Framework Of Multi-objective Evolutionary Algorithms Research Articles

An Interactive Knowledge-Based Multiobjective Evolutionary Algorithm Framework for Practical Optimization Problems

Experienced users often have useful knowledge and intuition in solving real-world optimization problems. User knowledge can be formulated as inter-variable relationships to assist an optimization algorithm in finding good solutions faster. Such inter-variable interactions can also be automatically learned from high-performing solutions discovered at intermediate iterations in an optimization run – a process called innovization. These relations, if vetted by the users, can be enforced among newly generated solutions to steer the optimization algorithm towards practically promising regions in the search space. Challenges arise for large-scale problems where the number of such variable relationships may be high. This paper proposes an interactive knowledge-based evolutionary multi-objective optimization () framework that extracts hidden variable-wise relationships as knowledge from evolving high-performing solutions, shares them with users to receive feedback, and applies them back to the optimization process to improve its effectiveness. The knowledge extraction process uses a systematic and elegant graph analysis method which scales well with number of variables. The working of the proposed is demonstrated on three large-scale real-world engineering design problems. The simplicity and elegance of the proposed knowledge extraction process and achievement of high-performing solutions quickly indicate the power of the proposed framework. The results presented should motivate further such interaction-based optimization studies for their routine use in practice.

Interaction-Based Prediction for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization poses great challenges to evolutionary algorithms due to the change of optimal solutions or Pareto front with time. Learning-based methods are popular to extract the changing pattern of optimal solutions for predicting new solutions. They tend to use all variables as features (i.e., inputs) to build prediction models. However, there are usually some irrelevant and redundant variables, which increase training difficulty and decrease prediction accuracy. This paper proposes a new interaction-based prediction method, which captures the correlation of variables with prediction targets and selects the most relevant variables to build prediction models using neural networks. In particular, the interaction between variables is detected to remove redundant variables. In addition, a correction procedure is developed to further improve predicted solutions according to the prediction error in past environments. The predicted solutions are used to update the population according to a specifically designed update strategy. Integrating the interaction-based prediction (IP) method into the framework of multiobjective evolutionary algorithm based on decomposition (MOEA/D), a new algorithm named IP-DMOEA is put forward. Experimental results on a typical dynamic multiobjective test suite demonstrate the better performance of the proposed IPDMOEA than state-of-the-art algorithms in terms of convergence speed and solution quality. The proposed IP-DMOEA is also successfully applied to the multirobot task scheduling problem.

Dual-Fuzzy-Classifier-Based Evolutionary Algorithm for Expensive Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have been widely used to solve multiobjective optimization problems (MOPs). Conventional MOEAs usually require a large number of function evaluations (FEs) for evaluating the quality of solutions. However, only a limited number of FEs are affordable in many real-world optimization problems where the FEs are computationally or economically expensive. The use of a large number of FEs decreases the effectiveness of MOEAs in solving these problems. This article proposes a dual fuzzy classifier-based surrogate model (DFC) and a DFC-based multiobjective evolutionary algorithm framework (DFC-MOEA) for expensive optimization problems. The DFC model is used for offspring pre-selection to choose high-quality offspring solutions and for categorization to divide unevaluated solutions into three categories. In the proposed framework, two fuzzy classifiers are built to predict the quality of each unevaluated solution. To strike a balance between convergence and diversity, one classifier is designed for predicting the dominance relation of unevaluated solutions (i.e., convergence), and another classifier is designed for predicting the crowdedness of unevaluated solutions (i.e., diversity). The integration of the proposed framework in three different types of MOEAs (i.e., a dominance-based MOEA, an indicator-based MOEA, and a decomposition-based MOEA) demonstrates its usefulness in handling expensive optimization problems. Comprehensive experiments on four well-known test suites and several real-world optimization problems demonstrate that the proposed framework is able to improve the performance of MOEAs under a limited number of FEs.

