Evolutionary Algorithm For Many-objective Optimization Research Articles

An Evolutionary Algorithm for Many-Objective Optimization Based on Indicator and Vector-Angle Decomposition

The evolutionary algorithms for many-objective optimization based on reference-point decomposition are widely concerned since they generally maintain good performance on many optimization problems, however, most of these algorithms show insufficient versatility on optimization problems with various types of Pareto fronts. To address this issue, we propose an evolutionary algorithm for manyobjective optimization based on indicator and vector-angle decomposition, termed IVAD. In the proposed algorithm, the objective vectors of current population, as a set of reference vectors, are used to dynamically partition the whole objective space. And the max-min-vector-angle selection strategy, by calculating the vector angles between each pair of solutions, is constructed to select well-diversity solutions. Furthermore, to enhance the balance between convergence and diversity, the elite replacement, based on I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ε+</sub> indicator and vector angle, is proposed for each cluster that the selected individuals belong to. The proposed algorithm is compared with state-of-the-art many-objective evolutionary algorithms based on reference-point and vectorangle decomposition on three test suites with up to 15 objectives. Experimental results demonstrate that the proposed IVAD obtains more competitive performance on many-objective optimization problems with various types of Pareto fronts, and enhances the ability to balance convergence and diversity.

An Angle-Based Bi-Objective Evolutionary Algorithm for Many-Objective Optimization

One of the main difficulties in solving many-objective optimization is the lack of selection pressure. For an optimization problem, its main purpose is to obtain a nondominated solution set with better convergence and diversity. In this paper, two estimation methods are proposed to convert a many-objective optimization problem into a simple bi-objective optimization problem, that is, the convergence and diversity estimation methods, so as to greatly improve the probability of certain dominance relation between solutions, and then increase the selection pressure. Based on the proposed estimation methods, a new many-objective evolutionary algorithm, termed ABOEA, is proposed. In the convergence estimation method, we use a modified ASF function to solve the performance degradation of the traditional norm distance on the irregular Pareto front. In the diversity estimation method, we innovatively propose a diversity estimation method based on the angle between solutions. Empirical experimental results demonstrate that the proposed algorithm shows its competitiveness against the state-of-art algorithms in solving many-objective optimization problems. Two estimation methods proposed in this paper can greatly improve the performance of algorithms in solving many-objective optimization problems.

An Evolutionary Algorithm for Multi and Many-Objective Optimization With Adaptive Mating and Environmental Selection

Multi-objective evolutionary algorithms (MOEAs) have received immense recognition due to their effectiveness and efficiency in tackling multi-objective optimization problems (MOPs). Recently, numerous studies on MOEAs revealed that when handling many-objective optimization problems (MaOPs) that have more than three objectives, MOEAs encounter challenges and the behavior of MOEAs resembles a random walk in search space as the proportion of nondominated solutions increases subsequently. This phenomenon is commonly observed in most classical Pareto-dominance-based MOEAs (PDMOEAs) such as NSGA-II, SPEAII, as these algorithms face difficulties in guiding the search process towards the optimal Pareto front due to lack of selection pressure. From the literature, it is evident that incorporating sum of normalized objectives into the framework of MOEAs would enhance the converging capabilities. Hence, in this work, we propose a novel multi-objective optimization algorithm with adaptive mating and environmental selection (ad-MOEA) which effectively incorporates the concept of sum of objectives in the mechanisms of mating and environmental selection to control the convergence and diversity adaptively. To demonstrate the effectiveness of the proposed ad-MOEA, we have conducted experiments on 26 test problems that includes DTLZ, WFG and MaOP test suites. Along with the benchmark problem, we have analyzed the performance of the proposed approach on real-world problems. The experimental results demonstrate the effectiveness of the proposed method with respect to the state-of-art methods.

