TY - GEN
T1 - In search of equitable solutions using multi-objective evolutionary algorithms
AU - Shukla, Pradyumn Kumar
AU - Hirsch, Christian
AU - Schmeck, Hartmut
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010
Y1 - 2010
N2 - Over the last two decades, evolutionary algorithms have been applied in solving multi-objective optimization problems. Most of these algorithms use the concept of Pareto-optimality to drive their search. However, many real-world multi-objective applications, in particular from location theory and general resource allocation models, require finding so-called equitably efficient points. These solutions form a subset of the Pareto-optimal set. In equitable efficiency, objective functions are considered impartial which makes the distribution of outcomes more important rather than assignment of several outcomes to an objective. In literature, we found two classical approaches to compute an equitably efficient point. These approaches rely on either solving a problem which is always non-differentiable or on solving a more difficult problem. In this paper, for the first time, a multi-objective evolutionary approach to this problem is proposed. The approach finds a diverse set of equitably optimal solutions and, in addition, tackles the non-differentiability which is inherently present in the classical approach. It is shown that even for simple differentiable problems, which belong to the realm of classical techniques, the evolutionary approach is a better choice than the classical ones. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of the evolutionary approach in solving a large class of both simple and complex equitable multi-objective optimization problems.
AB - Over the last two decades, evolutionary algorithms have been applied in solving multi-objective optimization problems. Most of these algorithms use the concept of Pareto-optimality to drive their search. However, many real-world multi-objective applications, in particular from location theory and general resource allocation models, require finding so-called equitably efficient points. These solutions form a subset of the Pareto-optimal set. In equitable efficiency, objective functions are considered impartial which makes the distribution of outcomes more important rather than assignment of several outcomes to an objective. In literature, we found two classical approaches to compute an equitably efficient point. These approaches rely on either solving a problem which is always non-differentiable or on solving a more difficult problem. In this paper, for the first time, a multi-objective evolutionary approach to this problem is proposed. The approach finds a diverse set of equitably optimal solutions and, in addition, tackles the non-differentiability which is inherently present in the classical approach. It is shown that even for simple differentiable problems, which belong to the realm of classical techniques, the evolutionary approach is a better choice than the classical ones. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of the evolutionary approach in solving a large class of both simple and complex equitable multi-objective optimization problems.
KW - Optimal point
KW - Inverted generational distance
KW - Warm start strategy
KW - Attainment surface
KW - Normal boundary intersection method
UR - http://www.scopus.com/inward/record.url?scp=78149260559&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-15844-5_69
DO - 10.1007/978-3-642-15844-5_69
M3 - Conference contribution
AN - SCOPUS:78149260559
SN - 3642158439
SN - 9783642158438
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 687
EP - 696
BT - Parallel Problem Solving from Nature, PPSN XI - 11th International Conference, Proceedings
T2 - 11th International Conference on Parallel Problem Solving from Nature, PPSN 2010
Y2 - 11 September 2010 through 15 September 2010
ER -