Evolutionary Multi-objective Optimization Research Articles

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 multi-objective evolutionary optimisation model for heterogeneous vehicles routing and relief items scheduling in humanitarian crises

In a disaster scenario, relief items distribution is required as early as possible for the disaster victims to reduce the associated risks. For the distribution tasks, an effective and efficient relief items distribution model is essential to generate relief items distribution schedules to minimise the impact of disaster to the disaster victims. However, developing efficient distribution schedules is challenging as the relief items distribution problem has multiple objectives to look after where the objectives are mostly contradictorily creating a barrier to simultaneous optimisation of each objective. Also, the relief items distribution model has added complexity with the consideration of multiple supply points having heterogeneous and limited vehicles with varying capacity, cost and time. In this paper, multi-objective evolutionary optimisation with the greedy heuristic search has been applied for the generation of relief items distribution schedules under heterogeneous vehicles condition at supply points. The evolutionary algorithm generates the disaster region distribution sequence by applying a global greedy heuristic search along with a local search that finds the efficient assignment of heterogeneous vehicles for the distribution. This multi-objective evolutionary approach provides Pareto optimal solutions that decision-makers can apply to generate effective distribution schedules to optimise the distribution time and vehicles’ operational cost. In addition, this optimisation process also incorporated the minimisation of unmet relief items demand at the disaster regions. The optimised distribution schedules with the proposed approach are compared with the single-objective optimisation, weighted single-objective optimisation and greedy multi-objective optimisation approaches. The comparative results showed that the proposed multi-objective evolutionary approach is an efficient alternative for finding the distribution schedules with optimisation of distribution time and operational cost for the relief items distribution with heterogeneous vehicles in humanitarian crisis.

Finding top-K solutions for the decision-maker in multiobjective optimization

Multiobjective optimization problems (MOPs) are the optimization problem with multiple conflicting objectives. Generally, an optimization algorithm can find a large number of optimal solutions for MOPs, which easily overwhelm decision makers (DMs) and make it difficult for decision-making. Preference-based evolutionary multiobjective optimization (EMO) aims to find the partial optima in the regions preferred by the DM. Although it narrows the scope of the optimal solutions, it usually still returns a population of optimal solutions (typically 100 or larger in EMO) with a small distance between adjacent optima. Top-K, which is a well-established research subject in many fields to find the best K solutions, may be a direction to reduce the number of optimal solutions. In this paper, first, we introduce the top-K notion into preference-based EMO and propose the top-K model to obtain the best K individuals of multiobjective optimization problems (MOPs). Then, with the top-K model, we propose NSGA-II-TopK and SPEA2-TopK to search for the top-K preferred solutions for preference-based continuous and combinatorial MOPs, respectively. Finally, the proposed algorithms with several representative preference-based EMO algorithms are compared in different preference situations for MOPs. Experimental results show the proposed algorithms have strong performances against the compared 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 novel multi-level population hybrid search evolution algorithm for constrained multi-objective optimization problems

Constrained multi-objective optimization problem (CMOP) considers the convergence, diversity and feasibility of the population in the optimization process, so it is challenging to find desirable solutions of CMOP. Existing evolutionary multi-objective optimization algorithms have good performance on unconstrained multi-objective optimization problems, but have difficulties in solving CMOPs in discrete feasible regions. Aiming at this issue, this paper proposes a novel multi-level population hybrid search evolution algorithm (MLHSEA). First, a new multi-level hybrid search strategy (i.e. MHSS) is designed in the algorithm, which divides the population into three-level subpopulations based on Pareto ranks, constraint violation degree values, and feasible thresholds. Each subpopulation has its own unique evolution strategy to maximize the evolutionary potential of each subpopulation, which is beneficial to make some feasible solutions break through the discrete feasible region and reach the Pareto frontier. Then, a new population fusion degree strategy (i.e. PFDS) is proposed to timely perform population fusion and information exchange according to the population fusion degree (PFD) of each sub-population, thus improving the searchability of the target space. Finally, a novel detection reset strategy (i.e. DRS) is proposed for the lowest inferior subpopulation. This strategy can make inferior subpopulations avoid unnecessary evolutionary iterations and improve population diversity. Based on constrained test suites with four different characteristics, the experimental results show that the proposed MLHSEA outperforms other state-of-the-art constrained multi-objective optimization algorithms in performance.

