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A feasible point <math>x</math> is called ''efficient'' if there is no feasible point <math>y</math> with <math>Px \leq Py</math>, <math>Px \neq Py</math>, where <math>\leq</math> denotes the component-wise ordering.
Often in the literature, the aim in multiple objective linear programming is to compute the set of all efficient extremal points.....<ref name="EckerKouada1978">{{cite journal|last1=Ecker|first1=J. G.|last2=Kouada|first2=I. A.|title=Finding all efficient extreme points for multiple objective linear programs|journal=Mathematical Programming|volume=14|issue=1|year=1978|pages=249–261|issn=0025-5610|doi=10.1007/BF01588968|s2cid=42726689}}</ref> There are also algorithms to determine the set of all maximal efficient faces.<ref name="EckerHegner1980">{{cite journal|last1=Ecker|first1=J. G.|last2=Hegner|first2=N. S.|last3=Kouada|first3=I. A.|title=Generating all maximal efficient faces for multiple objective linear programs|journal=Journal of Optimization Theory and Applications|volume=30|issue=3|year=1980|pages=353–381|issn=0022-3239|doi=10.1007/BF00935493|s2cid=120455645}}</ref> Based on these goals, the set of all efficient (extreme) points can be seen to be the solution of MOLP. This type of solution concept is called ''decision set based''.<ref name="Benson1998">{{cite journal|title=An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem|last1=Benson|first1=Harold P.|journal=Journal of Global Optimization|volume=13|issue=1|year=1998|pages=1–24|issn=0925-5001|doi=10.1023/A:1008215702611|s2cid=45440728}}</ref> It is not compatible with an optimal solution of a linear program but rather parallels the set of all optimal solutions of a linear program (which is more difficult to determine).
Efficient points are frequently called ''efficient solutions''. This term is misleading because a single efficient point can be already obtained by solving one linear program, such as the linear program with the same feasible set and the objective function being the sum of the objectives of MOLP.<ref name="Ehrgott2015">{{cite book|last1=Ehrgott|first1=M.|title=Multicriteria Optimization|publisher=Springer|year=2005|doi=10.1007/3-540-27659-9|isbn=978-3-540-21398-7|citeseerx=10.1.1.360.5223}}</ref>
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