A user-guided innovization-based evolutionary algorithm framework for practical multi-objective optimization problems

The knowledge of experienced users in solving real-world optimization problems can be formulated as inter-variable relationships to guide an optimization algorithm towards good solutions faster. Alternatively, such interactions can be learned algorithmically during the optimization by analysing good solutions—a process called innovization. Any common pattern extracted from good solutions can be used as a repair operator to modify candidate solutions. The key aspect is to strike a balance between the relevance of the pattern and the extent of its use in the repair operator. This article proposes a multi-objective evolutionary algorithm framework that combines problem-specific knowledge and online innovization approaches to solve two real-world large-scale multi-objective problems: a 879- and 1479-variable truss design and a 544-variable solid fuel rocket design. Four repair operators suitable for uncovering monotonic relations involving multiple decision variables are proposed. Performance variations resulting from different combinations of initial user knowledge and repair operators are also presented.

A novel dynamic reference point model for preference-based evolutionary multiobjective optimization

AbstractIn the field of preference-based evolutionary multiobjective optimization, optimization algorithms are required to search for the Pareto optimal solutions preferred by the decision-maker (DM). The reference point is a type of techniques that effectively describe the preferences of DM. So far, the reference point is either static or interactive with the evolutionary process. However, the existing reference point techniques do not cover all application scenarios. A novel case, i.e., the reference point changes over time due to the environment change, has not been considered. This paper focuses on the multiobjective optimization problems with dynamic preferences of the DM. First, we propose a change model of the reference point to simulate the change of the preference by the DM over time. Then, a dynamic preference-based multiobjective evolutionary algorithm framework with a clonal selection algorithm (ĝa-NSCSA) and a genetic algorithm (ĝa-NSGA-II) is designed to solve such kind of optimization problems. In addition, in terms of practical applications, the experiments on the portfolio optimization problems with the dynamic reference point model are tested. Experimental results on the benchmark problems and the practical applications show that ĝa-NSCSA exhibits better performance among the compared optimization algorithms.

A novel dynamic reference point model for preference-based evolutionary multiobjective optimization

In the field of preference-based evolutionary multiobjective optimization, optimization algorithms are required to search for the Pareto optimal solutions preferred by the decision maker (DM). The reference point is a type of techniques that effectively describe the preferences of DM. So far, the reference point is either static or interactive with the evolutionary process. However, the existing reference point techniques do not cover all application scenarios. A novel case, i.e., the reference point changes over time due to the environment change, has not been considered. This paper focuses on the multiobjective optimization problems with dynamic preferences of the DM. First, we propose a change model of the reference point to simulate the change of the preference by the DM over time. Then, a dynamic preference-based multiobjective evolutionary algorithm framework with a clonal selection algorithm (ĝa-NSCSA) and a genetic algorithm (ĝa-NSGA-II) is designed to solve such kind of optimization problems. In addition, in terms of practical applications, the experiments on the portfolio optimization problems with the dynamic reference point model are tested. Experimental results on the benchmark problems and the practical applications show that ĝa-NSCSA exhibits better performance among the compared optimization algorithms.

A dual-operator strategy for a multiobjective evolutionary algorithm based on decomposition

Evolutionary Algorithms (EAs) are a kind of population based on optimization method by adopting survival of the fittest rules. The performance of EAs can be greatly improved by appropriate genetic operators, so how to select an appropriate genetic operator is a key issue. In order to solve this problem, some genetic operators are mixed to use with a certain probability to improve their spatial search capabilities. However, it is difficult to solve most complex multi-objective problems (MOPs) based on a certain probability value. In this paper, under the concept of co-evolution and Duty Ratio, we built a genetic operator based on Differential Evolution (DE) and Simulated Binary Crossover (SBX), and the adjustment of Duty Ratio parameter is learned based on the historical used times of DE and SBX. Under the framework of Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), we propose our dual-operator strategy (DOS) based on learning strategy, namely MOEA/D-DOS. We compared MOEA/D-DOS with other six versions of multi-objective EAs, and the final result showed that MOEA/D-DOS has achieved the better results.

Multi-Objective Design of a Lunar GNSS

<h3>Abstract</h3> The success of future lunar missions depends on quality positioning, navigation, and timing (PNT) information. Earthbound GNSS signals can be received at lunar distances but suffer from poor geometric dilution of precision (GDOP) and provide no coverage of the lunar far side. This article explores the design space of a dedicated GNSS system in lunar orbit by using a multi-objective evolutionary algorithm framework to optimize GDOP, availability, space segment cost, station-keeping ΔV, and robustness to single-satellite failure. Results show that Pareto approximate solutions that achieve a global GDOP availability (GDOP ≤ 6.0) greater than 98% contain a minimum of 24 satellites in near-circular polar orbits at an altitude of ~2 lunar radii. The impact of single-satellite failure on GDOP outage is analyzed and a no-maneuver scenario is considered. Design rules characterizing optimal solutions are identified and trade-offs between station-keeping maneuver frequency, performance, and design lifetime are discussed.

