MOMBI

MOMBI: Many Objective Metaheuristic Based on the R2 Indicator

Source code in C language:

Weight vector generation by the Simplex Lattice Design method ver 1.0 (February 20, 2016, 7.2K)
MOMBI-II ver 1.0 (February 20, 2016, 402 K)
MOMBI ver 1.0 (June 23, 2013, 3.9 MB)

Publications:

R. Hernández Gómez and C. A. Coello Coello "Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization". In Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation (GECCO'2015), pp. 679-686, ACM, 2015. Bibtex

Abstract: In recent years, performance indicators were introduced as a selection mechanism in multi-objective evolutionary algorithms (MOEAs). A very attractive option is the R2 indicator due to its low computational cost and weak-Pareto compatibility. This indicator requires a set of utility functions, which map each objective to a single value. However, not all the utility functions available in the literature scale properly for more than four objectives and the diversity of the approximation sets is sensitive to the choice of the reference points during normalization. In this paper, we present an improved version of a MOEA based on the R2 indicator, which takes into account these two key aspects, using the achievement scalarizing function and statistical information about the population's proximity to the true Pareto optimal front. Moreover, we present a comparative study with respect to some other emerging approaches, such as NSGA-III (based on Pareto dominance), Delta_p-DDE (based on the Delta_p indicator) and some other MOEAs based on the R2 indicator, using the DTLZ and WFG test problems. Experimental results indicate that our approach outperforms the original algorithm as well as the other MOEAs in the majority of the test instances, making it a suitable alternative for solving many-objective optimization problems.

R. Hernández Gómez and C. A. Coello Coello. A New Multi-Objective Evolutionary Algorithm Based on the R2 Indicator. Master Thesis, Department of Computer Science, CINVESTAV-IPN, Mexico City, Mexico, November 2013.
Download Thesis (September 4th, 2014, 2.8M) Download Appendix of Results (September 4th, 2014, 30M)

R. Hernández Gómez and C. A. Coello Coello "MOMBI: A New Metaheuristic for Many-Objective Optimization Based on the R2 Indicator". In Congress on Evolutionary Computation (CEC'2013), vol. 1, pp. 2488-2495, IEEE Service Center, 2013. Bibtex
Download comparative study of MOEAs (June 12th, 2013, 279K)

Abstract: The incorporation of performance indicators as the selection mechanism of a multi-objective evolutionary algorithm (MOEA) is a topic that has attracted increasing interest in the last few years. This has been mainly motivated by the fact that Pareto-based selection schemes do not perform properly when solving problems with four or more objectives. The indicator that has been most commonly used for being incorporated in the selection mechanism of a MOEA has been the hypervolume. Here, however, we explore the use of the R2 indicator, which presents some advantages with respect to the hypervolume, the main one being its low computational cost. In this paper, we propose a new MOEA called Many-Objective Metaheuristic Based on the R2 Indicator (MOMBI), which ranks individuals using a utility function. The proposed approach is compared with respect to MOEA/D (based on scalarization) and SMS-EMOA (based on hypervolume) using several benchmark problems. Our preliminary experimental results indicate that MOMBI obtains results of similar quality to those produced by SMS-EMOA, but at a much lower computational cost. Additionally, MOMBI outperforms MOEA/D in most of the test instances adopted, particularly when dealing with high-dimensional problems having complicated Pareto fronts. Thus, we believe that our proposed approach is a viable alternative for solving many-objective optimization problems.