Computational generation of a spatial layout through syntactical evaluation and multi-objective evolutionary optimization

The space layout problem encompasses challenges that rely on a diverse range of contexts regarding urban planning and architectural design, during the traditional design phases which require immense effort and time for the evaluation of the spatial elements’ characteristic needs. In order to eliminate the burden of considering all multidimensional design aspects at the same time, this research presents a three-bodied computational method for locating the spaces of the given architectural design program in a project site, according to the defined list of design objectives and criteria. Besides the determination of the layout according to the requirements of the spatial elements, this research proposes an integration of the space syntax theory’s analytical compounds in terms of Justified Graph Analysis and Integration Values as the fitness criteria for the multi-objective evolutionary optimization in the computational model. To satisfy the integrity levels of each various characterized element within site organization, that are implied inherently by the architectural design program and generate a sustainable space network layout for the project site.

Optimization of multi-mode classification for process monitoring

Process monitoring seeks to identify anomalous plant operating states so that operators can take the appropriate actions for recovery. Instrumental to process monitoring is the labeling of known operating states in historical data, so that departures from these states can be identified. This task can be challenging and time consuming as plant data is typically high dimensional and extensive. Moreover, automation of this procedure is not trivial since ground truth labels are often unavailable. In this contribution, this problem is approached as a multi-mode classification one, and an automatic framework for labeling using unsupervised Machine Learning (ML) methods is presented. The implementation was tested using data from the Tennessee Eastman Process and an industrial pyrolysis process. A total of 9 ML ensembles were included. Hyperparameters were optimized using a multi-objective evolutionary optimization algorithm. Unsupervised clustering metrics (silhouette score, Davies-Bouldin index, and Calinski-Harabasz Index) were investigated as candidates for objective functions in the optimization implementation. Results show that ensembles and hyperparameter selection can be aided by multi-objective optimization. It was found that Silhouette score and Davies-Bouldin index are strong predictions of the ensemble’s performance and can then be used to obtain good initial results for subsequent fault detection and fault diagnosis procedures.

Path planning for autonomous mobile robots using multi-objective evolutionary particle swarm optimization.

In this article, a new path planning algorithm is proposed. The algorithm is developed on the basis of the algorithm for finding the best value using multi-objective evolutionary particle swarm optimization, known as the MOEPSO. The proposed algorithm is used for the path planning of autonomous mobile robots in both static and dynamic environments. The paths must follow the determined criteria, namely, the shortest path, the smoothest path, and the safest path. In addition, the algorithm considers the degree of mutation, crossover, and selection to improve the efficiency of each particle. Furthermore, a weight adjustment method is proposed for the movement of particles in each iteration to increase the chance of finding the best fit solution. In addition, a method to manage feasible waypoints within the radius of obstacles or blocked by obstacles is proposed using a simple random method. The main contribution of this article is the development of a new path planning algorithm for autonomous mobile robots. This algorithm can build the shortest, smoothest, and safest paths for robots. It also offers an evolutionary operator to prevent falling into a local optimum. The proposed algorithm uses path finding simulation in a static environment and dynamic environment in conjunction with comparing performance to path planning algorithms in previous studies. In the static environment (4 obstacles), the shortest path obtained from the proposed algorithm is 14.3222 m. In the static environment (5 obstacles), the shortest path obtained from the proposed algorithm is 14.5989 m. In the static environment (6 obstacles), the shortest path obtained from the proposed algorithm is 14.4743 m. In the dynamic environment the shortest path is 12.2381 m. The results show that the proposed algorithm can determine the paths from the starting point to the destination with the shortest distances that require the shortest processing time.

Incremental Non-Dominated Sorting algorithms based on Irreducible Domination Graphs

Non-Dominated Sorting process, NDS, plays an important role in Pareto based Evolutionary Multi-Objective Optimization Algorithms and it is one of the most time consuming tasks, mainly when steady-state Evolutionary Algorithms are considered, i.e. algorithms in which the updating of the Pareto layers must be accomplished every time a new solution is generated. In this paper we present a general framework to carry out the NDS process and three implementations based on a modification of the Irreducible Domination Graph structure, IDG, presented in Alberto and Mateo (2004) for accomplishing this task. The proposed algorithms are compared with other NDS algorithms designed specifically for the incremental update of the Pareto layers. The experiments carried out show that the proposed algorithms reduce, in general, the time needed as well as the number of Pareto comparisons when compared with the competitors.

