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Multidisciplinary design optimization

Multidisciplinary design optimization

Overview
Multi-disciplinary design optimization (MDO) is a field of engineering
Engineering
Engineering is the discipline, art and profession of acquiring and applying technical, scientific and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or inventions.The American Engineers' Council...

 that uses optimization
Optimization (mathematics)
In mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or...

 methods to solve design
Design
Design is the planning that lays the basis for the making of every object or system. It can be used both as a noun and as a verb and, in a broader way, it means applied arts and engineering . As a verb, "to design" refers to the process of originating and developing a plan for a product,...

 problems incorporating a number of disciplines. It is also known as multidisciplinary optimization and multidisciplinary system design optimization (MSDO).

MDO allows designers to incorporate all relevant disciplines simultaneously. The optimum of the simultaneous problem is superior to the design found by optimizing each discipline sequentially, since it can exploit the interactions between the disciplines.
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Encyclopedia
Multi-disciplinary design optimization (MDO) is a field of engineering
Engineering
Engineering is the discipline, art and profession of acquiring and applying technical, scientific and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or inventions.The American Engineers' Council...

 that uses optimization
Optimization (mathematics)
In mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or...

 methods to solve design
Design
Design is the planning that lays the basis for the making of every object or system. It can be used both as a noun and as a verb and, in a broader way, it means applied arts and engineering . As a verb, "to design" refers to the process of originating and developing a plan for a product,...

 problems incorporating a number of disciplines. It is also known as multidisciplinary optimization and multidisciplinary system design optimization (MSDO).

MDO allows designers to incorporate all relevant disciplines simultaneously. The optimum of the simultaneous problem is superior to the design found by optimizing each discipline sequentially, since it can exploit the interactions between the disciplines. However, including all disciplines simultaneously significantly increases the complexity
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in computer science that focuses on classifying computational problems according to their inherent difficulty. In this context, a computational problem is understood to be a task that is in principle amenable to being solved...

 of the problem.

These techniques have been used in a number of fields, including automobile
Automobile
An automobile, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...

 design, naval architecture
Naval architecture
Naval architecture is an engineering discipline dealing with the design, construction and repair of marine vehicles. Naval architecture involves basic and applied research, design, development, design evaluation and calculations during all stages of the life of a marine vehicle...

, electronics
Electronics
Electronics is a branch of science and technology that deals with the controlled flow of electrons. The ability to control electron flow is usually applied to information handling or device control. Electronics is distinct from electrical science and technology, which deals with the generation,...

, computer
Computer
A computer is a machine that manipulates data according to a set of instructions.Although mechanical examples of computers have existed through much of recorded human history, the first electronic computers were developed in the mid-20th century . These were the size of a large room, consuming as...

s, and electricity distribution
Electricity distribution
File:Electricity grid simple- North America.svg|thumb|380px|right|Simplified diagram of AC electricity distribution from generation stations to consumersrect 2 243 235 438 Power stationrect 276 317 412 556 Transformer...

. However, the largest number of applications have been in the field of aerospace engineering
Aerospace engineering
Aerospace engineering is the branch of engineering behind the design, construction and science of aircraft and spacecraft. It is broken into two major and overlapping branches: aeronautical engineering and astronautical engineering...

, such as aircraft
Aircraft
An aircraft is a vehicle which is able to fly by being supported by the air, or in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil An aircraft is a vehicle which is able to fly by being supported...

 and spacecraft
Spacecraft
A spacecraft is a craft or machine designed for spaceflight. On a sub-orbital spaceflight, a spacecraft enters space then returns to the Earth. For an orbital spaceflight, a spacecraft enters a closed orbit around the planetary body. Spacecraft used for human spaceflight carry people on board as...

 design. For example, the proposed Boeing
Boeing
The Boeing Company is a major aerospace and defense corporation, founded by William E. Boeing in Seattle, Washington. Boeing has expanded over the years, merging with McDonnell Douglas in 1997. Its international headquarters has been in Chicago, Illinois, since 2001...

 blended wing body
Blended wing body
Blended Wing Body, or BWB, designates an alternative airframe design which incorporates design features from both a traditional fuselage and wing design and flying wing design. The purported advantages of the BWB approach are efficient high-lift wings and a wide airfoil-shaped body...