A Decomposition-Based Multiobjective Optimization Evolutionary Algorithm with Adaptive Weight Generation Strategy

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is the seminal framework of multiobjective evolutionary algorithms (MOEAs). To alleviate the nonuniformly distributed solutions generated by a fixed set of evenly distributed weight vectors in the presence of nonconvex and disconnected problems, an adaptive vector generation mechanism is proposed. A coevolution strategy and a vector generator are synergistically cooperated to remedy the weight vectors. Optimal weight vectors are generated to replace the useless weight vectors to assure that optimal solutions are distributed evenly. Experiment results indicate that this mechanism is efficient in improving the diversity of MOEA/D.

Evolutionary optimization using epsilon method for resource-constrained multi-robotic disassembly line balancing

This paper concentrates on a resource-constrained multi-robotic disassembly line balancing (RC-MDLB) problem. In this RC-MDLB problem, different types of end-of-life products are disassembled simultaneously on the same line under the following conditions: allocating multiple robots to a workstation to simultaneously process the disassembly tasks that have no precedence relationship with each other, each robot needs a fixed number of limited resources to process tasks, and the total resources for each workstation is fixed. A mathematical model is presented for the RC-MDLB problem to minimize the cycle time and the number of robots being occupied simultaneously. A constrained multi-objective evolutionary algorithm framework and a constrained NSGA-II (E-NSGA-II) algorithm with epsilon method are proposed to handle the constraints of the RC-MDLB problem. The proposed E-NSGA-II is applied to a set of RC-MDLB problem instances introduced in this paper and compared with five representative multi-objective evolutionary algorithms. The experimental results reveal that the proposed E-NSGA-II presents outstanding performance on most of the cases analyzed.

A new framework of multi-objective evolutionary algorithms for feature selection and multi-label classification of video data

There are few studies in the literature to address the multi-objective multi-label feature selection for the classification of video data using evolutionary algorithms. Selecting the most appropriate subset of features is a significant problem while maintaining/improving the accuracy of the prediction results. This study proposes a framework of parallel multi-objective Non-dominated Sorting Genetic Algorithms (NSGA-II) for exploring a Pareto set of non-dominated solutions. The subsets of non-dominated features are extracted and validated by multi-label classification techniques, Binary Relevance (BR), Classifier Chains (CC), Pruned Sets (PS), and Random k-Labelset (RAkEL). Base classifiers such as Support Vector Machines (SVM), J48-Decision Tree (J48), and Logistic Regression (LR) are performed in the classification phase of the algorithms. Comprehensive experiments are carried out with local feature descriptors extracted from two multi-label data sets, the well-known MIR-Flickr dataset and a Wireless Multimedia Sensor (WMS) dataset that we have generated from our video recordings. The prediction accuracy levels are improved by 6.36% and 25.7% for the MIR-Flickr and WMS datasets respectively while the number of features is significantly reduced. The results verify that the algorithms presented in this new framework outperform the state-of-the-art algorithms.

A Compression-Based Multi-Objective Evolutionary Algorithm for Community Detection in Social Networks

Community detection is a key aspect for understanding network structures and uncovers the underlying functions or characteristics of complex systems. A community usually refers to a set of nodes that are densely connected among themselves, but sparsely connected to the remaining nodes of the network. Detecting communities has been proved to be a NP-hard problem. Therefore, evolutionary based optimization approaches can be used to solve it. But a primary challenge for them is the higher computational complexity when dealing with large scale networks. In this respect, a COMpression based Multi-Objective Evolutionary Algorithm with Decomposition (Com-MOEA/D) for community detection is proposed where the network is first compressed to a much more smaller scale by exploring network topologies. After that, a framework of multi-objective evolutionary algorithm based on decomposition is applied, in which a local information based genetic operator is proposed to speed up the convergence and improve the accuracy of the Com-MOEA/D algorithm. Experimental results on both real world and synthetic networks show the superiority of the proposed method over several state-of-the-art community detection algorithms.

