区间目标函数离散最优化问题近似解的代表性
On the representativeness of approximate solutions of discrete optimization problems with interval objective function
摘要：
本文考虑目标函数系数为区间不确定性的离散最优化问题。区间不确定性模型测量误差。可能的最优解是对于某些可能的系数值最优的解。可能解决方案的概率是获得解决方案为最优的系数的概率。同样，我们定义的概念，一个可能的近似解与给定的精度和概率的解决方案。可能的近似解是通过某种固定的近似算法（例如，通过贪婪算法）针对系数的某些可能值获得的近似解。这种解的概率是获得这种系数的概率，该系数使算法产生解作为其输出。如果最优解或近似可能解的概率小于某个边界值，则我们认为最优解或近似可能解是不敏感的。平均近似解是系数区间中点的可能近似解。该解可视为系数精确值的近似解。我们表明，个别离散最优化问题的实例与非代表性的平均值近似解的份额可能是足够宽的误差和边界值相当小的值。对于任何其他可能的近似解也是如此：它们都可能是不具有代表性的。
英文摘要：
We consider discrete optimization problems with interval uncertatinty of objective function coefficients. The interval uncertainty models measurements errors. A pos\-sible optimal solution is a solution that is optimal for some possible values of the coefficients. Pro\-ba\-bi\-li\-ty of a possible solution is the probability to obtain such coefficients that the solution is optimal. Similarly we define the notion of a possible approximate solution with given accuracy and probability of the solution. A possible approximate solution is an approximate solution that is obtained for some possible values of the coefficients by some fixed approximate algorithm, e.g. by the greedy algorithm. Pro\-ba\-bi\-li\-ty of a such solution is the probability to obtain such coefficients that the algorithm produces the solution as its output. We consider optimal or approximate possible solution un\-re\-pre\-sen\-ta\-ti\-ve if its probability less than some boundary value. The mean approximate solution is a possible approximate solution for midpoints of the coefficients intervals. The solution may be treated as approximate solution for exact values of the coefficients. We show that the share of individual discrete optimization problems instances with unrepresentative mean approximate solution may be wide enough for rather small values of error and the boundary value. The same is true for any other possible approximate solution: all of them may be unrepresentative.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