 (BWB) aircraft concept has used MDO extensively in the conceptual and preliminary design stages. The disciplines considered in the BWB design are aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

, structural analysis
Structural analysis
Structural analysis comprises the set of physical laws and mathematics required to study and predict the behavior of structures. The subjects of structural analysis are engineering artifacts whose integrity is judged largely based upon their ability to withstand loads; they commonly include...

, propulsion
Air propulsion
Air propulsion is the act of moving an object through the air. The most common types are propeller, jet engine, turboprop, ramjet, rocket propulsion, and, experimentally, scramjet, pulse jet, and pulse detonation engine...

, control theory
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

, and economics
Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

.

History


Traditionally engineering has normally been performed by teams, each with expertise in a specific discipline, such as aerodynamics or structures. Each team would use its members' experience and judgement to develop a workable design, usually sequentially. For example, the aerodynamics experts would outline the shape of the body, and the structural experts would be expected to fit their design within the shape specified. The goals of the teams were generally performance-related, such as maximum speed, minimum drag
Drag (physics)
In fluid dynamics, drag refers to forces that oppose the relative motion of an object through a fluid . Drag forces act in a direction opposite to the oncoming flow velocity...

, or minimum structural weight.

Between 1970 and 1990, two major developments in the aircraft industry changed the approach of aircraft design engineers to their design problems. The first was computer-aided design, which allowed designers to quickly modify and analyse their designs. The second was changes in the procurement policy of most airline
Airline
An airline provides air transport services for passengers or freight, generally with a recognized operating certificate or license. Airlines lease or own their aircraft with which to supply these services and may form partnerships or alliances with other airlines for mutual benefit.Airlines vary...

s and military organizations, particularly the military of the United States
Military of the United States
The United States armed forces are the overall unified military forces of the United States.The history of the United States armed forces dates to 1775, even before the Declaration of Independence marked the establishment of the United States...

, from a performance-centred approach to one that emphasized lifecycle
Product lifecycle management
Product lifecycle management is the process of managing the entire lifecycle of a product from its conception, through design and manufacture, to service and disposal...

 cost issues. This led to an increased concentration on economic factors and the attributes known as the "ilities
Ilities
Within systems engineering, quality attributes are non-functional requirements used to evaluate the performance of a system. These are sometimes named "ilities" after the suffix many of the words share...

" including manufacturability, reliability, maintainability
Maintainability
In software engineering, the ease with which a software product can be modified in order to:* correct defects* meet new requirements* make future maintenance easier, or* cope with a changed environment;these activities are known as software maintenance In software engineering, the ease with which a...

, etc.

Since 1990, the techniques have expanded to other industries. Globalization has resulted in more distributed, decentralized design teams. The high-performance personal computer
Personal computer
A personal computer is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end user, with no intervening computer operator...

 has largely replaced the centralized supercomputer
Supercomputer
A supercomputer is a computer that is at the frontline of current processing capacity, particularly speed of calculation. Supercomputers were introduced in the 1960s and were designed primarily by Seymour Cray at Control Data Corporation , and led the market into the 1970s until Cray left to form...

 and the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standardized Internet Protocol Suite to serve billions of users worldwide...

 and local area network
Local area network
A local area network is a computer network covering a small physical area, like a home, office, or small group of buildings, such as a school, or an airport...

s have facilitated sharing of design information. Disciplinary design software in many disciplines (such as NASTRAN
Nastran
NASTRAN is a finite element analysis program that was originally developed for NASA in the late 1960s under United States government funding for the Aerospace industry. The MacNeal-Schwendler Corporation was one of the principal and original developers of the public domain NASTRAN code...

, a finite element analysis program for structural design) have become very mature. In addition, many optimization algorithms, in particular the population-based algorithms, have advanced significantly.

Origins in structural optimization


Whereas optimization methods are nearly as old as calculus
Calculus
Calculus is a discipline in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental...