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 evolutionary multi-objective community mining algorithm for signed networks

Community detection in presence of both positive and negative interactions in signed community structures has recently enjoyed a large increase in interest. The general definition of community structure which considers both strong and weak connections of the individual nodes in a network is adopted in the literature for signed community detection. Despite the widespread use of this definition, it lacks complete reflection of specific topological properties such as type of ties, in terms of positive and negative connections. To remedy this difficulty, a new community detection model for signed networks is suggested in this paper. The main contribution of this paper is three-fold. First, the quantitative definition of community structure is revisited to properly reflect positive and negative characteristics of the ties in signed networks. Three definitions are introduced to explicitly identify the possible means of signed communities in three different forms. These are strong signed community, weak signed community, and irregular signed community. Then, a new multi-objective signed community detection model and a new anti-frustration heuristic operator are introduced. The proposed model and operator hypothesize a possible clustering of the signed complex network into signed communities under the framework of multi-objective evolutionary algorithm. The essential principle of both of them is to establish “more positive and less negative intra relations between the nodes of a signed community” and “more negative and less positive inter relations among different signed communities”. The performance of the proposed model is tested against other state-of-the-art signed community detection models. In the experiments, we demonstrate that, in general, our model outperforms the counterpart models, and moreover, the proposed anti-frustration heuristic operator harnesses the strength of all detection models, keeping our model with the highest level of detection reliability.

Ant Colony Optimization for the Control of Pollutant Spreading on Social Networks.

The rapid development of online social networks not only enables prompt and convenient dissemination of desirable information but also incurs fast and wide propagation of undesirable information. A common way to control the spread of pollutants is to block some nodes, but such a strategy may affect the service quality of a social network and leads to a high control cost if too many nodes are blocked. This paper considers the node selection problem as a biobjective optimization problem to find a subset of nodes to be blocked so that the effect of the control is maximized while the cost of the control is minimized. To solve this problem, we design an ant colony optimization algorithm with an adaptive dimension size selection under the multiobjective evolutionary algorithm framework based on decomposition (MOEA/D-ADACO). The proposed algorithm divides the biobjective problem into a set of single-objective subproblems and each ant takes charge of optimizing one subproblem. Moreover, two types of pheromone and heuristic information are incorporated into MOEA/D-ADACO, that is, pheromone and heuristic information of dimension size selection and that of node selection. While constructing solutions, the ants first determine the dimension size according to the former type of pheromone and heuristic information. Then, the ants select a specific number of nodes to build solutions according to the latter type of pheromone and heuristic information. Experiments conducted on a set of real-world online social networks confirm that the proposed biobjective optimization model and the developed MOEA/D-ADACO are promising for the pollutant spreading control.

A comprehensive multi-objective approach of service selection for service processes with twofold restrictions

To build complex business processes with QoS constraints by services with inter-service correlations is a challenge. Meeting this challenge involves the QoS-aware service selection problem for service processes with twofold restrictions (QoS constraints and inter-service correlations). Recently, QoS-aware service selection has been addressed from a multi-objective perspective. However, existing research fails to comprehensively consider both QoS constraints and inter-service correlations that widely exist in a real business world. Besides, none of them comprehensively considers both service selection at build time and run time, which may lead to high economic compensation caused by breach penalties at run time. In this paper, we present a comprehensive multi-objective optimization model for service selection with twofold restrictions. Furthermore, an improved multi-objective evolutionary algorithm framework for this model (MOEAQI) is proposed, which can provide a systematic solution for service selection at build time and run time respectively. In this framework, a constrained-domination principle is designed for the specific objectives and constraints in different phases, and several improved strategies are proposed to increase the searching effectiveness and efficiency. Finally, three sets of experiments with different problem sizes are constructed, and our approach is tested in comparison to the state-of-the-art algorithms for service selection problems including GDE3, E3MOGA and DASC. The performance of each algorithm is evaluated in the aspects of set coverage, spacing and computation time. Experimental results demonstrate that our approach is more effective than existing methods for service selection with twofold restrictions.

