Regularity Model-based Multiobjective Estimation Of Distribution Algorithm Research Articles

A practical regularity model based evolutionary algorithm for multiobjective optimization

It is well known that domain knowledge helps design efficient problem solvers. The regularity model based multiobjective estimation of distribution algorithm (RM-MEDA) is such a method that uses the regularity property of continuous multiobjective optimization problems (MOPs). However, RM-MEDA may fail to work when dealing with complicated MOPs. This paper aims to propose some practical strategies to improve the performance of RM-MEDA. We empirically study the modeling and sampling components of RM-MEDA that influence its performance. After that, some new components, including the population partition, modeling, and offspring generation procedures, are designed and embedded in the regularity model. The experimental study suggests that the new components are more efficient than those in RM-MEDA when using the regularity model. The improved version has also been verified on various complicated benchmark problems, and the experimental results have shown that the new version outperforms five state-of-the-art multiobjective evolutionary algorithms.

Combining a hybrid prediction strategy and a mutation strategy for dynamic multiobjective optimization

The environments of the dynamic multiobjective optimization problems (DMOPs), such as Pareto optimal front (POF) or Pareto optimal set (POS), usually frequently change with the evolution process. This kind of problem poses a higher challenge for evolutionary algorithms because it requires the population to quickly track (i.e., converge) to the position of a new environment and be widely distributed in the search space. The prediction-based response mechanism is a commonly used method to deal with environmental changes, but it’s only suitable for predictable changes. Moreover, the imbalance of population diversity and convergence in the process of tracking the dynamically changing POF has aggravated. In this paper, we proposed a new change response mechanism that combines a hybrid prediction strategy and a precision controllable mutation strategy (HPPCM) to solve the DMOPs. Specifically, the hybrid prediction strategy coordinates the center point-based prediction and the guiding individual-based prediction to make accurate predictions. Thus, the population can quickly adapt to the predictable environmental changes. Additionally, the precision controllable mutation strategy handles unpredictable environmental changes. It improves the diversity exploration of the population by controlling the variation degree of solutions. In this way, our change response mechanism can adapt to various environmental changes of DMOPs, such as predictable and unpredictable changes. This paper integrates the HPPCM mechanism into a prevalent regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) to optimize DMOPs. The results of comparative experiments with some state-of-the-art algorithms on various test instances have demonstrated the effectiveness and competitiveness of the change response mechanism proposed in this paper.

Solving dynamic multi-objective problems with a new prediction-based optimization algorithm.

This paper proposes a new dynamic multi-objective optimization algorithm by integrating a new fitting-based prediction (FBP) mechanism with regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) for multi-objective optimization in changing environments. The prediction-based reaction mechanism aims to generate high-quality population when changes occur, which includes three subpopulations for tracking the moving Pareto-optimal set effectively. The first subpopulation is created by a simple linear prediction model with two different stepsizes. The second subpopulation consists of some new sampling individuals generated by the fitting-based prediction strategy. The third subpopulation is created by employing a recent sampling strategy, generating some effective search individuals for improving population convergence and diversity. Experimental results on a set of benchmark functions with a variety of different dynamic characteristics and difficulties illustrate that the proposed algorithm has competitive effectiveness compared with some state-of-the-art algorithms.

An efficient NSCE algorithm for multi-objective reactive power system compensation with UPFC

<span id="docs-internal-guid-a50ef6a8-7fff-b6d7-8e58-d434be6097d4"><span>This paper proposes a novel approach based on the NSCE (elitist non dominated sorting cross entropy), for the optimization of the location and the size of a flexible AC transmission system device (FACTS) namely: unified power flow controller (UPFC) to achieve the optimal reactive power flow (ORPF). In the present work, the main objective is to minimize the real power losses, the cost investment of several UPFC and the deviation voltages using intelligent algorithms. The proposed study is multiobjective, in which, the power generator buses, the control voltages, the ratio tap changer of transformers and the reactive power injections from installed UPFC are considered as control variables. The proposed NSCE algorithm is validated on IEEE 30-bus test system. A comparison with elitist non dominated sorting genetic algorithm (NSGA-II) and a regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) is done and completed with hybridization of them.</span></span>

Novel Prediction Strategies for Dynamic Multiobjective Optimization

This paper proposes a new prediction-based dynamic multiobjective optimization (PBDMO) method, which combines a new prediction-based reaction mechanism and a popular regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for solving dynamic multiobjective optimization problems. Whenever a change is detected, PBDMO reacts effectively to it by generating three subpopulations based on different strategies. The first subpopulation is created by moving nondominated individuals using a simple linear prediction model with different step sizes. The second subpopulation consists of some individuals generated by a novel sampling strategy to improve population convergence as well as distribution. The third subpopulation comprises some individuals generated using a shrinking strategy based on the probability distribution of variables. These subpopulations are tailored to form a population for the new environment. The experimental results carried out on a variety of bi- and three-objective benchmark functions demonstrate that the proposed technique has competitive performance compared with some state-of-the-art algorithms.