, dating back to Isaac Newton
Isaac Newton
Sir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history...

, Leonhard Euler
Leonhard Euler
Leonhard Paul Euler was a pioneering Swiss mathematician and physicist who spent most of his life in Russia and Germany. His surname is in English ; the common English pronunciation is incorrect....

, Daniel Bernoulli
Daniel Bernoulli
Daniel Bernoulli was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics...

, and Joseph Louis Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange, born Giuseppe Lodovico Lagrangia was an Italian-born mathematician and astronomer, who lived most of his life in Prussia and France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...

, who used them to solve problems such as the shape of the catenary
Catenary
In physics and geometry, the catenary is the theoretical shape a hanging chain or cable will assume when supported at its ends and acted on only by its own weight. Its surface of revolution, the catenoid, is a minimal surface and will be the shape of a soap film bounded by two circles...

 curve, numerical optimization reached prominence in the digital age. Its systematic application to structural design dates to its advocacy by Schmit in 1960. The success of structural optimization in the 1970s motivated the emergence of multidisciplinary design optimization (MDO) in the 1980s. Jaroslaw Sobieski championed decomposition methods specifically designed for MDO applications. The following synopsis focuses on optimization methods for MDO. First, the popular gradient-based methods used by the early structural optimization and MDO community are reviewed. Then those methods developed in the last dozen years are summarized.

Gradient-based methods


There were two schools of structural optimization practitioners using gradient-based methods during the 1960s and 1970s: optimality criteria and mathematical programming. The optimality criteria school derived recursive formulas based on the Karush-Kuhn-Tucker (KKT) necessary conditions
Karush-Kuhn-Tucker conditions
In mathematics, the Karush–Kuhn–Tucker conditions are necessary for a solution in nonlinear programming to be optimal, provided some regularity conditions are satisfied. It is a generalization of the method of Lagrange multipliers to inequality constraints. The conditions are named for William...

 for an optimal design. The KKT conditions were applied to classes of structural problems such as minimum weight design with constraints on stresses, displacements, buckling, or frequencies [Rozvany, Berke, Venkayya, Khot, et al.] to derive resizing expressions particular to each class. The mathematical programming school employed classical gradient-based methods to structural optimization problems. The method of usable feasible directions, Rosen’s gradient projection (generalized reduce gradient) method, sequential unconstrained minimization techniques, sequential linear programming and eventually sequential quadratic programming methods were common choices. Schittkowski et al. reviewed the methods current by the early 1990s.

The gradient methods unique to the MDO community derive from the combination of optimality criteria with math programming, first recognized in the seminal work of Fleury and Schmit who constructed a framework of approximation concepts for structural optimization. They recognized that optimality criteria were so successful for stress and displacement constraints, because that approach amounted to solving the dual problem for Lagrange multipliers
Lagrange multipliers
In mathematical optimization, the method of Lagrange multipliers provides a strategy for finding the maximum/minimum of a function subject to constraints....

 using linear Taylor series approximations in the reciprocal design space. In combination with other techniques to improve efficiency, such as constraint deletion, regionalization, and design variable linking, they succeeded in uniting the work of both schools. This approximation concepts based approach forms the basis of the optimization modules in modern structural design software ASTROS, MSC.Nastran, Genesis, I-DEAS, iSight.

Approximations for structural optimization were initiated by the reciprocal approximation Schmit and Miura for stress and displacement response functions. Other intermediate variables were employed for plates. Combining linear and reciprocal variables, Starnes and Haftka developed a conservative approximation to improve buckling approximations. Fadel chose an appropriate intermediate design variable for each function based on a gradient matching condition for the previous point. Vanderplaats initiated a second generation of high quality approximations when he developed the force approximation as an intermediate response approximation to improve the approximation of stress constraints. Canfield developed a Rayleigh Quotient
Rayleigh quotient
In mathematics, for a given complex Hermitian matrix and nonzero vector , the Rayleigh quotient is defined as:For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose to the usual transpose . Note that for any real scalar ....

 approximation to improve the accuracy of eigenvalue approximations. Barthelemy and Haftka published a comprehensive review of approximations in 1993.