A New Hypervolume-Based Evolutionary Algorithm for Many-Objective Optimization

In this article, a new hypervolume-based evolutionary multiobjective optimization algorithm (EMOA), namely, R2HCA-EMOA (R2-based hypervolume contribution approximation EMOA), is proposed for many-objective optimization. The core idea of the algorithm is to use an R2 indicator variant to approximate the hypervolume contribution. The basic framework of the proposed algorithm is the same as SMS-EMOA. In order to make the algorithm computationally efficient, a utility tensor structure is introduced for the calculation of the R2 indicator variant. Moreover, a normalization mechanism is incorporated into R2HCA-EMOA to enhance the performance of the algorithm. Through experimental studies, R2HCA-EMOA is compared with three hypervolume-based EMOAs and several other state-of-the-art EMOAs on 5-, 10-, and 15-objective DTLZ, WFG problems, and their minus versions. Our results show that R2HCA-EMOA is more efficient than the other hypervolume-based EMOAs, and is superior to all the compared state-of-the-art EMOAs.

Técnica de seleção de variáveis em problemas de classificação de falhas aplicada em processo industrial usando o algoritmo genético MOEADD

Neste trabalho é proposto um método de seleção de variáveis denominado MOEADD-KNN-M, que é baseado no algoritmo genético MOEADD (Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition), no algoritmo de classificação KNN (K-nearest neighbors), e em operadores genéticos adaptados. A abordagem adotada no algoritmo proposto é bi-objetivo, onde um objetivo é minimizar a quantidade de variáveis da solução e outro objetivo é minimizar a taxa de erro de classificação de falhas. Foram realizados experimentos com o método proposto empregando dados de um processo industrial petroquímico real, denominado Tennessee Eastman para classificação de falhas, e os resultados obtidos foram comparados com outros algoritmos. Os resultados demonstraram que o método proposto leva a soluções com baixo erro de classificação e pouca quantidade de sensores, que são as quantidades procuradas para serem minimizadas. Sendo assim, essa abordagem se mostrou promissora para a aplicação na seleção de variáveis em problemas de classificação de falhas em processos industriais.

Explicit Control of Implicit Parallelism in Decomposition-Based Evolutionary Many-Objective Optimization Algorithms [Research Frontier

Over the past two decades, Evolutionary Multi-objective Optimization (EMO) algorithms have demonstrated their ability to find and maintain multiple trade-off solutions in two and three-objective problems, making EMO as one of the most emergent and exciting fields of research and application within Computational Intelligence (CI) area. The main reason for EMO's success is that the population-based EMO operators are able to establish an implicit parallel search within an evolving population to find multiple Pareto-optimal regions of the search space parallelly. For many-objective optimization problems involving a largedimensional objective space, the extent of implicit parallelism is argued here to be too generic, compared to the same in a lower-dimensional objective space. Decomposition-based EMO algorithms - a recent trend in EMO literature - which divide the overall computing task into a number of sub-tasks of focusing within a region of the search space have found to be successful in solving many-objective problems. In this paper, we study the effect of explicit control of an algorithm's implicit parallelism mechanism for achieving an enhanced performance of decomposition-based EMO algorithms. We consider three decomposition-based many-objective evolutionary algorithms (EAs) - MOEA/D, MOEA/D-M2M, and NSGA-III - for this purpose. We also investigate another explicit control strategy of suitably choosing a normalization method of objectives for improving the performance of MOEA/D and MOEA/ D-M2M methods, and report much improved performance than their original counterparts. The principles of this study are valid for any population-based search and optimization algorithms and can be extended to improve the performance other single-objective EA, EMO, and other relevant CI methods.

Evolutionary algorithms for many-objective cloud service composition: Performance assessments and comparisons

Service composition and optimal selection (SCOS) concerns the building of optimal composite service by integrating existing services with the aim of performing complex task. Due to a plethora of affordable cloud services providing similar functionalities while differing in quality of service (QoS), how to determine suitable candidates to orchestrate the best composite service, also known as QoS-aware SCOS problem, becomes more complicated. A number of evolutionary optimizers have been developed to resolve SCOS. Unfortunately, a large majority of these optimizers carry out the optimization by aggregating many diverse QoS attributes into a single objective or simply considering two or three representative QoS attributes. SCOS, particularly, from the perspective of many-objective optimization, has not received an appropriate attention. As more factors come into play, SCOS is strictly a many-objective problem. This study explores the scalability of recently state-of-the-art evolutionary many-objective optimization (EMaO) algorithms in addressing SCOS. Comparative results reveal that these EMaO algorithms, never before applied to many-objective SCOS, exhibit distinct search abilities with respect to the objective space dimensionality and problem scale. Based on the empirical observation, useful suggestions and insights for choosing suitable EMaO algorithms pertaining to different SCOS problems are given.

