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Achieving balance between convergence and diversity is a key issue in evolutionary multiobjective optimization. Most existing methodologies, which have demonstrated their niche on various practical problems involving two and three objectives, face significant challenges in many-objective optimization. This paper suggests a unified paradigm, which combines dominance- and decomposition-based approaches, for many-objective optimization. Our major purpose is to exploit the merits of both dominance- and decomposition-based approaches to balance the convergence and diversity of the evolutionary process. The performance of our proposed method is validated and compared with four state-of-the-art algorithms on a number of unconstrained benchmark problems with up to 15 objectives. Empirical results fully demonstrate the superiority of our proposed method on all considered test instances. In addition, we extend this method to solve constrained problems having a large number of objectives. Compared to two other recently proposed constrained optimizers, our proposed method shows highly competitive performance on all the constrained optimization problems.
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The physical properties of cement are strongly influenced by the development of microstructure and cement hydration. Therefore, the investigation of microstructure for cement paste enables us to understand the hydration process and to predict the physical properties. However, the unreliability of phase classification and segmentation in an image affect the description of microstructure, as well as the prediction of properties and the simulation of hydration. This paper studies the dynamic relationship between microstructure and physical properties from the image itself. The relationship between compressive strength and microstructure image features is built as the form of image feature kinetics using gene expression programming from observed microtomography images. A similarity weight tournament selection is also proposed to increase the diversity of population and improve the performance. Experimental results manifest that the evolved image feature kinetics not only perform well in fitting training data but also exhibit superior generalization ability.
It is well known that in evolutionary algorithms (EAs), different reproduction operators may be suitable for different problems or in different running stages. To improve the algorithm performance, the ensemble of multiple operators has become popular. Most ensemble techniques achieve this goal by choosing an operator according to a probability learned from the previous experience. In contrast to these ensemble techniques, in this paper we propose a cheap surrogate model-based multioperator search strategy for evolutionary optimization. In our approach, a set of candidate offspring solutions are generated by using the multiple offspring reproduction operators, and the best one according to the surrogate model is chosen as the offspring solution. Two major advantages of this approach are: 1) each operator can generate a solution for competition compared to the probability-based approaches and 2) the surrogate model building is relatively cheap compared to that in the surrogate-assisted EAs. The model is used to implement multioperator ensemble in two popular EAs, that is, differential evolution and particle swarm optimization. Thirty benchmark functions and the functions presented in the CEC 2013 are chosen as the test suite to evaluate our approach. Experimental results indicate that the new approach can improve the performance of single operator-based methods in the majority of the functions.
Many multiobjective evolutionary algorithms rely on the nondominated sorting procedure to determine the relative quality of individuals with respect to the population. In this paper, we propose a new method to decrease the cost of this procedure. Our approach is to determine the nondominated individuals at the start of the evolutionary algorithm run and to update this knowledge as the population changes. In order to do this efficiently, we propose a special data structure called the M-front, to hold the nondominated part of the population. The M-front uses the geometric and algebraic properties of the Pareto dominance relation to convert orthogonal range queries into interval queries using a mechanism based on the nearest neighbor search. These interval queries are answered using dynamically sorted linked lists. Experimental results show that our method can perform significantly faster than the state-of-the-art Jensen–Fortin’s algorithm, especially in many-objective scenarios. A significant advantage of our approach is that, if we change a single individual in the population we still know which individuals are dominated and which are not.
An effective and efficient successful-parent-selecting framework is proposed to improve the performance of differential evolution (DE) by providing an alternative for the selection of parents during mutation and crossover. The proposed method adapts the selection of parents by storing successful solutions into an archive, and the parents are selected from the archive when a solution is continuously not updated for an unacceptable amount of time. The proposed framework provides more promising solutions to guide the evolution and effectively helps DE escaping the situation of stagnation. The simulation results show that the proposed framework significantly improves the performance of two original DEs and six state-of-the-art algorithms in four real-world optimization problems and 30 benchmark functions.
In recent decades, a plethora of dedicated evolutionary algorithms (EAs) have been crafted to solve domain-specific complex problems more efficiently. Many advanced EAs have relied on the incorporation of domain-specific knowledge as inductive biases that is deemed to fit the problem of interest well. As such, the embedment of domain knowledge about the underlying problem within the search algorithms is becoming an established mode of enhancing evolutionary search performance. In this paper, we present a study on evolutionary memetic computing paradigm that is capable of learning and evolving knowledge meme that traverses different but related problem domains, for greater search efficiency. Focusing on combinatorial optimization as the area of study, a realization of the proposed approach is investigated on two NP-hard problem domains (i.e., capacitated vehicle routing problem and capacitated arc routing problem). Empirical studies on well-established routing problems and their respective state-of-the-art optimization solvers are presented to study the potential benefits of leveraging knowledge memes that are learned from different but related problem domains on future evolutionary search.
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