Multi-objective Estimation Of Distribution Algorithm Research Articles

An improved estimation of distribution algorithm for rescue task emergency scheduling considering stochastic deterioration of the injured

Efficient allocating and scheduling emergency rescue tasks are a primary issue for emergency management. This paper considers emergency scheduling of rescue tasks under stochastic deterioration of the injured. First, a mathematical model is established to minimize the average mathematical expectation of all tasks’ completion time and casualty loss. Second, an improved multi-objective estimation of distribution algorithm (IMEDA) is proposed to solve this problem. In the IMDEA, an effective initialization strategy is designed for obtaining a superior population. Then, three statistical models are constructed, which include two tasks existing in the same rescue team, the probability of first task being processed by a rescue team, and the adjacency between two tasks. Afterward, an improved sampling method based on referenced sequence is employed to efficiently generate offspring population. Three multi-objective local search methods are presented to improve the exploitation in promising areas around elite individuals. Furthermore, the parameter calibration and effectiveness of components of IMEDA are tested through experiments. Finally, the comprehensive comparison with state-of-the-art multi-objective algorithms demonstrates that IMEDA is a high-performing approach for the considered problem.

Knowledge-based multi-objective estimation of distribution algorithm for solving reliability constrained cloud workflow scheduling

Knowledge-based multi-objective estimation of distribution algorithm for solving reliability constrained cloud workflow scheduling

An Adaptive Evolutionary Multi-Objective Estimation of Distribution Algorithm and Its Application to Multi-UAV Path Planning

This paper concerns the multi-UAV cooperative path planning problem, which is solved by multi-objective optimization and by an adaptive evolutionary multi-objective estimation of distribution algorithm (AEMO-EDA). Since the traditional multi-objective optimization algorithms tend to fall into local optimum solutions when dealing with optimization problems in three dimensions, we suggest an advanced estimation of distribution algorithm. The main idea of this algorithm is to integrate the adaptive deflation of the selection rate, adaptive evolution of the covariance matrix, comprehensive evaluation of individual convergence and diversity, and reference point-based non-dominated ranking. A multi-UAV path planning model involving multi-objective optimization is established, and the designed algorithm is simulated and compared with other three high-dimensional multi-objective optimization algorithms. The results show that the AEMO-EDA proposed in this paper has stronger convergence and wider population distribution diversity in applying to the multi-UAV cooperative path planning model, as well as better global convergence. The algorithm can provide an stable path for each UAV and promote the intelligent operation of the UAV system.

A new knowledge-guided multi-objective optimisation for the multi-AGV dispatching problem in dynamic production environments

ABSTRACT The efficiency of material supply for workstations using Automatic Guided Vehicles (AGVs) is largely determined by the performance of the AGV dispatching scheme. This paper proposes a new solution approach for the AGV dispatching problem (AGVDP) for material replenishment in a general manufacturing workshop where workstations are in a matrix layout, and where uncertainty in replenishment time of workstations and stochastic unloading efficiencies of AGVs are dynamic contextual factors. We first extend the literature proposing a mixed integer optimisation model with a delivery satisfaction soft constraint of material orders and two objectives: transportation costs and delivery time deviation. We then develop a new knowledge-guided estimation of distribution algorithm with delivery satisfaction evaluation for solving the model. Our algorithm fuses three knowledge-guided strategies to enhance optimisation capabilities at its respective execution stages. Comprehensive numerical experiments with instances built from a real-world scenario validate the proposed model and algorithm. Results demonstrate that the new algorithm outperforms three popular multi-objective evolutionary algorithms, a discrete version of a recent multi-objective particle swarm optimisation, and a multi-objective estimation of distribution algorithm. Findings of this work provide major implications for workshop management and algorithm design.

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.

Solving dynamic multi-objective problems using polynomial fitting-based prediction algorithm

Recently, dynamic multi-objective optimization has received growing attention due to its popularity in real-world applications. Inspired by polynomial fitting, this paper proposes a polynomial fitting-based prediction algorithm (PFPA) and incorporates it into the model-based multi-objective estimation of distribution algorithm (RM-MEDA) for solving dynamic multi-objective optimization problems. When an environment change is detected, the main mission of PFPA is to predict high-quality search populations for tracking the moving Pareto-optimal set effectively. Firstly, the non-dominated solutions obtained in past environments are utilized to predict high-quality solutions based on a multi-step movement strategy. Secondly, a polynomial fitting-based strategy is designed to fit the distribution of variables according to the obtained search populations, and capture the relationship between variables in the new search environment. Thirdly, some effective search agents are generated for improving population convergence and diversity based on characteristics of variables. To evaluate the performance of the proposed algorithm, experimental results on a set of benchmark functions, with a variety of different dynamic characteristics and difficulties, and two classical dynamic engineering design problems show that PFPA is competitive with some state-of-the-art 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>

An incremental-learning model-based multiobjective estimation of distribution algorithm

Knowledge obtained from the properties of a Pareto-optimal set can guide an evolutionary search. Learning models for multiobjective estimation of distributions have led to improved search efficiency, but they incur a high computational cost owing to their use of a repetitive learning or iterative strategy. To overcome this drawback, we propose an algorithm for incremental-learning model-based multiobjective estimation of distributions. A learning mechanism based on an incremental Gaussian mixture model is embedded within the search procedure. In the proposed algorithm, all new solutions generated during the evolution are passed to a data stream, which is fed incrementally into the learning model to adaptively discover the structure of the Pareto-optimal set. The parameters of the model are updated continually as each newly generated datum is collected. Each datum is learned only once for the model, regardless of whether it has been preserved or deleted. Moreover, a sampling strategy based on the learned model is designed to balance the exploration/exploitation dilemma in the evolutionary search. The proposed algorithm is compared with six state-of-the-art algorithms for several benchmarks. The experimental results show that there is a significant improvement over the representative algorithms.

