Quantitative Comparison of Approximate Solution Sets for Bi‐criteria Optimization Problems*
提出集成偏好泛函（IPF）来定量比较双目标优化问题中近帕累托最优解集的质量，帮助决策者评估不同启发式算法的后验解集。
ABSTRACT We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near‐pareto‐optimal solutions to bi‐criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives.