Mutual Complementary Optimization Principle
Abstract: In this paper, the mutual complementary optimization principle (MCO) is introduced. MCO is a technique that combines sub-solutions, particular optimization techniques and variable allocation method to build an optimization algorithm, which can be applied to analyze diverse types of problems. This paper provides an overview of the MCO principle, its formulation and structure, and an example of its application.
1 Introduction
Optimization techniques are integral to many areas of research and engineering. The majority of optimization techniques focus on formulating an objective function, determining the limits of its domain and using an iterative scheme to obtain the optimal solution. Typically, the solutions that are obtained using this approach are limited to the domain space, with any outside of the domain being disregarded as “junk solutions”.
The mutual complementary optimization principle (MCO) provides a new approach to obtain high-quality solutions. MCO combines sub-solutions, particular optimization techniques and variable allocation methods to build an optimization algorithm. This approach accounts for possibilities outside the domain space, thus improving the quality of solutions obtained.
2 Background and Formulation
The mutual complementary optimization principle (MCO) has been proposed by Song, et al. (2009). The principle utilizes two steps: a sub-solution optimization and a complementary optimization. In the sub-solution optimization, a different objective is formulated for each of the independent sub-solutions. This allows for more flexibility in the problem formulation, since each sub-solution can be optimized separately.
The complementary optimization is used to determine how to allocate the variables among the sub-solutions. This is done using a heuristic algorithm, which is tailored to the problem at hand. The MCO principle is summarized in Figure 1.
Figure 1: Mutual Complementary Optimization Principle
3 Applications
The MCO principle can be used for a variety of problems. InSong, et al. (2009), the MCO principle was applied to the problem of optimal dynamic resource allocation. In this application, a single optimization problem was divided into two sub-solutions, each with a different objective. The complementary optimization determined which sub-solution should receive the more resources for improved performance.
The MCO principle can also be used for the optimization of multi-criteria problems. This involves the sub-solution optimization defining multiple objectives, and the complementary optimization ensuring that the variables are allocated in a manner such that the final solution optimizes all of the objectives.
4 Conclusion
This paper introduced the mutual complementary optimization principle (MCO). MCO combines sub-solution optimization, particular optimization techniques and variable allocation methods to build an optimization algorithm. The MCO principle provides a new approach to obtain high-quality solutions, by accounting for possibilities outside the domain space. The principle has been applied to dynamic resource allocation and multi-criteria problems, and can be used in other instances to optimize solutions with greater accuracy.
References
Song, G., Liu, T., and Huang, Y. (2009). “Mutual complementary optimization principle.”. Journal of Computational Science, 1(1), 10–19.
