Paper Info
Title
Efficient Computation Of Two-Dimensional Solution Sets Maximizing The Epsilon-Indicator
Abstract
The majority of empirical comparisons of multi-objective evolutionary algorithms (MOEAs) are performed on synthetic benchmark functions. One of the advantages of synthetic test functions is the a-priori knowledge of the optimal Pareto front. This allows measuring the proximity to the optimal front for the solution sets returned by the different MOEAs. Such a comparison is only meaningful if the cardinality of all solution sets is bounded by some fixed k. In order to compare MOEAs to the theoretical optimum achievable with k solutions, we determine best possible epsilon-indicator values achievable with solution sets of size k, up to an error of delta. We present a new algorithm with runtime O (k . log(2) (delta(-1))), which is an exponential improvement regarding the dependence on the error delta compared to all previous work. We show mathematical correctness of our algorithm and determine optimal solution sets for sets of cardinality k 2 {2, 3, 4, 5, 10, 20, 50, 100, 1000} for the well known test suits DTLZ, ZDT, WFG and LZ09 up to error delta = 10(-25).
Year
Venue
Field
2015
2015 IEEE CONGRESS ON EVOLUTIONARY COMPUTATION (CEC)
Evolutionary algorithm,Cardinality,Multi-objective optimization,Artificial intelligence,Approximation algorithm,Mathematical optimization,Algorithm design,Evolutionary computation,Algorithm,Solution set,Machine learning,Mathematics,Bounded function
DocType
Citations 
PageRank 
Conference
2
0.37
References 
Authors
15
3
Name
Order
Citations
PageRank
Karl Bringmann142730.13
Tobias Friedrich2548.19
Patrick Klitzke3281.29