论文（设计）基于满意度水平的多目标群决策问题的迭代算法.doc

基于满意度水平的多目标群决策问题的迭代算法摘要基于满意度水平的概念,本文提出了在实现决策个体各自的满意度水平的基础上,使群体的联合满意度极大化的群决策规则。根据这一规则去求多目标群决策问题的最佳调和解。由于目标间的冲突性,当各决策个体的满意度水平过高时,会导致群决策的最佳调和解集为空集。本文讨论并给出了降低和修正各决策个体满意度水平的迭代方法,并将整个求解过程总结为一种算法,使之易于在计算机上实现;文中最后还给出了数值算例。关键词:满意度,权,最佳调和解1引言现已有为数不少的解决多目标群决策问题的方法。集结个人的效用成为群效用,然后对群效用极大化求解1,2就是其中一种常用的方法。这种方法在概念上非常清楚,其理论价值也较高,但是由于个人效用函数常不易确定,即使确定出来也不是唯一的在基数效用函数的基础上经过正线性变换,仍然能作为效用函数而同样正确地反映一个人的偏好。于是效用函数的基点和单位不尽相同,难于进行人与人之间的效用比较,从而就难于正确地构造群效用函数,这就使该方法在实际应用上存在相当的困难。另一种常用的方法是用对策论方法。诚然,对策论方法可以比较有效地用于解决某些具有冲突目标的实际问题3,但对策论中的方法几乎都基于类似Nash平衡点这样的解概念,而许多实际目标群决策问题并不存在这样的解。鉴于群效用函数难以建立及Nash解存在性的难以保证,我们试图绕过上述困难,另辟蹊径。基于满意度水平的概念,本文设计了一种算法,用这种算法可以求得一种方案,该方案就群体的联合满意度来说是最优的,同时对各决策个体来说又是较为满意和较为公平合理的。2 满意度概念设决策群体G由n个有效决策个体DMi(i=1,2,n)组成。其中每个DMi的决策问题经过规范化处理后可表达为 8结束语本文引入了决策个体对各个目标的满意度的概念,用赋权的方法导出了决策个体的总体满意度和群体的联合满意度,提出了在满足各决策个体各自满意度水平的基础上,使群体的联合满意度极大化作为群的折衷决策的规则,根据这一规则得出群决策的最佳调和解。当个体的满意度水平过高而使调和解不存在时,首先确定各个体的让步总量,然后通过求解使个体的总体满意度极大化问题,算出个体在各目标上的让步分量。整个调整过程通过迭代逐步进行。在降低和修正各满意度水平的过程中,既考虑了各决策个体在决策中的实际地位,又使个体的总体满意度尽可能大,因而是合理的。对示例的仿真结果表明该算法是有效的、实用的。本文所考虑的群决策问题是针对这样的情形:决策个体在群决策中的地位虽有量上的差别,但无层次上的差别。若群决策中的决策个体处在若干个不同的优先级(层次)上,即他们的地位之间具有“主从”不对称性,对于这种情形的多目标群决策问题将另文讨论。131997年3月郭耀煌等:基于满意度水平的多目标群决策问题的迭代算法作者：郭耀煌徐飞张炜(西南交通大学经济管理学院)来源：第11卷第1期管理工程学报Vol.11No.11997年3月Editor's note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the world's first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, I've still seen many important weather and space events, but right now, if you were sitting next to me, you'd hear my foot tapping rapidly under my desk. I'm anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.It's like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line "we" would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and "capcom" (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, "Fearless Felix" will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, he'll be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes it's not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it won't. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way I'd miss this.