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I'm working on a project for an evolutionary algorithms course, and the problem we're trying to solve is multi-objective. We'll use NSGA-II but we also wanted to compare with some other MOEAs, however, we haven't been able to find good comparisons/benchmarks of these algorithms, so we don't really know how to decide.

Any insights will be appreciated.

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  • $\begingroup$ There are like a whole lot of it, try ZDT, WFG, some also have "complicated" Pareto set (I think it's from MOEA/D-DE paper), look at newer MOEA papers and see the references of the benchmark functions they use. $\endgroup$
    – Sanyou
    Oct 16, 2021 at 12:46
  • $\begingroup$ @Sanyou If you have an answer to the question (which adds something to the existing answers), you should formally write it below. $\endgroup$
    – nbro
    Oct 16, 2021 at 13:35

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The DEAP library (a Python library for EAs) contains some benchmarks. In particular, you may want to look at the following functions

Function(s) Reference/paper
kursawe ?
schaffer_mo [1]
dtlz1, dtlz2, dtlz3, dtlz4, dtlz5, dtlz6, dtlz7 [2]
fonseca [3]
poloni [4]
dent [5]

Besides the DEAP library repository, you might want to look at several well established MOEA frameworks such as PyMoo (Python) and PlatEMO (MatLab). Both have implementations of well known MOEAs and benchmark functions. You can look through their collection of benchmark functions for inspiration, and also implement your algorithm with those framework so that you can easily test your method's performance on their benchmark functions.

PlatEMO even has a GUI for experimental study, where you can choose the algorithms and the benchmark functions to test, followed by a Wilcoxon’s rank sum test to see how your algorithm really perform compared with other algorithms. For PyMoo you can create a new test file by following the existing examples, but, as far as I know, it doesn't have an experimental study platform similar to PlatEMO yet.

You may also be interested in the paper Scalable and Customizable Benchmark Problems for Many-Objective Optimization (2020).

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    $\begingroup$ +1 for mentioning the DEAP library, knowing that there are several well established Multi Objective Optimization libraries, I think the OP can start browsing benchmark function provided in the libraries, besides the obvious benefit of using the library as the platform to implement, evaluate, and compare the OP proposed algorithm with other algorithms. $\endgroup$
    – Sanyou
    Oct 16, 2021 at 13:53

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