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A hierarchical satisfying optimal algorithm incorporating different importance and preemptive priorities is formulated. With the priority structure given by the decision-maker in the constrained multi-objective multi-degree-of-freedom optimization (CMMO) problem, the commonly used quadratic programming model is converted into a two-level optimization problem solved by the tolerant lexicographic method and the varying-domain optimization method. In contrast to previous works, the proposed approach allows the decision-maker to determine a desirable achievement degree for each goal to reflect explicitly the relative importance of these goals. The resulting solutions satisfy both the preemptive priority structure and have the maximum achievement degrees in sum. The power of the proposed approach is demonstrated with an example.
A hierarchical satisfying optimal algorithm incorporating different importance and preemptive priorities is formulated. With the priority structure given by the decision-maker in the constrained multi-objective multi-degree-of-freedom optimization (CMMO) problem, the commonly used quadratic programming model is converted into a two-level optimization problem solved by the tolerant lexicographic method and the varying-domain optimization method. importance of these goals. The power of the proposed approach is rendered with an example.