A Double Learning Models-Based Multi-Objective Estimation of Distribution Algorithm

The recently developed regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) and inverse models-based multi-objective evolutionary algorithm (IM-MOEA) have been shown to be two effective methods for solving some complex multi-objective optimization problems (MOPs). However, RM-MEDA and IM-MOEA are still challenged when solving MOPs with many local Pareto fronts, and usually generate poor solutions when the population has no obvious regularity. In order to overcome these limits, an ensemble of RM-MEDA and IM-MOEA, denoted as RM-IM-EDA, is proposed in this paper. This ensemble is based on a dynamic mixture of the sampling in the decision space by the regularity-based learning model and the sampling in the objective space using the inverse learning models. In addition, a sequence-based deterministic initialization method is introduced to identify the properties of fitness landscape. The objective behind this scheme is to reduce the probability of sinking into the local Pareto optimum. For the comparison purposes, the proposed RM-IM-EDA is tested on 32 benchmark problems. Experiment results statistically affirm the efficiency of the proposed approach to obtain better results compared with each individual algorithm and other four state-of-the-art MEDAs.

MCEDA: A novel many-objective optimization approach based on model and clustering

To solve many-objective optimization problems (MaOPs) by evolutionary algorithms (EAs), the maintenance of convergence and diversity is essential and difficult. Improved multi-objective optimization evolutionary algorithms (MOEAs), usually based on the genetic algorithm (GA), have been applied to MaOPs, which use the crossover and mutation operators of GAs to generate new solutions. In this paper, a new approach, based on decomposition and the MOEA/D framework, is proposed: model and clustering based estimation of distribution algorithm (MCEDA). MOEA/D means the multi-objective evolutionary algorithm based on decomposition. The proposed MCEDA is a new estimation of distribution algorithm (EDA) framework, which is intended to extend the application of estimation of distribution algorithm to MaOPs. MCEDA was implemented by two similar algorithm, MCEDA/B (based on bits model) and MCEDA/RM (based on regular model) to deal with MaOPs. In MCEDA, the problem is decomposed into several subproblems. For each subproblem, clustering algorithm is applied to divide the population into several subgroups. On each subgroup, an estimation model is created to generate the new population. In this work, two kinds of models are adopted, the new proposed bits model and the regular model used in RM-MEDA (a regularity model based multi-objective estimation of distribution algorithm). The non-dominated selection operator is applied to improve convergence. The proposed algorithms have been tested on the benchmark test suite for evolutionary algorithms (DTLZ). The comparison with several state-of-the-art algorithms indicates that the proposed MCEDA is a competitive and promising approach.

Transfer Learning-Based Dynamic Multiobjective Optimization Algorithms

One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is the optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing the "experiences" to construct a prediction model via statistical machine learning approaches. However most of the existing methods ignore the non-independent and identically distributed nature of data used to construct the prediction model. In this paper, we propose an algorithmic framework, called Tr-DMOEA, which integrates transfer learning and population-based evolutionary algorithm for solving the DMOPs. This approach takes the transfer learning method as a tool to help reuse the past experience for speeding up the evolutionary process, and at the same time, any population based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this, we incorporate the proposed approach into the development of three well-known algorithms, nondominated sorting genetic algorithm II (NSGA-II), multiobjective particle swarm optimization (MOPSO), and the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA), and then employ twelve benchmark functions to test these algorithms as well as compare with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed method through exploiting machine learning technology.

A full variate Gaussian model-based RM-MEDA without clustering process

A regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) is an excellent multi-objective estimation of distribution algorithm proposed in recent years. However, the performance of RM-MEDA is seriously affected by its clustering process. In order to avoid the influence of the clustering process, this paper presents a novel full variate Gaussian model-based (FGM-based) RM-MEDA without clustering process, named FRM-MEDA. In FRM-MEDA, the clustering process is removed from the original algorithm and the full variate Gaussian model (FGM) is introduced to keep the population diversity and make up the loss of the performance caused by removing the clustering process. Meanwhile, the introduction of FGM makes the FRM-MEDA faster and more stable when solving all the test instances. In addition, variable variance of FGM is presented to enhance the exploring ability of FRM-MEDA. The experiments demonstrate that the proposed algorithm significantly outperforms the RM-MEDA without clustering process and the RM-MEDA with K equal to AVE K .

