Roman Denysiuk

Many-objective optimization using differential evolution with variable-wise mutation restriction

In this paper, we propose an evolutionary algorithm for handling many-objective optimization problems called MyO-DEMR (many-objective differential evolution with mutation restriction). The algorithm uses the concept of Pareto dominance coupled with the inverted generational distance metric to select the population of the next generation from the combined multi-set of parents and offspring. Furthermore, we suggest a strategy for the restriction of the difference vector in DE operator in order to improve the convergence property in multi-modal fitness landscape. We compare MyO-DEMR with other state-of-the-art multiobjective evolutionary algorithms on a number of multiobjective optimization problems having up to 20 dimensions. The results reveal that the proposed selection scheme is able to effectively guide the search in high-dimensional objective space. Moreover, MyO-DEMR demonstrates significantly superior performance on multi-modal problems comparing with other DE-based approaches.

Multiobjective approach to optimal control for a tuberculosis model

Mathematical modelling can help to explain the nature and dynamics of infection transmissions, as well as support a policy for implementing those strategies that are most likely to bring public health and economic benefits. The paper addresses the application of optimal control strategies in a tuberculosis model. The model consists of a system of ordinary differential equations, which considers reinfection and post-exposure interventions. We propose a multiobjective optimization approach to find optimal control strategies for the minimization of active infectious and persistent latent individuals, as well as the cost associated to the implementation of the control strategies. Optimal control strategies are investigated for different values of the model parameters. The obtained numerical results cover a whole range of the optimal control strategies, providing valuable information about the tuberculosis dynamics and showing the usefulness of the proposed approach.

A New Hybrid Evolutionary Multiobjective Algorithm Guided by Descent Directions

Hybridization of local search based algorithms with evolutionary algorithms is still an under-explored research area in multiobjective optimization. In this paper, we propose a new multiobjective algorithm based on a local search method. The main idea is to generate new non-dominated solutions by adding a linear combination of descent directions of the objective functions to a parent solution. Additionally, a strategy based on subpopulations is implemented to avoid the direct computation of descent directions for the entire population. The evaluation of the proposed algorithm is performed on a set of benchmark test problems allowing a comparison with the most representative state-of-the-art multiobjective algorithms. The results show that the proposed approach is highly competitive in terms of the quality of non-dominated solutions and robustness.

MOEA/VAN: Multiobjective Evolutionary Algorithm Based on Vector Angle Neighborhood

Natural selection favors the survival and reproduction of organisms that are best adapted to their environment. Selection mechanism in evolutionary algorithms mimics this process, aiming to create environmental conditions in which artificial organisms could evolve solving the problem at hand. This paper proposes a new selection scheme for evolutionary multiobjective optimization. The similarity measure that defines the concept of the neighborhood is a key feature of the proposed selection. Contrary to commonly used approaches, usually defined on the basis of distances between either individuals or weight vectors, it is suggested to consider the similarity and neighborhood based on the angle between individuals in the objective space. The smaller the angle, the more similar individuals. This notion is exploited during the mating and environmental selections. The convergence is ensured by minimizing distances from individuals to a reference point, whereas the diversity is preserved by maximizing angles between neighboring individuals. Experimental results reveal a highly competitive performance and useful characteristics of the proposed selection. Its strong diversity preserving ability allows to produce a significantly better performance on some problems when compared with stat-of-the-art algorithms.

Clustering-Based Selection for Evolutionary Many-Objective Optimization

This paper discusses a selection scheme allowing to employ a clustering technique to guide the search in evolutionary many-objective optimization. The underlying idea to avoid the curse of dimensionality is based on transforming the objective vectors before applying a clustering and the selection of cluster representatives according to the distance to a reference point. The experimental results reveal that the proposed approach is able to effectively guide the search in high-dimensional objective spaces, producing highly competitive performance when compared with state-of-the-art algorithms.

MOEA/PC: Multiobjective Evolutionary Algorithm Based on Polar Coordinates

The need to perform the search in the objective space constitutes one of the fundamental differences between multiobjective and single-objective optimization. The performance of any multiobjective evolutionary algorithm (MOEA) is strongly related to the efficacy of its selection mechanism. The population convergence and diversity are two different but equally important goals that must be ensured by the selection mechanism. Despite the equal importance of the two goals, the convergence is often used as the first sorting criterion, whereas the diversity is considered as the second one. In some cases, this can lead to a poor performance, as a severe loss of diversity occurs.

Weighted Stress Function Method for Multiobjective Evolutionary Algorithm Based on Decomposition

Multiobjective evolutionary algorithm based on decomposition MOEA/D is a well established state-of-the-art framework. Major concerns that must be addressed when applying MOEA/D are the choice of an appropriate scalarizing function and setting the values of main control parameters. This study suggests a weighted stress function method WSFM for fitness assignment in MOEA/D. WSFM establishes analogy between the stress-strain behavior of thermoplastic vulcanizates and scalarization of a multiobjective optimization problem. The experimental results suggest that the proposed approach is able to provide a faster convergence and a better performance of final approximation sets with respect to quality indicators when compared with traditional methods. The validity of the proposed approach is also demonstrated on engineering problems.

Multiobjective approach to optimal control for a dengue transmission model

During the last decades, the global prevalence of dengue progressed dramatically. It is a disease which is now endemic in more than one hundred countries of Africa, America, Asia and the Western Pacific. This study addresses a mathematical model for the dengue disease transmission and finding the most effective ways of controlling the disease. The model is described by a system of ordinary differential equations representing human and vector dynamics. Multiobjective optimization is applied to find the optimal control strategies, considering the simultaneous minimization of infected humans and costs due to insecticide application. The obtained results show that multiobjective optimization is an effective tool for finding the optimal control. The set of trade-off solutions encompasses a whole range of optimal scenarios, providing valuable information about the dynamics of infection transmissions. The results are discussed for different values of model parameters.

Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem

We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection, and Acquired Immunodeficiency Syndrome (AIDS) proposed in Silva and Torres (Discr Contin Dyn Syst 35(9):4639–4663, 2015). We introduce and analyze a multiobjective formulation of an optimal control problem, where the two conflicting objectives are minimization of the number of HIV-infected individuals with AIDS clinical symptoms and coinfected with AIDS and active TB; and costs related to prevention and treatment of HIV and/or TB measures. The proposed approach eliminates some limitations of previous works. The results of the numerical study provide comprehensive insights about the optimal treatment policies and the population dynamics resulting from their implementation. Some nonintuitive conclusions are drawn. Overall, the simulation results demonstrate the usefulness and validity of the proposed approach.

Multiobjective evolutionary algorithm based on vector angle neighborhood

This work was supported by the Portuguese Fundacao para a Ciencia e Tecnologia under grant PEst-C/CTM/LA0025/2013 (Projecto Estrategico - LA 25 - 2013-2014 - Strategic Project - LA 25 - 2013-2014).