Pressure point driven evolutionary algorithm for many-objective optimization

Abstract How to form good trade-offs between convergence and diversity for many-objective optimization is an ongoing challenge. With the increase in objectives, the ratio of non-dominated solutions in a population increases sharply, which challenges individual discrimination and selection pressures. Besides, the Pareto fronts of many-objective optimization problems (MaOPs) have various shapes, such as disconnected, degenerate, biased deceptive, and mixed shapes, which further challenge the trade-offs between convergence and diversity. To address the above issues, we propose a pressure point driven Evolutionary Algorithm (proEA). Specifically, a pressure point based strategy is developed to update the pressure point, such strengthening the selection pressure. Then, the reference vector based environmental selection strategy is improved by integrating an angle-based selection strategy to account for the complicated shapes of Pareto fronts. Finally, a series of numerical experiments are conducted to compare the proposed proEA with five representative algorithms in the context of 36 test instances with 5, 7, 10, and 15 objectives. The experimental results demonstrate the superiority of algorithm proEA.

A New Two-Stage Evolutionary Algorithm for Many-Objective Optimization

Convergence and diversity are interdependently handled during the evolutionary process by most existing many-objective evolutionary algorithms (MaOEAs). In such a design, the degraded performance of one would deteriorate the other, and only solutions with both are able to improve the performance of MaOEAs. Unfortunately, it is not easy to constantly maintain a population of solutions with both convergence and diversity. In this paper, an MaOEA based on two independent stages is proposed for effectively solving many-objective optimization problems (MaOPs), where the convergence and diversity are addressed in two independent and sequential stages. To achieve this, we first propose a nondominated dynamic weight aggregation method by using a genetic algorithm, which is capable of finding the Pareto-optimal solutions for MaOPs with concave, convex, linear and even mixed Pareto front shapes, and then these solutions are employed to learn the Pareto-optimal subspace for the convergence. Afterward, the diversity is addressed by solving a set of single-objective optimization problems with reference lines within the learned Pareto-optimal subspace. To evaluate the performance of the proposed algorithm, a series of experiments are conducted against six state-of-the-art MaOEAs on benchmark test problems. The results show the significantly improved performance of the proposed algorithm over the peer competitors. In addition, the proposed algorithm can focus directly on a chosen part of the objective space if the preference area is known beforehand. Furthermore, the proposed algorithm can also be used to effectively find the nadir points.

A Research Mode Based Evolutionary Algorithm for Many-Objective Optimization

The development of algorithms to solve Many-objective optimization problems (MaOPs) has attracted significant research interest in recent years. Solving various types of Pareto front (PF) is a daunting challenge for evolutionary algorithm. A Research mode based evolutionary algorithm (RMEA) is proposed for many-objective optimization. The archive in the RMEA is used to store non-dominated solutions that can reflect the shape of the PF to guide the reference vector adaptation. Information concerning the population is collected, once the number of non-dominated solutions reaches its limit after many generations without exceeding a given threshold, RMEA introduces a research mode that generates more reference vectors to search through the solutions. The proposed algorithm showed competitive performance with four state-of-the-art evolutionary algorithms in a large number of experiments.

The distributed many-objective economic/emission load dispatch benchmark problem

Abstract This paper considers a new kind of economic/emission load dispatch-based problem framework. In the proposed framework, non-synchronous and distant generators are connected to different demanding areas, unlike conventional distributed dispatch problems. Only some of the generators are physically connected to the demanding areas, which are shared by some other generators. Hence, each generator affects other generators. Additionally, the proposed framework is enriched with an over-produced power that can be sold to the neighboring regions. Since many aspects, constraints and objectives are introduced in this new framework, the number of objectives is increased. To solve this experimental problem, many-objective optimization algorithms are applied, and the results are compared with each other. These algorithms are the multi-objective evolutionary algorithm based on decomposition, inverse modeling-based multi-objective evolutionary algorithm, grid-based evolutionary algorithm for many-objective optimization, reference vector-guided evolutionary algorithm, and strength Pareto evolutionary algorithm with shift-based density estimator. Additionally, to evaluate the performances of many-objective optimization algorithms, the multi-objective version of the problem is solved with a constraint-based classical optimization algorithm, achievement scalarization functions, and sequential quadratic programming. The results suggest that as the model converges to a more realistic problem, the number of objectives is increased, and more efficient algorithms are needed to solve these problems.