Using Dominated Solutions at Edges to the Diversity and the Uniformity of Non-dominated Solution Distributions in NSGA-II

This paper proposes a method for improving the diversity of the Pareto front and the uniformity of non-dominated solution distributions in a fast elitist non-dominated sorting genetic algorithm (NSGA-II), which is an evolutionary multi-objective optimization algorithm. Conventional NSGA-II has excellent convergence to the Pareto front, but it has been reported that for some test cases, it does not produce a more diverse solution distribution than the strength Pareto evolutionary algorithm 2 (SPEA2). In addition, selection using the crowding distance may cause a bias in the selected solution distribution. To avoid this problem, we propose a method that archives dominated solutions that may be effective in improving diversity in the conventional search process when used for genetic operations, and mates these archived solutions with non-dominated solutions at the edge of rank 1 for each objective function. We experimentally compare this approach with the conventional method on the typical ZDT suite of multi-objective test problems and a two-objective constrained knapsack problem. By evaluating the performance based on Pareto front diagrams, the number of non-dominated solutions, the maximum spread and hypervolume values, we show that the proposed method is effective at improving the diversity at both ends of the Pareto optimal front and the solution distribution.

Robustness Enhancement of Neural Networks via Architecture Search with Multi-Objective Evolutionary Optimization

Along with the wide use of deep learning technology, its security issues have drawn much attention over the years. Adversarial examples expose the inherent vulnerability of deep learning models and make it a challenging task to improve their robustness. Model robustness is related not only to its parameters but also to its architecture. This paper proposes a novel robustness enhanced approach for neural networks based on a neural architecture search. First, we randomly sample multiple neural networks to construct the initial population. Second, we utilize the individual networks in the population to fit and update the surrogate models. Third, the population of neural networks is evolved through a multi-objective evolutionary algorithm, where the surrogate models accelerate the performance evaluation of networks. Finally, the second and third steps are performed alternately until a network architecture with high accuracy and robustness is achieved. Experimental results show that the proposed method outperforms some classical artificially designed neural networks and other architecture search algorithms in terms of robustness.

Incremental learning-inspired mating restriction strategy for Evolutionary Multiobjective Optimization

The prior knowledge from the problem property can boost the evolutionary multiobjective optimization (EMO). The existing machine learning model for knowledge mining in the EMO has led to enhanced performance on multiobjective optimization problems with complicated Pareto fronts (MOPs-cPF), but the high computational cost resulting from model training should not be taken as a natural expense. To overcome this drawback, this paper proposes an incremental learning-inspired mating restriction strategy (ILMR) for solving MOP-cPF efficiently. In ILMR, a mating restriction is implemented based on an incremental learning model that establishes the mating pool for each solution in the population and incrementally updates as the population evolves. Specifically, it consists of two interdependent parts, i.e., a learning module and a forgetting module. In one evolutionary cycle, the learning module is used to learn new knowledge from the high-quality offspring solutions, while the forgetting module is utilized to remove the information provided by relatively poor solutions in the population. Moreover, a multiobjective evolutionary algorithm with ILMR, named MEILM, is proposed and compared with six state-of-the-art algorithms on a variety of MOP-cPF. The experimental results show that there are significant improvements benefitting from the proposed mating restriction strategy.

Multiobjective Deep Clustering and its Applications in Single-cell RNA-seq Data

Single-cell RNA sequencing is a transformative technology that enables us to study the heterogeneity of the tissue at the cellular level. Clustering is used as the key computational approach to group cells under the transcriptome profiles from single-cell RNA-seq data. However, accurate identification of distinct cell types is facing the challenge of high dimensionality, and it could cause uninformative clusters when clustering is directly applied on the original transcriptome. To address such challenge, an evolutionary multiobjective deep clustering (EMDC) algorithm is proposed to identify single-cell RNA-seq data in this study. First, EMDC removes redundant and irrelevant genes by applying the differential gene expression analysis to identify differentially expressed genes across biological conditions. After that, a deep autoencoder is proposed to project the high-dimensional data into different low-dimensional nonlinear embedding subspaces under different bottleneck layers. Then, the basic clustering algorithm is applied in those nonlinear embedding subspaces to generate some basic clustering results to produce the cluster ensemble. To lessen the unnecessary cost produced by those clusterings in the ensemble, the multiobjective evolutionary optimization is designed to prune the basic clustering results in the ensemble, unleashing its cell type discovery performance under three objective functions. Multiple experiments have been conducted on 30 synthetic single-cell RNA-seq datasets and six real single-cell RNA-seq datasets, which reveal that EMDC outperforms eight other clustering methods and three multiobjective optimization algorithms in cell type identification. In addition, we have conducted extensive comparisons to effectively demonstrate the impact of each component in our proposed EMDC.

