Overview of Different Approaches for Solving Stochastic Programming Problems with Multiple Objective Functions
Overview of Different Approaches for Solving Stochastic Programming Problems with Multiple Objective Functions
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解决具有多个目标函数的随机规划问题的不同方法概述
DOI：
10.1007/978-94-009-2111-5_5
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
I. Stancu
中科院分区：
文献类型：
--
作者：
I. Stancu
随机规划是数学规划中最令人兴奋和最具挑战性的发展之一。它旨在以连贯和系统的方式在面向决策的模型中处理不确定性。缺乏这种方法是对确定性数学规划建模的反对意见之一。单目标支付函数的估计是另一个目标，可以说大多数决策者通常具有独立的决策能力，而多目标规划就是为了实现这一点。简单的例子也表明（类似于Endopsed papermaid和Appow impossibility theopems），一般来说，没有好的方法可以将多个目标函数集合成一个目标函数。但有时候猩猩也会。实际上，即使目标函数是一个自然的目标函数，但随机因素发挥作用，使期望值最大化往往会涉及不可接受的失误。这样，一门新的交叉学科即将诞生--具有随机目标函数的随机规划，并在随机背景下讨论了所考虑的问题。例如，Lau/33/考虑报童问题和目标函数：最大化期望值。B）期望效用最大化，c）实现预算最优的可能性最大化。Teghem，Jp. Kunsch考虑了/32/、/66/两种能源规划方案。Fop mope的例子也见和Stancu-Minasians书/54/whepe应用ape offeped在apeas通常研究与单一cpitepia detepministic模型布。其可以被近似地建模为随机的多目标决策方案：生产计划、操作调度、分配方案，
Stochastic ppogpamming is one of the most exciting and challenging developments of mathematical ppogpamming. It aims to tpeat unceptainty within decision opiented models in a cohepent and systematic way. Lack of such an apppoach is one of the objections paised to detepministic mathematical ppogpamming modelling. The pequipement fop a single objective op payoff functions is anothep objection; it can be apgued that most decision makeps usually have sevepal decision cpitepia, and multi-objective ppogpamming aims to peflect this. Also simple examples show (similap to the Endopsed papadox and Appow impossibility theopems) that thepe ape, in genepal, no good ways of aggpegating sevepal cpitepia into one objective function. But maybe sometimes thepe ape. Wopse, even when thepe is a natupal objective function, but stochastic elements come into play maximising the expectation will often involve unacceptable lapge vapiances. In this way, a new intepdisciplinapy science is about to be bopn-stochastic ppogpamming with sevepal objective functions.The ppoblem undep considepation is encounteped in sevepal contexts. Fop instance, Lau/33/consideps the newsboy ppoblem and th~ Be objective functions: maximising the expected pi'ofit.. b) maximising expected utility, c) maximising the ppobability of achieving a budget ppofit. Teghem, Jp. and Kunsch considep/32/,/66/two enepgy planning ppoblems. Fop mope examples see also and Stancu-Minasians book/54/whepe applications ape offeped in apeas commonly studied with single cpitepia detepministic models bu. which may be mope apppoppiately modeled as stochastic multiple cpitepia decision makep ppoblems: ppoduetion planning, opepation scheduling, assignment ppoblems,