An Opposition-Based Evolutionary Algorithm for Many-Objective Optimization with Adaptive Clustering Mechanism.

Balancing convergence and diversity has become a key point especially in many-objective optimization where the large numbers of objectives pose many challenges to the evolutionary algorithms. In this paper, an opposition-based evolutionary algorithm with the adaptive clustering mechanism is proposed for solving the complex optimization problem. In particular, opposition-based learning is integrated in the proposed algorithm to initialize the solution, and the nondominated sorting scheme with a new adaptive clustering mechanism is adopted in the environmental selection phase to ensure both convergence and diversity. The proposed method is compared with other nine evolutionary algorithms on a number of test problems with up to fifteen objectives, which verify the best performance of the proposed algorithm. Also, the algorithm is applied to a variety of multiobjective engineering optimization problems. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in solving challenging real-world problems.

Adaptive Sorting-Based Evolutionary Algorithm for Many-Objective Optimization

Evolutionary algorithms have shown their promise in coping with many-objective optimization problems. However, the strategies of balancing convergence and diversity and the effectiveness of handling problems with irregular Pareto fronts (PFs) are still far from perfect. To address these issues, this paper proposes an adaptive sorting-based evolutionary algorithm based on the idea of decomposition. First, we propose an adaptive sorting-based environmental selection strategy. Solutions in each subpopulation (partitioned by reference vectors) are sorted based on their convergence. Those with better convergence are further sorted based on their diversity, then being selected according to their sorting levels. Second, we provide an adaptive promising subpopulation sorting-based environmental selection strategy for problems which may have irregular PFs. This strategy provides additional sorting-based selection effort on promising subpopulations after the general environmental selection process. Third, we extend the algorithm to handle constraints. Finally, we conduct an extensive experimental study on the proposed algorithm by comparing with start-of-the-state algorithms. Results demonstrate the superiority of the proposed algorithm.

A diversity ranking based evolutionary algorithm for multi-objective and many-objective optimization

Abstract In recent years, a variety of multi-objective evolutionary algorithms (MOEAs) have been proposed in the literature. As pointed out in some recent studies, the performance of most existing MOEAs is sensitive to the Pareto front (PF) shapes of the problem to be solved, and it is difficult for these algorithms to manage diversity on various types of Pareto fronts (PFs) effectively. To address these issues, this paper proposes an evolutionary algorithm based on diversity ranking method for multi-objective and many-objective optimization. The proposed evolutionary algorithm introduces reference vector adaptation method to solve different shapes of Pareto fronts, and proposes the diversity ranking method to manage diversity. The extensive experimental results demonstrate that the proposed algorithm can solve various types of Pareto fronts, surpassing several state-of-the-art evolutionary algorithms for multi-objective and many-objective optimization.

An adaptive decomposition-based evolutionary algorithm for many-objective optimization

Penalty boundary intersection (PBI) is one popular method in decomposition based evolutionary multi-objective algorithms, where the penalty factor is crucial for striking a balance between convergence and diversity in a high-dimensional objective space. Meanwhile, the distribution of the obtained solutions highly depends on the setting of the weight vectors. This paper proposes an adaptive decomposition-based evolutionary algorithm for many-objective optimization, which introduces one adaptation mechanism for PBI-based decomposition and the other for adjusting the weight vector. The former assigns a specific penalty factor for each subproblem by using the distribution information of both population and the weight vectors, while the latter adjusts the weight vectors based on the objective ranges to handle problems with different scales on the objectives. We have compared the proposed algorithm with seven state-of-the-art many-objective evolutionary algorithms on a number of benchmark problems. The empirical results demonstrate the superiority of the proposed algorithm.

