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| * But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5) | | * But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5) |
| * 它是一个弱帕累托最优,因为没有其他任何分配对上述两个主体是更优的(没有强帕累托改进)。 | | * 它是一个弱帕累托最优,因为没有其他任何分配对上述两个主体是更优的(没有强帕累托改进)。 |
− | * 但它不是一个强帕累托最优,因为这个George在其中得到第二顺位的资源的分配对George是严格更优的且对Alice是弱更优的(它是一个弱帕累托改进),它的分配方案为(10,5) | + | * 但它不是一个强帕累托最优,因为这个George在其中得到第二顺位的资源的分配对George是严格更优的且对Alice是弱更优的(它是一个弱帕累托改进),它的'''<font color="#32CD32">分配方案</font>'''为(10,5) |
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| As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1). | | As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1). |
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− | 作为一个示例,考虑一个有两个项的项分配问题,Alice 值为3,2,George 值为4,1。考虑将第一个项目分配给 Alice,第二个项目分配给 George,其中'''<font color="#ff8000">分配方案</font>'''为(3,1)。 | + | 作为一个示例,考虑一个有两个项的项分配问题,Alice 值为3,2,George 值为4,1。考虑将第一个项目分配给 Alice,第二个项目分配给 George,其中'''<font color="#32CD32">分配方案</font>'''为(3,1)。 |
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| * However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2). | | * However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2). |
| * 它是一个帕累托最优,因为其他任何离散分配(在不分离物品的情况下)都会使得某个主体变差。 | | * 它是一个帕累托最优,因为其他任何离散分配(在不分离物品的情况下)都会使得某个主体变差。 |
− | * 但是,它不是部分帕累托最优的,因为它是受该分配帕累托支配的。它分配给了Alice第一个资源的一半和第二个资源的全部,分配给了George第一个资源的一半。它的分配方案是(3.5,2)。 | + | * 但是,它不是部分帕累托最优的,因为它是受该分配帕累托支配的。它分配给了Alice第一个资源的一半和第二个资源的全部,分配给了George第一个资源的一半。它的'''<font color="#32CD32">分配方案</font>'''是(3.5,2)。 |
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| * "The <math>\epsilon</math>-constraints method".<ref>{{cite journal|title=On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization|journal=IEEE Transactions on Systems, Man, and Cybernetics|volume=SMC-1|issue=3|year=1971|pages=296–297|issn=0018-9472|doi=10.1109/TSMC.1971.4308298}}</ref><ref name="Mavrotas2009">{{cite journal|last1=Mavrotas|first1=George|title=Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems|journal=Applied Mathematics and Computation|volume=213|issue=2|year=2009|pages=455–465|issn=00963003|doi=10.1016/j.amc.2009.03.037}}</ref> | | * "The <math>\epsilon</math>-constraints method".<ref>{{cite journal|title=On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization|journal=IEEE Transactions on Systems, Man, and Cybernetics|volume=SMC-1|issue=3|year=1971|pages=296–297|issn=0018-9472|doi=10.1109/TSMC.1971.4308298}}</ref><ref name="Mavrotas2009">{{cite journal|last1=Mavrotas|first1=George|title=Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems|journal=Applied Mathematics and Computation|volume=213|issue=2|year=2009|pages=455–465|issn=00963003|doi=10.1016/j.amc.2009.03.037}}</ref> |
− | * “约束法”。 | + | * “ϵ-约束法”。 |
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