In MOO the aim of optimization algorithms is finding a set of (good) solution (well) distributed along the (optimal) Pareto Front. There is a trade-of between the quality of the found solutions and their distribution along the Pareto Front. Thus, how can the performance of different MOO algorithms be compared?
Is there a way we can apply fractal based or voronoi index based approach to solve the mentioned multi object optimization (MOO) problem ? They are very much part of the evolutionary computational models and non-linear systems.
The following three aspects should be considered for comparing the performance of multi-objective optimization algorithms:
(1) Closeness to the true Pareto front, also referred as convergence to the known Pareto optimal front, can be measured using distance from true Pareto front
(2) Spread (Distribution) along the Pareto front, can be measured using spacing metric, diversity metric
(3) Number of solutions in the non-dominated set
Moreover, there are metrics such as hyper-volume, coverage, R Metric which considers combination of convergence and spread of solutions.
If we know the true Pareto front for the given problem then the closeness to the true Pareto front can be measured. In case, we don't have information regarding true Pareto front, then hyper-volume and space metric can be used.
1. Number of Pareto solutions.
2. The diversity of non-dominated solutions which are achieved by an algorithm.
3. The nearness among the Pareto solutions and Ideal point (0,0) (After normalization).
4. A combination Pareto set is constructed and the percentage of the solution belonging to each test is computed (Quality metric).
Hi Antonio.
A set of non-dominated solutions generated by an optimiser can be characterised in three key areas: Proximity, Diversity, and Pertinence. There are many different performance metrics available in the literature to assess these characteristics.
I personally would recommend the Hypervolume Indicator, this is because this performance indicator does not require knowledge of the true Pareto-front. This feature is important when benchmarking on real-world problems (rather than synthetic ones).
Something to take into consideration is whether you have selected a sufficient sample size and non-parametric test to identify the significance of your results.
Recently IGD measure is used by authors to compare their solutions.
The IGD description and benchmarks can be find at :
http://dces.essex.ac.uk/staff/zhang/MOEAcompetition/cec09testproblem0904.pdf.pdf
This paper could be helpful to you: Sarker, R. and Coello, C. (2002) “Assessment Methodologies for Multiobjective Evolutionary Algorithms”, In Evolutionary Optimization, R. Sarker, M. Mohammadian and X. Yao (edited), Kluwer Academic Publishers, Boston, pp177-195.
generally comparison of the algorithm in terms of "whether there is a variance in your result" you can apply ANOVA followed by a post-hoc test such as t-test to find the best one among the algorithms
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