because it enhances robustness and understanding of the numerical results. Moreover, subproblems can be solved in parallel using the optimization technique most suitable for the underlying mathematical form of the subproblem. Hierarchical overlapping coordination (HOC) is an interesting strategy for solving decomposed problems. It simultaneously uses two or more design problem decompositions, each of them associated with different partitions of the design variables and constraints. Coordination is achieved by the exchange of information between decompositions. This article presents the HOC algorithm and several new sufficient conditions for convergence of the algorithm to the optimum in the case of convex problems with linear constraints. One of these equivalent conditions involves the rank of the constraint matrix that is computationally efficient to verify. Computational results obtained by applying the HOC algorithm to quadratic programming problems of various sizes are included for illustration.

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.

5 - Multidisciplinary Design and Optimization Methods

Collaborative optimization (CO), a decomposition-based multidisciplinary design optimization (MDO) method, is generally used in aeronautical systems. However, the subsystems optimizations of CO method are nested into system optimization of it in the execution process, numerous subsystem analyses are required to achieve consistency for entire system. For this problem, a nonnested collaborative optimization (NNCO) method is developed, in which system and subsystem optimizations are solved sequentially and repeatedly, and system consistancy is coordinated by a loop process together with the update of penalty parameters. Through test results of common analytical problems, which are generally used in the experiments of CO method, it's shown that the NNCO method requires two third fewer calls of the subsystem analysis than the CO method at least. Further more, CO and NNCO method are used to solve a satellite MDO problem, 0.05 and 8.05 hours are consumed for these two methods respectively. The efficiency of NNCO method in practical engineering design problem is proved.

Web-Based Teaching of Open-Ended Multidisciplinary Engineering Design Problems

A hybrid multi-agent system architecture for enterprise integration using computer networks

In practical design studies, most of designers solve multidisciplinary problems with large size and complex design system. These multidisciplinary problems have hundreds of analysis and thousands of variables. The sequence of process to solve these problems affects the speed of total design cycle. Thus it is very important for designer to reorder the original design processes to minimize total computational cost. This is accomplished by decomposing large multidisciplinary problem into several multidisciplinary analysis subsystem (MDASS) and processing it in parallel. This paper proposes new strategy for parallel decomposition of multidisciplinary problem to raise design efficiency by using genetic algorithm and shows the relationship between decomposition and multidisciplinary design optimization (MDO) methodology.

Truss size and topology optimization problems have recently been solved mainly by many different metaheuristic methods, and these methods usually require a large number of structural analyses due to their mechanism of population evolution. A branched multipoint approximation technique has been introduced to decrease the number of structural analyses by establishing approximate functions instead of the structural analyses in Genetic Algorithm (GA) when GA addresses continuous size variables and discrete topology variables. For large-scale trusses with a large number of design variables, an enormous change in topology variables in the GA causes a loss of approximation accuracy and then makes optimization convergence difficult. In this paper, a technique named the label–clip–splice method is proposed to improve the above hybrid method in regard to the above problem. It reduces the current search domain of GA gradually by clipping and splicing the labeled variables from chromosomes and optimizes the mixed-variables model efficiently with an approximation technique for large-scale trusses. Structural analysis of the proposed method is extremely reduced compared with these single metaheuristic methods. Numerical examples are presented to verify the efficacy and advantages of the proposed technique.