Recent MDO methods


MDO practitioners have investigated optimization
Optimization (mathematics)
In mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or...

 methods in several broad areas in the last dozen years. These include decomposition method
Decomposition method
In constraint satisfaction, a decomposition method translates a constraint satisfaction problem into another constraint satisfaction problem that is binary and acyclic. Decomposition methods work by grouping variables into sets, and solving a subproblem for each set...

s, approximation
Approximation
An approximation is an inexact representation of something that is still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.Approximations may be used because...

 methods, evolutionary algorithm
Evolutionary algorithm
In artificial intelligence, an evolutionary algorithm is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses some mechanisms inspired by biological evolution: reproduction, mutation, recombination, and selection...

s, memetic algorithm
Memetic algorithm
Memetic algorithms represent one of the recent growing areas of research in evolutionary computation. The term MA is now widely used as a synergy of evolutionary or any population-based approach with separate individual learning or local improvement procedures for problem search...

s, response surface methodology
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...

, reliability-based optimization, and multiobjective optimization
Multiobjective optimization
Multi-objective optimization , also known as multi-criteria or multi-attribute optimization, is the process of simultaneously optimizing two or more conflicting objectives subject to certain constraints....

 approaches.

The exploration of decomposition methods has continued in the last dozen years with the development and comparison of a number of approaches, classified variously as hierarchic and non-hierarchic, or collaborative and non-collaborative.
Approximation methods spanned a diverse set of approaches, including the development of approximations for surrogate models, variable fidelity models, and trust region management strategies. The development of multipoint approximations blurred the distinction with response surface methods. Kriging
Kriging
Kriging is a group of geostatistical techniques to interpolate the value of a random field at an unobserved location from observations of its value at nearby locations....

 methods became popular.

Response surface methodology
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...

, developed extensively by the operations research community, received much attention in the MDO community in the last dozen years. A driving force for their use has been the development of massively parallel systems for high performance computing, which are naturally suited to distributing the function evaluations from multiple disciplines that are required for the construction of response surfaces. Distributed processing is particularly suited to the design process of complex systems in which analysis of different disciplines may be accomplished naturally on different computing platforms and even by different teams.

Evolutionary methods led the way in the exploration of non-gradient methods for MDO applications. They also have benefited from the availability of massively parallel high performance computers, since they inherently require many more function evaluations than gradient-based methods. Their primary benefit lies in their ability to handle discrete design variables and the potential to find globally optimal solutions.

Reliability-based optimization (RBO) is a growing area of interest in MDO. Like response surface methods and evolutionary algorithms, RBO benefits from parallel computation, because the numeric integration to calculate the probability of failure requires many function evaluations. One of the first approaches employed approximation concepts to integrate the probability of failure. The classical first-order reliability method (FORM) and second-order reliability method (SORM) are still popular. Grandhi used appropriate normalized variables about the most probable point of failure, found by a two-point adaptive nonlinear approximation to improve the accuracy and efficiency. Southwest Research Institute
Southwest Research Institute
Southwest Research Institute , headquartered in San Antonio, Texas, is one of the oldest and largest independent, nonprofit, applied research and development organizations in the United States. Founded in 1947 by Thomas Slick, Jr., SwRI provides contract research and development services to...

 has figured prominently in the development of RBO, implementing state-of-the-art reliability methods in commercial software. RBO has reached sufficient maturity to appear in commercial structural analysis programs like MSC's Nastran
Nastran
NASTRAN is a finite element analysis program that was originally developed for NASA in the late 1960s under United States government funding for the Aerospace industry. The MacNeal-Schwendler Corporation was one of the principal and original developers of the public domain NASTRAN code...

.

Problem formulation


Problem formulation is normally the most difficult part of the process. It is the selection of design variables, constraints, objectives, and models of the disciplines. A further consideration is the strength and breadth of the interdisciplinary coupling in the problem.

