Author: Community

The hypervolume and hypervolume contributions are widely used in multiobjective evolutionary optimization. However, their exact calculation is NP-hard. By definition, hypervolume is an m-D integral (where m is the number of objectives). Using polar coordinate, this paper transforms the hypervolume into an (m – 1)-D integral, and then proposes two approximation methods for computing the hypervolume and hypervolume contributions. Numerical experiments have been conducted to investigate the performance of our proposed methods.

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for solving high-dimensional expensive problems. The basic idea of SAEAs is the integration of nature-inspired searching ability of evolutionary algorithms and prediction ability of surrogate models. This paper proposes a novel evolutionary sampling assisted optimization (ESAO) method which combines the two abilities to consider global exploration and local exploitation. Differential evolution is employed to generate offspring using mutation and crossover operators. A global radial basis functions surrogate model is built for prescreening of the offspring’s objective function values and identifying the best one, which will be evaluated with the true function. The best offspring will replace its parent’s position in the population if its function value is smaller than that of its parent. A local surrogate model is then built with selected current best solutions. An optimizer is applied to find the optimum of the local model. The optimal solution is then evaluated with the true function. Besides, a better point found in the local search will be added into the population in the global search. Global and local searches will alternate if one search cannot lead to a better solution. Comprehensive analysis is conducted to study the mechanism of ESAO and insights are gained on different local surrogates. The proposed algorithm is compared with two state-of-the-art SAEAs on a series of high-dimensional problems and results show that ESAO behaves better both in effectiveness and robustness on most of the test problems. Besides, ESAO is applied to an airfoil optimization problem to show its effectiveness.

This letter introduces a novel modified replicator dynamics model, which includes external influences on the population. This framework models a realistic market into which companies, the external dynamic influences, invest resources in order to bolster their product’s standing and increase their market share. The dynamic influences change in each time step of the game, and directly modify the payoff matrix of the population’s interactions. The model can learn from real data how each influence affects the market, and can be used to simulate and predict the outcome of a real system. We specifically analyze how a new technology can compete and attempt to unseat an entrenched technology as the market leader. We establish a relationship between the external influences and the population payoff matrix and show how the system can be implemented to predict outcomes in a real market by simulating the rise of the Android mobile operating system over its primary competition, the iPhone, from 2009 to 2017.

The analysis of gene expression data is useful for detecting the biological information of genes. Biclustering of microarray data has been proposed as a powerful computational tool to discover subsets of genes that exhibit consistent expression patterns along subsets of conditions. In this paper, we propose a novel biclustering algorithm called the bi-phase evolutionary biclustering algorithm. The first phase is for the evolution of rows and columns, and the other is for the evolution of biclusters. The interaction of the two phases ensures a reliable search direction and accelerates the convergence to good solutions. Furthermore, the population is initialized using a conventional hierarchical clustering strategy to discover bicluster seeds. We also developed a seed-based parallel implementation of evolutionary searching to search biclusters more comprehensively. The performance of the proposed algorithm is compared with several popular biclustering algorithms using synthetic datasets and real microarray datasets. The experimental results show that the algorithm demonstrates a significant improvement in discovering biclusters.

Constrained multiobjective optimization problems (CMOPs) are frequently encountered in real-world applications, which usually involve constraints in both the decision and objective spaces. However, current artificial CMOPs never consider constraints in the decision space (i.e., decision constraints) and constraints in the objective space (i.e., objective constraints) at the same time. As a result, they have a limited capability to simulate practical scenes. To remedy this issue, a set of CMOPs, named DOC, is constructed in this paper. It is the first attempt to consider both the decision and objective constraints simultaneously in the design of artificial CMOPs. Specifically, in DOC, various decision constraints (e.g., inequality constraints, equality constraints, linear constraints, and nonlinear constraints) are collected from real-world applications, thus making the feasible region in the decision space have different properties (e.g., nonlinear, extremely small, and multimodal). On the other hand, some simple and controllable objective constraints are devised to reduce the feasible region in the objective space and to make the Pareto front have diverse characteristics (e.g., continuous, discrete, mixed, and degenerate). As a whole, DOC poses a great challenge for a constrained multiobjective evolutionary algorithm (CMOEA) to obtain a set of well-distributed and well-converged feasible solutions. In order to enhance current CMOEAs’ performance on DOC, a simple and efficient two-phase framework, named ToP, is proposed in this paper. In ToP, the first phase is implemented to find the promising feasible area by transforming a CMOP into a constrained single-objective optimization problem. Then in the second phase, a specific CMOEA is executed to obtain the final solutions. ToP is applied to four state-of-the-art CMOEAs, and the experimental results suggest that it is quite effective.

