Required relationship between objective function and Pareto frontier orders: Practical implications

It is well known that the weighted sum aggregate objective function fails t o capture Pareto points that are located on a concave region of the Pareto frontier. Conditions are established for a general aggregate objective func tion to capture points on a concave Pareto frontier region. Specifically, t hese conditions are developed in terms of the relative orders of the Pareto frontier and aggregate objective function. These critical conditions can b e used in practice to allow an aggregate objective function to capture any potentially desirable Pareto point. Conversely, failure to satisfy these cr itical conditions can represent a pivotal failure point of the general appl ication of design optimization because we may fail to obtain the design we seek.