Solving Large-Scale Multiobjective Optimization Problems With Sparse Optimal Solutions via Unsupervised Neural Networks

Evolution algorithm with adaptive genetic operator and dynamic scoring mechanism for large-scale sparse many-objective optimization

Large-scale sparse multi-objective optimization problems are prevalent in numerous real-world scenarios, such as neural network training, sparse regression, pattern mining and critical node detection, where Pareto optimal solutions exhibit sparse characteristics. Ordinary large-scale multi-objective optimization algorithms implement undifferentiated update operations on all decision variables, which reduces search efficiency, so the Pareto solutions obtained by the algorithms fail to meet the sparsity requirements. SparseEA is capable of generating sparse solutions and calculating scores for each decision variable, which serves as a basis for crossover and mutation in subsequent evolutionary process. However, the scores remain unchanged in iterative process, which restricts the sparse optimization ability of the algorithm. To solve the problem, this paper proposes an evolution algorithm with the adaptive genetic operator and dynamic scoring mechanism for large-scale sparse many-objective optimization (SparseEA-AGDS). Within the evolutionary algorithm for large-scale Sparse (SparseEA) framework, the proposed adaptive genetic operator and dynamic scoring mechanism adaptively adjust the probability of cross-mutation operations based on the fluctuating non-dominated layer levels of individuals, concurrently updating the scores of decision variables to encourage superior individuals to gain additional genetic opportunities. Moreover, to augment the algorithm's capability to handle many-objective problems, a reference point-based environmental selection strategy is incorporated. Comparative experimental results demonstrate that the SparseEA-AGDS algorithm outperforms five other algorithms in terms of convergence and diversity on the SMOP benchmark problem set with many-objective and also yields superior sparse Pareto optimal solutions.

TS-SSA: An improved two-stage sparrow search algorithm for large-scale many-objective optimization problems

Large-scale many-objective optimization problems (LSMaOPs) are a current research hotspot. However, since LSMaOPs involves a large number of variables and objectives, state-of-the-art methods face a huge search space, which is difficult to be explored comprehensively. This paper proposes an improved sparrow search algorithm (SSA) that manages convergence and diversity separately for solving LSMaOPs, called two-stage sparrow search algorithm (TS-SSA). In the first stage of TS-SSA, this paper proposes a many-objective sparrow search algorithm (MaOSSA) to mainly manages the convergence through the adaptive population dividing strategy and the random bootstrap search strategy. In the second stage of TS-SSA, this paper proposes a dynamic multi-population search strategy to mainly manage the diversity of the population through the dynamic population dividing strategy and the multi-population search strategy. TS-SSA has been experimentally compared with 10 state-of-the-art MOEAs on DTLZ and LSMOP benchmark test problems with 3-20 objectives and 300-2000 decision variables. The results show that TS-SSA has significant performance and efficiency advantages in solving LSMaOPs. In addition, we apply TS-SSA to a real case (automatic test scenarios generation), and the result shows that TS-SSA outperforms other algorithms on diversity.

Neural Net-Enhanced Competitive Swarm Optimizer for Large-Scale Multiobjective Optimization

The competitive swarm optimizer (CSO) classifies swarm particles into loser and winner particles and then uses the winner particles to efficiently guide the search of the loser particles. This approach has very promising performance in solving large-scale multiobjective optimization problems (LMOPs). However, most studies of CSOs ignore the evolution of the winner particles, although their quality is very important for the final optimization performance. Aiming to fill this research gap, this article proposes a new neural net-enhanced CSO for solving LMOPs, called NN-CSO, which not only guides the loser particles via the original CSO strategy, but also applies our trained neural network (NN) model to evolve winner particles. First, the swarm particles are classified into winner and loser particles by the pairwise competition. Then, the loser particles and winner particles are, respectively, treated as the input and desired output to train the NN model, which tries to learn promising evolutionary dynamics by driving the loser particles toward the winners. Finally, when model training is complete, the winner particles are evolved by the well-trained NN model, while the loser particles are still guided by the winner particles to maintain the search pattern of CSOs. To evaluate the performance of our designed NN-CSO, several LMOPs with up to ten objectives and 1000 decision variables are adopted, and the experimental results show that our designed NN model can significantly improve the performance of CSOs and shows some advantages over several state-of-the-art large-scale multiobjective evolutionary algorithms as well as over model-based evolutionary algorithms.

Two-stage sparse multi-objective evolutionary algorithm for channel selection optimization in BCIs

Background

Channel selection has become the pivotal issue affecting the widespread application of non-invasive brain-computer interface systems in the real world. However, constructing suitable multi-objective problem models alongside effective search strategies stands out as a critical factor that impacts the performance of multi-objective channel selection algorithms. This paper presents a two-stage sparse multi-objective evolutionary algorithm (TS-MOEA) to address channel selection problems in brain-computer interface systems.

Methods

In TS-MOEA, a two-stage framework, which consists of the early and late stages, is adopted to prevent the algorithm from stagnating. Furthermore, The two stages concentrate on different multi-objective problem models, thereby balancing convergence and population diversity in TS-MOEA. Inspired by the sparsity of the correlation matrix of channels, a sparse initialization operator, which uses a domain-knowledge-based score assignment strategy for decision variables, is introduced to generate the initial population. Moreover, a Score-based mutation operator is utilized to enhance the search efficiency of TS-MOEA.

Results

The performance of TS-MOEA and five other state-of-the-art multi-objective algorithms has been evaluated using a 62-channel EEG-based brain-computer interface system for fatigue detection tasks, and the results demonstrated the effectiveness of TS-MOEA.

