What Is Optimization Toolbox?

3 Standard AlgorithmsWeighted Sum MethodThe weighted sum strategy converts the multiobjective problem of minimizingthe vector into a scalar problem by constructing a weighted sum of allthe objectives.(3-48)The problem can then be optimized using a standard unconstrainedoptimization algorithm. The problem here is in attaching weightingcoefficients to each of the objectives. The weighting coefficients do notnecessarily correspond directly to the relative importance of the objectivesor allow tradeoffs between the objectives to be expressed. Further, thenoninferior solution boundary can be nonconcurrent, so that certain solutionsare not accessible.This can be illustrated geometrically. Consider the two-objective case in thefigure below. In the objective function space a line, L,is drawn.The minimization can be interpreted as finding the value of c or which L justtouches the boundary of as it proceeds outwards from the origin. Selectionof weights and , therefore, defines the slope of L, which in turn leads tothe solution point where L touches the boundary of .Figure 3-9:Geometrical Representation of the Weighted Sum Method3-46