cMLSGA: A Co-Evolutionary Multi-Level Selection Genetic Algorithm for Multi-Objective Optimization

In practical optimisation the dominant characteristics of the problem are often not known prior. Therefore, there is a need to develop general solvers as it is not always possible to tailor a specialised approach to each application. The hybrid form of Multi-Level Selection Genetic Algorithm (MLSGA) already shows good performance on range of problems due to its diversity-first approach, which is rare among Evolutionary Algorithms. To increase the generality of its performance this paper proposes a distinct set of co-evolutionary mechanisms, which defines co-evolution as competition between collectives rather than individuals. This distinctive approach to co-evolutionary provides less regular communication between sub-populations and different fitness definitions between individuals and collectives. This encourages the collectives to act more independently creating a unique sub-regional search, leading to the development of co-evolutionary MLSGA (cMLSGA). To test this methodology nine genetic algorithms are selected to generate several variants of cMLSGA, which incorporates these approaches at the individual level. The new mechanisms are tested on over 100 different functions and benchmarked against the 9 state-of-the-art competitors in order to find the best general solver. The results show that the diversity of co-evolutionary approaches is more important than their individual performances. This allows the selection of two competing algorithms that improve the generality of cMLSGA, without large loss of performance on any specific problem type. When compared to the state-of-the-art, the proposed methodology is the most universal and robust, leading to an algorithm more likely to solve complex problems with limited knowledge about the search space.