The MVMO algorithm (Mean-Variance Mapping Optimization) has two main features: I) normalized search range for each dimension (associated to each optimization variable); ii) use of a mapping function to generate a new value of a selected optimization variable based on the mean and variance derived from the best solutions achieved so far. The current version of MVMO offers several alternatives. The single parent-offspring version is designed for use in case the evaluation budget is small and the optimization task is not too challenging. The population based MVMO requires more function evaluations, but the results are usually better. Both variants of MVMO can be improved considerably if additionally separate local search algorithms are incorporated. In this case, MVMO is basically responsible for the initial global search. This paper presents the results of a study on the use of the hybrid version of MVMO, called MVMO-PH (population based, hybrid), to solve the IEEE-CEC 2018 test suite for single objective optimization with continuous (real-number) decision variables. Additionally, two new mapping functions representing the unique feature of MVMO are presented.

Mean-Variance Mapping Optimization (MVMO) belongs to the family of evolutionary algorithms, and has proven to be competitive in solving computationally expensive problems proposed in the Icompetitions CEC2014, CEC2015, and CEC2016. MVMO can tackle such problems by evolving a set of solutions (population based approach) or a single solution (single parent-offspring approach). The evolutionary mechanism of MVMO performs within a normalized search space in the range [0, 1]. The power of MVMO stems from its ability - based on statistical analysis of the evolving solution based on a mapping function - to adaptively shift the search priority from exploration to exploitation. This paper introduces a newly defined mapping function as well as a new rule for using an embedded local search strategy, and presents several tests conducted by using the test bed of the CEC2018 competition. Numerical results indicate significant improvements on the results obtained in CEC2016 competition.