Hybrid Evolutionary Scheduling for Energy-Efficient Fog-Enhanced Internet of Things

In recent years, the rapid development of the Internet of Things (IoT) has produced a large amount of data that needs to be processed in a timely manner. Traditional cloud computing systems can provide us with plentiful resources to process such data. However, the increasing requirements of IoT applications on data privacy, energy consumption savings and location-aware data processing pushes the emergence and the interplay of fog computing and cloud computing. This paper examines the resource scheduling issue under such a system to minimize makespan and energy consumption. A multi-objective estimation of distribution algorithm (EDA) as well as a partition operator is adopted to divide the graph and determine the task processing permutation and processor assignment. Single and multiple application simulation were both conducted. The comparative results show that the Pareto set produced by our proposed algorithm is able to dominate a large proportion of those solutions by the heuristic method and the simple EDA under single application simulation. When it comes to multi-application simulation, IoT devices can have a much longer lifetime with our proposed scheduling algorithm as well having similar performance to the other algorithms on fog node energy consumption and much better on makespan.

An evolutionary fuzzy scheduler for multi-objective resource allocation in fog computing

With rapid development of the Internet of Things (IoT), a vast amount of raw data produced by IoT devices needs to be processed promptly. Compared to cloud computing, fog computing nodes are closer to data resource for decreasing the end-to-end transmission latency. Considering the limited resource of IoT devices, offloading computationally-intensive tasks to the servers with high computing capability is essential in the IoT–fog–cloud system to complete those tasks on time. In this work, we propose a fuzzy logical offloading strategy for IoT applications characterized by uncertain parameters to optimize both agreement index and robustness. A multi-objective Estimation of Distribution Algorithm (EDA) is designed to learn and optimize the fuzzy offloading strategy from a diversity of the applications. The algorithm partitions applications into independent clusters, so that each cluster can be allocated to the corresponding tier for further processing. Thus, system resources are saved by making scheduling decisions in a reduced search space. Simulation studies on benchmark problems and real-world cases are carried out to verify the efficiency of our proposed algorithm. Pareto sets produced by our algorithm outperformed classic heuristic solutions for 88.3% benchmark cases and dominated Pareto sets of two state-of-art multi-objective algorithms for 92.7% and 94.4% cases correspondingly.

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.

An Efficient Probabilistic Approach Based on Area Grey Incidence Decision Making for Optimal Distributed Generation Planning

The increase in the scale of distribution networks significantly reduces the efficiency of intelligent planning for distributed generation (DG). To improve the efficiency of intelligent DG planning and avoid the impact of uncertainty concerning renewable energy on it, this paper proposes a sensitivity index for the bus-embedded multi-objective estimation of distribution algorithm (MEDA) based on the semi-invariant probabilistic power flow approach to achieve an optimal solution. The sensitivity indices of the buses are comprehensively enabled to obtain a new index and determine their sensitivity sequences based on the area grey incidence decision-making method. Subsequently, according to the uncertainty of wind turbine generators and photovoltaics, a probability model is established, and the semi-invariant method is used to solve for the probabilistic power flow according to a correlation model. Finally, the sensitivity of the proposed bus-embedded MEDA to enhancing the efficiency of the solution is examined. The optimal DG allocation scheme is obtained with the goal of achieving the lowest total cost in the planning year. Finally, the feasibility and effectiveness of the proposed model and method are verified using simulations of the IEEE 33-bus, IEEE 69-bus, and IEEE 118-bus test systems.

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.

Dynamic Multi-objective Estimation of Distribution Algorithm based on Domain Adaptation and Nonparametric Estimation

Although dynamic optimization and multi-objective optimization have made considerable progress individually, solving dynamic multi-objective optimization problems remains a monumental challenge since their multiple, conflicting objectives could change over time. In this paper, we propose a Domain Adaptation and Nonparametric Estimation-based Estimation of Distribution Algorithm, called DANE-EDA, to solve dynamic multi-objective optimization problems. Notable features of the proposed algorithm include the importance sampling, nonparametric density estimation, probabilistic prediction, and a domain adaptation technique seamlessly unified under an innovative framework. The design takes full advantage of the powerful Monte-Carlo method and transfer learning technique. This kind of combination will help the proposed algorithm to maintain a delicate exploration-exploitation trade-off from temporal and spatial perspectives. At the same time, it will help the proposed algorithm to overcome the shortcomings caused by transfer learning, specifically, the loss of the diversity. After proving convergence and analyzing the computational complexity of the DANE-EDA, we compare the proposed method with nine EDAs or dynamic multi-objective optimization algorithms on twelve different test instances. The experimental results affirm the effectiveness of the proposed method in addressing dynamic multi-objective optimization problems.

A multi-objective optimization model and its evolution-based solutions for the fingertip localization problem

Exact fingertip positions are of particular importance to the fingertip-based human–computer interaction. We build a multi-objective optimization model for the problem of fingertip localization, and present a method to solve the above model based on evolutionary algorithms. When building the model, we take the positions of a series of pixels as the decision variable, the shape of the hand-edge curve corresponding to each of the pixels as one objective function, and the distance between each of the pixels and the gravity center of the palm as the other objective function. In addition, based on the correlation among the positions of pixels of the fingertip regions, we present a multi-objective estimation of distribution algorithm to solve the model so as to obtain the best pixel set, thus gaining the fingertip positions. The experimental results demonstrate the effectiveness of the proposed model and algorithm.

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 .