Design variables


A design variable is a specification that is controllable from the point of view of the designer. For instance, the thickness of a structural member can be considered a design variable. Another might be the choice of material. Design variables can be continuous (such as a wing span), discrete (such as the number of ribs in a wing), or boolean (such as whether to build a monoplane or a biplane
Biplane
A biplane is a fixed-wing aircraft with two main wings. The Wright brothers' Wright Flyer used a biplane design, as did most aircraft in the early years of aviation. While a biplane wing structure has a structural advantage, it produces more drag than a similar monoplane wing...

). Design problems with continuous variables are normally solved more easily.

Design variables are often bounded, that is, they often have maximum and minimum values. Depending on the solution method, these bounds can be treated as constraints or separately.

Constraints


A constraint is a condition that must be satisfied in order for the design to be feasible. An example of a constraint in aircraft design is that the lift
Lift (force)
A fluid flowing past the surface of a body exerts a force on it. Lift is defined to be the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is defined to be the component of the fluid-dynamic force parallel to the flow...

 generated by a wing must be equal to the weight of the aircraft. In addition to physical laws, constraints can reflect resource limitations, user requirements, or bounds on the validity of the analysis models. Constraints can be used explicitly by the solution algorithm or can be incorporated into the objective using Lagrange multipliers.

Objectives


An objective is a numerical value that is to be maximized or minimized. For example, a designer may wish to maximize profit or minimize weight. Many solution methods work only with single objectives. When using these methods, the designer normally weights the various objectives and sums them to form a single objective. Other methods allow multiobjective optimization, such as the calculation of a Pareto front
Pareto efficiency
Pareto efficiency, or Pareto optimality, is an important concept in economics with broad applications in game theory, engineering and the social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution...

.

Models


The designer must also choose models to relate the constraints and the objectives to the design variables. These models are dependent on the discipline involved. They may be empirical models, such as a regression
Regression
Regression could refer to:* Regression , a defensive reaction to some unaccepted impulses* Regression analysis, a statistical technique for estimating the relationships among variables...

 analysis of aircraft prices, theoretical models, such as from computational fluid dynamics
Computational fluid dynamics
Computational fluid dynamics is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the millions of calculations required to simulate the interaction of liquids and gases with...

, or reduced-order models of either of these. In choosing the models the designer must trade off fidelity with analysis time.

The multidisciplinary nature of most design problems complicates model choice and implementation. Often several iterations are necessary between the disciplines in order to find the values of the objectives and constraints. As an example, the aerodynamic loads on a wing affect the structural deformation of the wing. The structural deformation in turn changes the shape of the wing and the aerodynamic loads. Therefore, in analysing a wing, the aerodynamic and structural analyses must be run a number of times in turn until the loads and deformation converge.

Standard form


Once the design variables, constraints, objectives, and the relationships between them have been chosen, the problem can be expressed in the following form:
find that minimizes subject to , and


where is an objective, is a vector of design variables, is a vector of inequality constraints, is a vector of equality constraints, and and are vectors of lower and upper bounds on the design variables. Maximization problems can be converted to minimization problems by multiplying the objective by -1. Constraints can be reversed in a similar manner. Equality constraints can be replaced by two inequality constraints.

Problem solution


The problem is normally solved using appropriate techniques from the field of optimization. These include gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

-based algorithms, population-based algorithms, or others. Very simple problems can sometimes be expressed linearly; in that case the techniques of linear programming
Linear programming
In mathematics, linear programming is a technique for optimization of a linear objective function, subject to linear equality and linear inequality constraints...

 are applicable.

Gradient-based methods

  • Adjoint equation
    Adjoint equation
    An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts. Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation. Methods based on solution of adjoint...

  • Newton's method
    Newton's method
    In numerical analysis, Newton's method , named after Isaac Newton and Joseph Raphson, is perhaps the best known method for finding successively better approximations to the zeroes of a real-valued function...

  • Steepest descent
  • Conjugate gradient
  • Sequential quadratic programming
    Sequential quadratic programming
    Sequential quadratic programming is one of the most popular and robust algorithms for nonlinear continuous optimization. The method is based on solving a series of subproblems designed to minimize a quadratic model of the objective subject to a linearization of the constraints...


