Jan and Deb, extended the well-know NSGA-II to deal with many-objective optimization problem, using a reference point approach, with non-dominated sorting mechanism. The newly developed algorithm is simply called: NSGA-III. The main reference paper is available to download, here. In this post, we are going to share with you, the MATLAB implementation of NSGA-III, as an open source project. The ...

One of the classic approaches to deal with multi-objective optimization problems, is decomposition, which means that a multi-objective is decomposed to several (theoretically infinite) single-objective optimization problems. Decomposed objective functions, can be defined using several methods, like weighted sum of objectives and distance (or norm) of difference vector of objectives and a predefined ideal point in the objective space. However, ...

Pareto Envelope-based Selection Algorithm II (PESA-II) is a multi-objective evolutionary optimization algorithm, which uses the mechanism of genetic algorithm together with selection based on Pareto envelope. PESA-II uses an external archive to store the approximate Pareto solutions. Parents and mutants are selected from this external archive, based on the grids created based on the geographical distribution of archive members. This ...

Strength Pareto Evolutionary Algorithm 2 (SPEA2) is an extended version of SPEA multi-objective evolutionary optimization algorithm. This algorithm utilized a mechanism like k-Nearest Neighbor (kNN) and a specialized ranking system to sort the members of the population, and select the next generation of population, from combination of current population and off-springs created by genetic operators (mutation and crossover). SPEA2 is ...

Non-dominated Sorting Genetic Algorithm II (NSGA-II) is a multi-objective genetic algorithm, proposed by Deb et al., in 2002. It is an extension and improvement of NSGA, which is proposed earlier by Srinivas and Deb, in 1995. In the structure of NSGA-II, in addition to genetic operators, crossover and mutation, two specialized multi-objective operators and mechanisms are defined and utilized: Non-dominated ...