Finding the overall Pareto optimal front while addressing the effect of an increasing number of objectives has become an essential and challenging issue for multiobjective optimization in real-world applications. Preference information provided by a decision maker can guide the search for preferred regions of the Pareto front and accelerate the convergence of the population. In this paper, a new variant of the Pareto dominance relation, called preference angle and reference information-based dominance, is proposed to create a stricter partial order among nondominated solutions. In the proposed method, the Euclidean distance and angle information between candidate solutions and reference points are calculated to evaluate the degree of convergence and population diversity, respectively. In addition, an adaptive threshold is designed to adjust the judgment condition of ar-dominance using an iterative process in a prespecified interval. The proposed algorithm increases the convergence speed of the population and reduces the number of solutions in the nonpreferred region. Comparative evaluation experiments are presented with respect to two performance metrics for a variety of benchmark test problems and real-world aluminum electrolytic production cases. The results demonstrate that the proposed approach is effective for highly complex, multiobjective optimization problems when compared with five state-of-the-art evolutionary algorithms.

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Phylogenetic inference allows building a hypothesis about the evolutionary relationships between a group of species, which is usually represented as a tree. The phylogenetic inference problem can be seen as an optimization problem, searching for the most qualified tree among all the possible topologies according to a selected criterion. These criteria can be based on different principles. Due to the combinatorial number of possible topologies, diverse heuristics and meta-heuristics have been proposed to find approximated solutions according to one criterion. However, these methods may result in several phylogeny trees which could be in conflict with one another. In order to deal with this problem, models based on multiobjective optimization with different configurations have been used. In this paper, we propose an ad-hoc multiobjective memetic algorithm (MO-MA) to infer phylogeny using two objectives: 1) maximum parsimony and 2) likelihood. Several population operators and local search strategies are proposed and evaluated in order to measure their contribution to the algorithm. Additionally, we perform a comparison among different configurations and tree rearrangement strategies. The results show that the proposed MO-MA is able to identify a Pareto set of solutions that include new trees which were nondominated by solutions from the current state of the art single-objective optimization tools. Furthermore, the MO-MA improves the results presented in the literature for multiobjective approaches in all of the studied data sets. These results make our proposal a good alternative for phylogenetic inference.

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Engineering designs can involve multiple stages, where at each stage, the design models are incrementally modified and optimized. In contrast to traditional dynamic optimization problems, where the changes are caused by some objective factors, the changes in such incremental optimization problems (IOPs) are usually caused by the modifications made by the decision makers during the design process. While existing work in the literature is mainly focused on traditional dynamic optimization, little research has been dedicated to solving such IOPs. In this paper, we study how to adopt cooperative coevolution to efficiently solve a specific type of IOPs, namely, those with increasing decision variables. First, we present a benchmark function generator on the basis of some basic formulations of IOPs with increasing decision variables and exploitable modular structure. Then, we propose a contribution-based cooperative coevolutionary framework coupled with an incremental grouping method for dealing with them. On one hand, the benchmark function generator is capable of generating various benchmark functions with various characteristics. On the other hand, the proposed framework is promising in solving such problems in terms of both optimization accuracy and computational efficiency. In addition, the proposed method is further assessed using a real-world application, i.e., the design optimization of a stepped cantilever beam.