Population-based methods

  • Genetic algorithm
    Genetic algorithm
    A genetic algorithm is a search technique used in computing to find exact or approximate solutions to optimization and search problems. Genetic algorithms are categorized as global search heuristics...

    s
  • Memetic algorithm
    Memetic algorithm
    Memetic algorithms represent one of the recent growing areas of research in evolutionary computation. The term MA is now widely used as a synergy of evolutionary or any population-based approach with separate individual learning or local improvement procedures for problem search...

    s
  • Particle swarm optimization
    Particle swarm optimization
    Particle swarm optimization is an algorithm modelled on swarm intelligence that finds a solution to an optimization problem in a search space, or model and predict social behavior in the presence of objectives.-Overview:...


Other methods

  • Random search
  • Grid search
  • Simulated annealing
    Simulated annealing
    Simulated annealing is a generic probabilistic metaheuristic for the global optimization problem of applied mathematics, namely locating a good approximation to the global minimum of a given function in a large search space. It is often used when the search space is discrete...

  • Harmony search
    Harmony search
    Harmony search is a metaheuristic algorithm mimicking the improvisation process of musicians. In the process, each musician plays a note for finding a best harmony all together...

  • Direct search
    Brute-force search
    In computer science, brute-force search or exhaustive search, also known as generate and test, is a trivial but very general problem-solving technique that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's...

  • IOSO
    IOSO
    IOSO is a multiobjective, multidimensional nonlinear optimization technology.-IOSO Approach:IOSO Technology is based on the response surface methodology approach....

     (Indirect Optimization based on Self-Organization)


Most of these techniques require large numbers of evaluations of the objectives and the constraints. The disciplinary models are often very complex and can take significant amounts of time for a single evaluation. The solution can therefore be extremely time-consuming. Many of the optimization techniques are adaptable to parallel computing
Parallel computing
Parallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently . There are several different forms of parallel computing: bit-level,...

. Much current research is focused on methods of decreasing the required time.

Also, no existing solution method is guaranteed to find the global optimum
Global optimization
Global optimization is a branch of applied mathematics and numerical analysis that deals with the optimization of a function or a set of functions to some criteria.- General :The most common form is the minimization of one real-valued function...

 of a general problem (see No free lunch in search and optimization). Gradient-based methods find local optima with high reliability but are normally unable to escape a local optimum. Stochastic methods, like simulated annealing and genetic algorithms, will find a good solution with high probability, but very little can be said about the mathematical properties of the solution. It is not guaranteed to even be a local optimum. These methods often find a different design each time they are run.

Commercial MDO Tools

  • HyperWorks HyperStudy (Altair Engineering
    Altair Engineering
    Altair Engineering is a product design and development, engineering software and grid computing software company. Altair was founded by Jim Scapa, George Christ, and Mark Kistner in 1985. Over its history, it has had various locations near Detroit, Michigan, USA...

    )
  • VisualDOC (Vanderplaats Research and Development)
  • HEEDS (Red Cedar Technology
    Red Cedar Technology
    Red Cedar Technology is a software development and engineering services company. Red Cedar Technology was founded by Michigan State University professors Ron Averill and Erik Goodman in 1999. The headquarters is located in East Lansing, MI, near MSU's campus. Red Cedar Technology develops and...

    )
  • IOSO
    IOSO
    IOSO is a multiobjective, multidimensional nonlinear optimization technology.-IOSO Approach:IOSO Technology is based on the response surface methodology approach....

     (Sigma Technology)
  • iSight (Engineous Software)
  • LS-OPT (Livermore Software Development Corporation)
  • modeFRONTIER
    ModeFRONTIER
    modeFRONTIER is a multi-objective optimization and design environment, written to couple CAD/computer aided engineering tools, Finite Element Structural Analysis and Computational Fluid Dynamics software. It is developed by ESTECO srl and provides an environment for product engineers and designers...

    (Esteco)
  • ModelCenter (Phoenix Integration)
  • Optimus (Noesis Solutions)