选择Pareto非劣解最优方案的量化方法:性价比法

针对多目标优化问题,提出了便于决策者以其偏好选择Pareto非劣解的量化方法——性价比法.通过剖析决策者选择最优方案的基本原则,发现如果从理性出发,以市场法则进行比选,则决策者无论有何偏好,以较低价格得到较高性能的产品,即获得高性价比应是其共同的愿望.仔细观察Pareto前沿分布,可以看到其排布特点具有恒递增或恒递减趋势,且大多分布不均匀,这意味着其中蕴含有不同的变化率及敏感性,从中可以挖掘出新的内在规律性.由这一认识出发,借鉴"性价比"概念,构造出各相邻非劣解对应目标函数值的平均变化率,得到了类似于"性价比"概念的灵敏比;将灵敏比无量纲化后,根据支配关系,筛选出Pareto非劣解集中新的非支配子集,进一步缩小了选择范围.以上述成果为基础,提出了各Pareto非劣解相对于不同目标函数偏向度的计算方法,实现了Pareto非劣解的量化评价,进而有助于决策者根据偏好选择非劣解.最后,通过具体实例的计算,验证了文中所述方法的可行性和有效性.本文研究对于多目标优化的求解与应用具有很好的参考价值.

A quantitative method to select the best option from Pareto non dominated solutions:Cost performance method

Aiming at multi-objective optimization, we present a quantitative method-cost performance method for decision-makers to select the Pareto non-inferior solution according to their preference. By analyzing the basic principle of optimal solution selecting, we find that, from the perspective of rationality and market rules, no matter what preference decision-makers have, getting products with higher performance at lower price, known as cost-effective products, is their common desire. By observing the distribution of Pareto front carefully, the constant increasing or decreasing trend of the distribution can be found, and most of Pareto front are not evenly distributed, it means there are different change rate and sensitivity among Pareto non-inferior solutions, so new inner regularity can be find from these characteristics. Combining with this discovery and learning from the concept of effective on cost, we construct the average change rate of the objective function values of the adjacent non-inferior solutions, and obtain the sensitivity ratio which is similar to the concept of cost performance. After nondimensionalizing the sensitivity ratios, the new subset of non-dominated solutions can be screened out from Pareto non-inferior solution set based on dominance relationship, and this method can narrows the selection range. According to the above research results, we present the calculation method of preference degree of each Pareto non-inferior solution on different objective function and achieve quantitative evaluation of Pareto non-inferior solution which can help decision maker to select the Pareto non-inferior solution with their preference. Finally, a practical example is illustrated to verify the feasibility and validity of the proposed method. This study has high reference value for solution and application of multi-objective optimization.