Mean-variance mapping optimization (MVMO) is a novel optimization algorithm. The algorithm has been conceived and developed by Prof. István Erlich, the head of the Institute of Electrical Power Systems at the University Duisburg-Essen.

MVMO falls into the category of the so-called "population-based stochastic optimization techniques". The basic concept shares certain similarities with other heuristic approaches. But the novel feature is its use of special mapping function applied for mutating the offspring on the basis of the mean and variance of the n-best population attained so far. The output of this mapping function is always inside the range [0,1]. This means violation of the variable limits during the search process cannot occur. The shape and location of the mapping curve are adjusted according to the progress of the search process, and MVMO updates the candidate solution around the best solution in every iteration step. Thanks to the well-designed balance between search diversification and intensification, MVMO can find the optimum quickly with minimum risk of premature convergence.

So far MVMO has successfully been applied for the solution of different power system optimization problems such as:

• the solution of the optimal reactive power dispatch problem
• the optimal simultaneous dispatch of energy and reserve
• the optimal transmission expansion planning
• the identification of gaussian mixture models
• the identification of dynamic equivalents
• the optimal location and coordinated tuning of power system damping controllers

Numerical comparisons between MVMO and some basic and enhanced evolutionary algorithms have shown that MVMO exhibits a better performance, especially in terms of convergence speed.

The first swarm implementation of MVMO, named as MVMO^S, extends the innate power of global searching of the classical MVMO by starting the search with a set of particles (i.e. swarm), each having its own memory and represented by the corresponding archive and mapping function, as well as by allowing information exchange and dynamic reduction of the swarm size trough simple rules.

Along this spirit, a hybrid variant of MVMO, referred to as MVMO-SH, has been recently developed. Apart from being a swarm intelligence based procedure, it incorporates local search and multi-parent crossover strategies to increase the search diversity while striving for a balance between exploration and exploitation. Enhanced schemes for mutation via mapping function and crossover are also incorporated. Unlike existing swarm-based optimization algorithms, MVMO-SH does not strictly require several particles to proceed. Hence, a single particle approach, which entails that MVMO-SH performs as MVMO, may be sufficient for less challenging optimization problems.

A free MATLAB based source code of the MVMO-SH optimization tool including a demo is available for download here. The download file includes:

• The main MVMO-SH script
• Several benchmark examples demonstrating how MVMO-SH can be used to solve different optimization problems

The demo is designed in a didactic manner. Users not fully familiar with the algorithm can easily understand the rationale behind it and adapt it to their specific problems with relative ease and a few modifications.

This webpage is also intended to serve as a platform for MVMO-SH development and application. This includes sharing experiences in the use of MVMO-SH, exchange of new ideas, literature and source codes. The platform will enable the community of users to contribute to further development of the algorithm and the underlying theoretical concept.