Selection methods and diversity preservation in many-objective evolutionary algorithms

PurposeOne of the main components of multi-objective, and therefore, many-objective evolutionary algorithms, is the selection mechanism. It is responsible for performing two main tasks simultaneously. First, it has to promote convergence by selecting solutions which are as close as possible to the Pareto optimal set. And second, it has to promote diversity in the solution set provided. In the current work, an exhaustive study that involves the comparison of several selection mechanisms with different features is performed. Particularly, Pareto-based and indicator-based selection schemes, which belong to well-known multi-objective optimisers, are considered. The paper aims to discuss these issues.Design/methodology/approachEach of those mechanisms is incorporated into a common multi-objective evolutionary algorithm framework. The main goal of the study is to measure the diversity preserved by each of those selection methods when addressing many-objective optimisation problems. The Walking Fish Group test suite, a set of optimisation problems with a scalable number of objective functions, is taken into account to perform the experimental evaluation.FindingsThe computational results highlight that the the reference-point-based selection scheme of the Non-dominated Sorting Genetic Algorithm III and a modified version of the Non-dominated Sorting Genetic Algorithm II, where the crowding distance is replaced by the Euclidean distance, are able to provide the best performance, not only in terms of diversity preservation, but also in terms of convergence.Originality/valueThe performance provided by the use of the Euclidean distance as part of the selection scheme indicates this is a promising line of research and, to the best of the knowledge, it has not been investigated yet.

Multi-objective clustering technique based on [formula omitted]-nodes update policy and similarity matrix for mining communities in social networks

This paper proposes a relatively all-purpose network clustering technique based on the framework of multi-objective evolutionary algorithms, which can effectively dispose the issue of community detection in unsigned social networks, as well as in signed social networks. Firstly, we formulate a generalized similarity function to construct a similarity matrix, and then a pre-partitioning strategy is projected according to the similarity matrix. The pre-partitioning strategy merely considers nodes with high similarity values, which avoids the interference of noise nodes during the label update phase. In this way, at the initial phase of the algorithm, nodes with strong connections are fleetly gathered into sub-communities. Secondly, we elaborately devise a crossover operator, called cross-merging operator, to merge sub-communities generated by the pre-partitioning technique. Moreover, a special mutation operator, based on the similarity matrix of nodes, is implemented to adjust boundary nodes connecting different communities. Finally, to handle different types of networks, we, therefore, have presented the novel multi-objective optimization models for this issue. Through a bulk of rigorous experiments on both unsigned and signed social networks, the preeminent clustering performance illustrate that the proposed algorithm is capable of mining communities effectively.

GALAXY: A new hybrid MOEA for the optimal design of Water Distribution Systems

AbstractA new hybrid optimizer, called genetically adaptive leaping algorithm for approximation and diversity (GALAXY), is proposed for dealing with the discrete, combinatorial, multiobjective design of Water Distribution Systems (WDSs), which is NP‐hard and computationally intensive. The merit of GALAXY is its ability to alleviate to a great extent the parameterization issue and the high computational overhead. It follows the generational framework of Multiobjective Evolutionary Algorithms (MOEAs) and includes six search operators and several important strategies. These operators are selected based on their leaping ability in the objective space from the global and local search perspectives. These strategies steer the optimization and balance the exploration and exploitation aspects simultaneously. A highlighted feature of GALAXY lies in the fact that it eliminates majority of parameters, thus being robust and easy‐to‐use. The comparative studies between GALAXY and three representative MOEAs on five benchmark WDS design problems confirm its competitiveness. GALAXY can identify better converged and distributed boundary solutions efficiently and consistently, indicating a much more balanced capability between the global and local search. Moreover, its advantages over other MOEAs become more substantial as the complexity of the design problem increases.

A multi-objective evolutionary algorithm for multi-period dynamic emergency resource scheduling problems

The resource distribution in post-disaster is an important part of emergency resource scheduling. In this paper, we first design a multi-objective optimization model for multi-period dynamic emergency resource scheduling (ERS) problems. Then, using the framework of multi-objective evolutionary algorithm based on decomposition (MOEA/D), an MOEA is proposed to solve this model. In the proposed algorithm, new evolutionary operators are designed with the intrinsic properties of multi-period dynamic ERS problems in mind. The experimental results show that the proposed algorithm can get a set of better candidate solutions than the non-dominated sorting genetic algorithm II (NSGA-II).