Evolutionary Multi-Objective Optimization Applied to Industrial Refrigeration Systems for Energy Efficiency

Refrigeration systems based on cooling towers and chillers are widely used equipment in industrial buildings, such as shopping centers, gas and oil refineries and power plants, among many others. Cooling towers are used to recover the heat rejected by the refrigeration system. In this work, the refrigeration is composed of cooling towers dotted with ventilators and compression chillers. The growing environmental concerns and the current scenario of scarce water and energy resources have lead to the adoption of actions to obtain the maximum energy efficiency in such refrigeration equipment. This backs up the application of computational intelligence to optimize the operating conditions of the involved equipment and cooling processes. In this context, we utilize multi-objective optimization algorithms to determine the optimal operational setpoints of the cooling system regarding the cooling towers, its fans and the included chillers. We use evolutionary multi-objective optimization to provide the best trade-offs between two conflicting objectives: maximization of the effectiveness of the cooling towers and minimization of the overall power requirement of the refrigeration system. The optimization process respects the constraints to guarantee the correct and safe operation of the equipment when the evolved solution is implemented. In this work, we apply three evolutionary multi-objective algorithms: Non-dominated Sorting Genetic Algorithm (NSGA-II), Micro-Genetic Algorithm (Micro-GA) and Strength Pareto Evolutionary Algorithm (SPEA2). The results obtained are analyzed under different scenarios and models of the cooling system’s equipment, allowing for the selection of the best algorithm and best equipment’s model to achieve energy efficiency of the studied refrigeration system.

Fast Greedy Subset Selection From Large Candidate Solution Sets in Evolutionary Multiobjective Optimization

Subset selection plays an important role in the field of evolutionary multiobjective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive (UEA), subset selection is an essential post-processing procedure to select a prespecified number of solutions as the final result. In this article, we discuss the efficiency of greedy subset selection for the hypervolume, inverted generational distance (IGD), and IGD plus (IGD+) indicators. Greedy algorithms usually efficiently handle the subset selection. However, when a large number of solutions are given (e.g., subset selection from tens of thousands of solutions in a UEA), they often become time consuming. Our idea is to use the submodular property, which is known for the hypervolume indicator, to improve their efficiency. First, we prove that the IGD and IGD+ indicators are also submodular. Next, based on the submodular property, we propose an efficient greedy inclusion algorithm for each indicator. We demonstrate through computational experiments that the proposed algorithms are much faster than the standard greedy subset selection algorithms. The proposed algorithms also help the research on performance indicators.

An Ensemble Surrogate-Based Framework for Expensive Multiobjective Evolutionary Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have become very popular for tackling computationally expensive multiobjective optimization problems (EMOPs), as the surrogate models in SAEAs can approximate EMOPs well, thereby reducing the time cost of the optimization process. However, with the increased number of decision variables in EMOPs, the prediction accuracy of surrogate models will deteriorate, which inevitably worsens the performance of SAEAs. To deal with this issue, this article suggests an ensemble surrogate-based framework for tackling EMOPs. In this framework, a global surrogate model is trained under the entire search space to explore the global area, while a number of surrogate submodels are trained under different search subspaces to exploit the subarea, so as to enhance the prediction accuracy and reliability. Moreover, a new infill sampling criterion is designed based on a set of reference vectors to select promising samples for training the models. To validate the generality and effectiveness of our framework, three state-of-the-art evolutionary algorithms [nondominated sorting genetic algorithm III (NSGA-III), multiobjective evolutionary algorithm based on decomposition with differential evolution (MOEA/D-DE) and reference vector-guided evolutionary algorithm (RVEA)] are embedded, which significantly improve their performance for solving most of the test EMOPs adopted in this article. When compared to some competitive SAEAs for solving EMOPs with up to 30 decision variables, the experimental results also validate the advantages of our approach in most cases.

