What Is Optimization Toolbox?

Multiobjective OptimizationMultiobjective Optimization• “Introduction” on page 3-43• “Weighted Sum Method” on page 3-46• “Epsilon-Constraint Method” on page 3-47• “Goal Attainment Method” on page 3-49• “Algorithm Improvements for the Goal Attainment Method” on page 3-50IntroductionThe rigidity of the mathematical problem posed by the general optimizationformulation given in GP (Equation 3-1) is often remote from that of a practicaldesign problem. Rarely does a single objective with several hard constraintsadequately represent the problem being faced. More often there is a vector ofobjectivesthat must be traded off in someway.Therelativeimportanceoftheseobjectives is not generally known untilthe system’s best capabilities are determined and tradeoffs between theobjectives fully understood. As the number of objectives increases, tradeoffsare likely to become complex and less easily quantified. There is muchreliance on the intuition of the designer and his or her ability to expresspreferences throughout the optimization cycle. Thus, requirements for amultiobjective design strategy are to enable a natural problem formulation tobeexpressed,yettobeabletosolvetheproblemandenterpreferencesintoanumerically tractable and realistic design problem.Multiobjective optimization is concerned with the minimization of a vector ofobjectives F(x) that can be the subject of a number of constraints or bounds.(3-44)Note that, because F(x) is a vector, if any of the components of F(x) arecompeting,thereisnouniquesolutiontothisproblem.Instead,theconceptof noninferiority [41] (also called Pareto optimality [4] and [6]) must be used3-43