Joshua Knowles

The Pareto Archived Evolution Strategy (PAES)


The Pareto Archived Evolution Strategy (PAES) is a multiobjective optimizer which uses a simple (1+1) local search evolution strategy. Nonetheless, it is capable of finding diverse solutions in the Pareto optimal set because it maintains an archive of nondominated solutions which it exploits to estimate accurately the quality of new candidate solutions.

Three versions, (1+1), (1+lambda) and (mu+lambda)-PAES have been developed. Each of these versions has been tested against two well known multiobjective evolutionary algorithms - the Niched Pareto Genetic Algorithm (NPGA) and a nondominated sorting GA (NSGA). Tests were carried out using five test functions (f2-f6) and results have been processed using statistical techniques introduced by Fonseca and Fleming. C code for each of the test functions and the statistical techniques are available below. Please drop me an email if you use any of these resources.

PAES is described in detail in two of the publications listed below. The submission to Evolutionary Computation is the largest paper and includes use of Fonseca and Fleming's statistical techniques to measure the performance of PAES with respect to five test functions.

In August 1999, PAES was tested on six different test functions. These functions, designed by Kalyanmoy Deb, each to capture and isolate a specific problem feature known to present difficulties to multiobjective optimizers, were first used in a paper by Zitzler, Deb and Thiele (Technical Report 70, TIK) in which eight multiobjective evolutionary algorithms were compared. We use the raw results from the study by Zitzler et al. to compare the performance of PAES with the eight algorithms tested in that study. The results showed that PAES exhibits at least comparable performance to the best algorithm from the Zitzler et al. study, the Strength Pareto Evolutionary Algorithm (SPEA), on four of the six Deb test functions. The raw results from the Zitzler et al. study are available here. The third paper below describes this work in more detail.

For the first time, we are making a skeleton version of our PAES code available for download here. See the resources section below. If you do download this code, please drop me an e-mail to let me know.


  • Knowles, J.D. and Corne, D.W. (2003) Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Transactions on Evolutionary Computation, 7(2), pp. 100-116. April. Draft version. Original available from IEEE Press. More about archives is available here.
  • Knowles, J.D., Corne, D.W. (2000) Approximating the nondominated front using the Pareto Archived Evolution Strategy. Evolutionary Computation, 8(2), pp. 149-172. Draft version. Final version obtainable from MIT press.
  • Knowles, J.D., Corne, D.W. (1999) The Pareto Archived Evolution Strategy : A New Baseline Algorithm for Pareto Multiobjective Optimisation. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC'99), pages 98-105.
  • Knowles, J.D., Corne, D.W. (1999) Local Search, Multiobjective Optimization and the Pareto Archived Evolution Strategy. In Proceedings of the Third Australia-Japan Joint Workshop on Intelligent and Evolutionary Systems, pages 209-216.