ESOEA: Ensemble of single objective evolutionary algorithms for many-objective optimization

Inspired by the success of decomposition based evolutionary algorithms and the necessary search for a versatile many-objective optimization algorithm which is adaptive to several kinds of characteristics of the search space, the proposed work presents an adaptive framework which addresses many-objective optimization problems by using an ensemble of single objective evolutionary algorithms (ESOEA). It adopts a reference-direction based approach to decompose the population, followed by scalarization to transform the many-objective problem into several single objective sub-problems which further enhances the selection pressure. Additionally, with a feedback strategy, ESOEA explores the directions along difficult regions and thus, improving the search capabilities along those directions. For experimental validation, ESOEA is integrated with an adaptive Differential Evolution and experimented on several benchmark problems from the DTLZ, WFG, IMB and CEC 2009 competition test suites. To assess the efficacy of ESOEA, the performance is noted in terms of convergence metric, inverted generational distance, and hypervolume indicator, and is compared with numerous other multi- and/or many-objective evolutionary algorithms. For a few test cases, the resulting Pareto-fronts are also visualized which help in the further analysis of the results and in establishing the robustness of ESOEA.

A region search evolutionary algorithm for many-objective optimization

Achieving a balance between convergence and diversity in many-objective optimization is a great challenge. This paper suggests an evolutionary algorithm based on a region search strategy to deal with different kinds of benchmark problems. In the proposed algorithm, each solution is associated with a region, and the region search strategy is applied to constrain the updating process; this strategy will enhance the diversity of population without losing convergence. A new normalization procedure is used for dealing with scaled problems. Moreover, the comparison of two solutions is based on both dominance relation and perpendicular distance; the result shows the algorithm's reliability for solving both convex and concave problems. The performance of the proposed algorithm is validated by several well-known benchmark problems with different properties. Seven state-of-the-art algorithms are compared and the experimental results demonstrate that the introduced algorithm performs the best on almost all benchmark problems. Furthermore, the proposed strategy depicts a high computational efficiency for solving the problems with a high dimension of objectives.

A novel two-archive strategy for evolutionary many-objective optimization algorithm based on reference points

Current evolutionary many-objective optimization algorithms face two challenges: one is to ensure population diversity for searching the entire solution space. The other is to ensure quick convergence to the optimal solution set. In this paper, we propose a novel two-archive strategy for evolutionary many-objective optimization algorithm. The uniform archive strategy, based on reference points, is used to keep population diversity in the evolutionary process, and to ensure that an evolutionary algorithm is able to search the entire solution space. The single elite archive strategy is used to ensure that individuals with the best single objective value are able to evolve into the next generation and have more opportunities to generate offspring. This strategy aims to improve the convergence rate. Then this novel two-archive strategy is applied to improving the Non-dominated Sorting Genetic Algorithm (NSGA-III). Simulation experiments are conducted on benchmark test sets and experimental results show that our proposed algorithm with the two-archive strategy has a better performance than other state-of-art algorithms.

Generation of large-bandwidth x-ray free electron laser with evolutionary many-objective optimization algorithm

X-ray free-electron lasers (XFELs) are cutting-edge scientific instruments for a wide range of disciplines. Conventionally, the narrow bandwidth is pursued in an XFEL. However, in recent years, the large-bandwidth XFEL operation schemes are proposed for X-ray spectroscopy and X-ray crystallography, in which over-compression is a promising scheme to produce broad-bandwidth XFEL pulses through increasing the electron beam energy chirp. In this paper, combining with the beam yaw correction to overcome the transverse slice misalignment caused by the coherent synchrotron radiation, finding out the over-compression working point of the linac is treated as a many-objective (having four or more objectives) optimization problem, thus the non-dominated sorting genetic algorithm III is applied to the beam dynamic optimization for the first time. Start-to-end simulations demonstrate a full bandwidth of 4.6% for Shanghai soft x-ray free-electron laser user facility.

A Classification-Based Surrogate-Assisted Evolutionary Algorithm for Expensive Many-Objective Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have been developed mainly for solving expensive optimization problems where only a small number of real fitness evaluations are allowed. Most existing SAEAs are designed for solving low-dimensional single or multiobjective optimization problems, which are not well suited for many-objective optimization. This paper proposes a surrogate-assisted many-objective evolutionary algorithm that uses an artificial neural network to predict the dominance relationship between candidate solutions and reference solutions instead of approximating the objective values separately. The uncertainty information in prediction is taken into account together with the dominance relationship to select promising solutions to be evaluated using the real objective functions. Our simulation results demonstrate that the proposed algorithm outperforms the state-of-the-art evolutionary algorithms on a set of many-objective optimization test problems.