An improved multiobjective estimation of distribution algorithm for environmental economic dispatch of hydrothermal power systems

Environmental economic dispatch of fixed head of hydrothermal power systems is viewed as a mulitobjective optimization problem in this paper. The practical hydrothermal system possesses various constraints which make the problem of finding global optimum difficult. This paper develops an improved multiobjective estimation of distribution algorithm to solving the above problem. A local learning operation is added into the original regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) in the improved approach so as to improve the local search ability and enhance the convergence efficiency. Furthermore, a repair mechanism is employed to repair the searched infeasible solutions in order to be able to search in the feasible region. In the experiment, the results obtained by the proposed approach have been compared with those from other three MOEAs: NSGA-II, NNIA, and RM-MEDA. Results from some pervious reported methods have also been employed to compare with our method. In addition, the results demonstrate the superiority of this proposed method as a promising MOEA to solve this power system multiobjective optimization problem.

A general framework for evolutionary multiobjective optimization via manifold learning

Under certain mild condition, the Pareto-optimal set (PS) of a continuous multiobjective optimization problem, with m objectives, is a piece-wise continuous (m−1)-dimensional manifold. This regularity property is important, yet has been unfortunately ignored in many evolutionary multiobjective optimization (EMO) studies. The first work that explicitly takes advantages of this regularity property in EMO is the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA). However, its performance largely depends on its model parameter, which is problem dependent. Manifold learning, also known as nonlinear dimensionality reduction, is able to discover the geometric property of a low-dimensional manifold embedded in the high-dimensional ambient space. This paper presents a general framework that applies advanced manifold learning techniques in EMO. At each generation, we first use a principal curve algorithm to obtain an approximation of the PS manifold. Then, the Laplacian eigenmaps algorithm is employed to find the low-dimensional representation of this PS approximation. Afterwards, we identify the neighborhood relationship in this low-dimensional representation, which is also applicable for the original high-dimensional data. Based on the neighborhood relationship, we can interpolate new candidate solutions that obey the geometric property of the PS manifold. Empirical results validate the effectiveness of our proposal.

Improved RM-MEDA with local learning

In this paper, local learning is proposed to improve the speed and the accuracy of convergence performance of regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA), a typical multi-objective optimization algorithm via estimation of distribution. RM-MEDA employs a model-based method to generate new solutions, however, this method is easy to generate poor solutions when the population has no obvious regularity. To overcome this drawback, our proposed method add a new solution generation strategy, local learning, to the original RM-MEDA. Local learning produces solutions by sampling some solutions from the neighborhood of elitist solutions in the parent population. As it is easy to search some promising solutions in the neighborhood of an elitist solution, local learning can get some useful solutions which help the population attain a fast and accurate convergence. The experimental results on a set of test instances with variable linkages show that the implement of local learning can accelerate convergence speed and add a more accurate convergence to the Pareto optimal.

A regularity model-based multiobjective estimation of distribution algorithm with reducing redundant cluster operator

A regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) has been proposed for solving continuous multiobjective optimization problems with variable linkages. RM-MEDA is a kind of estimation of distribution algorithms and, therefore, modeling plays a critical role. In RM-MEDA, the population is split into several clusters to build the model. Moreover, the fixed number of clusters is recommended in RM-MEDA when solving different kinds of problems. However, based on our experiments, we find that the number of clusters is problem-dependent and has a significant effect on the performance of RM-MEDA. Motivated by the above observation, in this paper we improve the clustering process and propose a reducing redundant cluster operator (RRCO) to build more precise model during the evolution. By combining RRCO with RM-MEDA, we present an improved version of RM-MEDA, named IRM-MEDA. In this paper, we also construct four additional continuous multiobjective optimization test instances. The experimental results have shown that IRM-MEDA outperforms RM-MEDA in terms of efficiency and effectiveness. In particular, IRM-MEDA performs on average 31.67% faster than RM-MEDA.

RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm

Under mild conditions, it can be induced from the Karush-Kuhn-Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous (m - 1)-D manifold, where m is the number of objectives. Based on this regularity property, we propose a regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a (m - 1)-D piecewise continuous manifold. The local principal component analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sorting-based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RM-MEDA outperforms three other state-of-the-art algorithms, namely, GDE3, PCX-NSGA-II, and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RM-MEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RM-MEDA have also been identified and discussed in this paper.