A decomposition-based many-objective evolutionary algorithm with adaptive weight vector strategy

Evolutionary multi-objective optimization methods have become increasingly popular in finding a representative set of Pareto optimal solutions for multi-objective optimization problems (MOPs). As an important multi-objective optimization method, MOEA/D has been successfully applied to resolve various of MOPs. However, there still exist two issues in MOEA/D. First, the distribution of result set is greatly limited in complex Pareto Front (PF) shapes. Second, the effectiveness is relatively poor for solving many-objective optimization problems (MaOPs). Although many researchers attempt to improve MOEA/D, these two issues have not been solved well. This paper proposes a modified MOEA/D method called MOEA/D-VW which involves three optimization strategies. First, an adaptive weight vector adjustment strategy is adopted to fine-tune the subproblems, thus changing the evolution direction of the subpopulation. Second, a weight vector initialization strategy with preference parameters is added into MOEA/D-VW. Third, a modified crossover operator is leveraged to generate new population with good diversity and overcome the problem of high computational cost. Experiments are carried out on the set of 23 continuous optimization problems. The experimental results show that the performance and the distribution of the Pareto Set (PS) of MOEA/D-VW are effectively improved. Meanwhile, the experimental results demonstrate that the modified crossover operator can effectively reduce the computational cost of MOEA/D-VW.

An environment-driven hybrid evolutionary algorithm for dynamic multi-objective optimization problems

In dynamic multi-objective optimization problems, the environmental parameters may change over time, which makes the Pareto fronts shifting. To address the issue, a common idea is to track the moving Pareto front once an environmental change occurs. However, it might be hard to obtain the Pareto optimal solutions if the environment changes rapidly. Moreover, it may be costly to implement a new solution. By contrast, robust Pareto optimization over time provides a novel framework to find the robust solutions whose performance is acceptable for more than one environment, which not only saves the computational costs for tracking solutions, but also minimizes the cost for switching solutions. However, neither of the above two approaches can balance between the quality of the obtained non-dominated solutions and the computation cost. To address this issue, environment-driven hybrid dynamic multi-objective evolutionary optimization method is proposed, aiming to fully use strengths of TMO and RPOOT under various characteristics of environmental changes. Two indexes, i.e., the frequency and intensity of environmental changes, are first defined. Then, a criterion is presented based on the characteristics of dynamic environments and the switching cost of solutions, to select an appropriate optimization method in a given environment. The experimental results on a set of dynamic benchmark functions indicate that the proposed hybrid dynamic multi-objective evolutionary optimization method can choose the most rational method that meets the requirements of decision makers, and balance the convergence and robustness of the obtained non-dominated solutions.

Application Analysis of Multi-Intelligence Optimization Decision-Making Method in College Students’ Ideological and Political Education System

Today’s society is a society with diversified information. The rapid change of information also affects the ideological and political education in universities. Therefore, the fixed thinking of ideological and political education in universities tells students, which is an educational way in line with the development of the times. We should follow up with the rapidly changing times at any time, change with the times, and update the thinking and systematic way of the ideological and political education system at any time. In the ideological and political education of college students, diversified teaching methods and multiobjective recommendation systems are implemented and then combined with traditional ideological and political teaching methods. The two ways complement each other and promote each other so as to achieve higher learning efficiency and better learning effect. The optimization algorithm of multiobjective recommendation should be used to further improve the ideological and political education system. By analyzing the optimization results and performance comparison of various algorithms, we find the most suitable algorithm model for optimizing the ideological and political education system. The multiobjective-recommended ideological and political education system for college students needs to fully improve the teaching tasks of teachers and students in two stages. A reasonable and scientific system recommendation mechanism should take into account students’ own learning preferences, subject types, ideological and political teacher information, curriculum information, curriculum evaluation, curriculum relevance, and other multiobjective data. This paper achieves the highest performance and the lowest time cost of the ideological and political education system through multiobjective evolutionary optimization method.

Parallel multi-objective evolutionary optimization based dynamic community detection in software ecosystem

Building a dynamic network in a software ecosystem and detecting its communities can not only observe the structure of the dynamic network, but also reveal the evolution of these communities. However, previous methods cannot timely and accurately detect its communities. In view of this, we propose a method of dynamic community detection based on parallel multi-objective evolutionary optimization in this paper. In the proposed method, a dynamic network in a software ecosystem is first built based on the relationship between entities. The relationship is often time-dependent. Then, changed/unchanged connected components of the current network and time-dependent/independent sub-networks are obtained by recognizing the change of this network. Further, previous communities of each unchanged connected component remain unchanged, whereas ones of each time-dependent sub-network are detected based on parallel multi-objective evolutionary optimization. In this way, communities of each changed connected component are obtained based on ones of the time-dependent sub-network and previous ones of the time-independent sub-network, and ones of the current network after the change are formed. Five dynamic networks in a software ecosystem are built using data crawled in GitHub. Based on them, a series of experimental results demonstrate that the proposed method is advantageous.