On Multiple-Objective Design Optimization by Goal Methods

In the design of various engineering systems and, in lparticular, the integrated/simultaneous design of large space structures and their vibration control systems, there are more than one objectives for which the design must be optimized. Since the usefullness of the method of weighted sum for solving non-convex multiple-objective optimization problems is severely limited, the designer normally needs to find other methods, such as various goal methods, for general applications. The current goal methods, i.e., least deviations from the goals, goal programming, global criterion, and goal attainment, are found to have a common drawback. The "optimal" solutions thereby obtained may not even meet the basic multiple-objective optimality requirement that they be Pareto optimal, i.e., inferior to no other solution. Therefore, inferior solutions may be mistaken as the optimal solutions of the original multiple-objective problem.