Conclusion

The proposed two-stage framework can help TS-MOEA escape stagnation and facilitate a balance between diversity and convergence. Integrating the sparsity of the correlation matrix of channels and the problem-domain knowledge can effectively reduce the computational complexity of TS-MOEA while enhancing its optimization efficiency.

Multipopulation-Based Differential Evolution for Large-Scale Many-Objective Optimization

In recent years, numerous efficient many-objective optimization evolutionary algorithms have been proposed to find well-converged and well-distributed nondominated optimal solutions. However, their scalability performance may deteriorate drastically to solve large-scale many-objective optimization problems (LSMaOPs). Encountering high-dimensional solution space with more than 100 decision variables, some of them may lose diversity and trap into local optima, while others may achieve poor convergence performance. This article proposes a multipopulation-based differential evolution algorithm, called LSMaODE, which can solve LSMaOPs efficiently and effectively. In order to exploit and explore the exponential decision space, the proposed algorithm divides the population into two groups of subpopulations, which are optimized with different strategies. First, the randomized coordinate descent technique is applied to 10% of individuals to exploit the decision variables independently. This subpopulation maintains diversity in the decision space to avoid premature convergence into local optimum. Second, the remaining 90% of individuals are optimized with the nondominated guided random interpolation strategy, which interpolates individual among three nondominated solutions randomly. The strategy can guide the population convergent toward the nondominated solutions quickly, meanwhile, maintain good distribution in objective space. Finally, the proposed LSMaODE is evaluated on the LSMOP test suites from the scalability in both decision and objective dimensions. The performance is compared against five state-of-the-art large-scale many-objective evolutionary algorithms. The experimental results show that LSMaODE provides highly competitive performance.

A Multi-Population Multi-Objective Evolutionary Algorithm Based on the Contribution of Decision Variables to Objectives for Large-Scale Multi/Many-Objective Optimization

Most existing multiobjective evolutionary algorithms treat all decision variables as a whole to perform genetic operations and optimize all objectives with one population at the same time. Considering different control attributes, different decision variables have different optimization effects on each objective, so decision variables can be divided into convergence- or diversity-related variables. In this article, we propose a new metric called the optimization degree of the convergence-related decision variable to each objective to calculate the contribution objective of each decision variable. All decision variables are grouped according to their contribution objectives. Then, a multiobjective evolutionary algorithm, namely, decision variable contributing to objectives evolutionary algorithm (DVCOEA), has been proposed. In order to balance the convergence and diversity of the population, the DVCOEA algorithm combines the multipopulation multiobjective framework, where two different optimization strategies are designed to optimize the subpopulation and individuals in the external archive, respectively. Finally, DVCOEA is compared with several state-of-the-art algorithms on a number of benchmark functions. Experimental results show that DVCOEA is a competitive approach for solving large-scale multi/many-objective problems.

Latent space search based multimodal optimization with personalized edge-network biomarker for multi-purpose early disease prediction

Considering that cancer is resulting from the comutation of several essential genes of individual patients, researchers have begun to focus on identifying personalized edge-network biomarkers (PEBs) using personalized edge-network analysis for clinical practice. However, most of existing methods ignored the optimization of PEBs when multimodal biomarkers exist in multi-purpose early disease prediction (MPEDP). To solve this problem, this study proposes a novel model (MMPDENB-RBM) that combines personalized dynamic edge-network biomarkers (PDENB) theory, multimodal optimization strategy and latent space search scheme to identify biomarkers with different configurations of PDENB modules (i.e. to effectively identify multimodal PDENBs). The application to the three largest cancer omics datasets from The Cancer Genome Atlas database (i.e. breast invasive carcinoma, lung squamous cell carcinoma and lung adenocarcinoma) showed that the MMPDENB-RBM model could more effectively predict critical cancer state compared with other advanced methods. And, our model had better convergence, diversity and multimodal property as well as effective optimization ability compared with the other state-of-art methods. Particularly, multimodal PDENBs identified were more enriched with different functional biomarkers simultaneously, such as tissue-specific synthetic lethality edge-biomarkers including cancer driver genes and disease marker genes. Importantly, as our aim, these multimodal biomarkers can perform diverse biological and biomedical significances for drug target screen, survival risk assessment and novel biomedical sight as the expected multi-purpose of personalized early disease prediction. In summary, the present study provides multimodal property of PDENBs, especially the therapeutic biomarkers with more biological significances, which can help with MPEDP of individual cancer patients.

Multi-Objective Optimization Method for Signalized Intersections in Intelligent Traffic Network

Urban intersections are one of the most common sources of traffic congestion. Especially for multiple intersections, an appropriate control method should be able to regulate the traffic flow within the control area. The intersection signal-timing problem is crucial for ensuring efficient traffic operations, with the key issues being the determination of a traffic model and the design of an optimization algorithm. So, an optimization method for signalized intersections integrating a multi-objective model and an NSGAIII-DAE algorithm is established in this paper. Firstly, the multi-objective model is constructed including the usual signal control delay and traffic capacity indices. In addition, the conflict delay caused by right-turning vehicles crossing straight-going non-motor vehicles is considered and combined with the proposed algorithm, enabling the traffic model to better balance the traffic efficiency of intersections without adding infrastructure. Secondly, to address the challenges of diversity and convergence faced by the classic NSGA-III algorithm in solving traffic models with high-dimensional search spaces, a denoising autoencoder (DAE) is adopted to learn the compact representation of the original high-dimensional search space. Some genetic operations are performed in the compressed space and then mapped back to the original search space through the DAE. As a result, an appropriate balance between the local and global searching in an iteration can be achieved. To validate the proposed method, numerical experiments were conducted using actual traffic data from intersections in Jinzhou, China. The numerical results show that the signal control delay and conflict delay are significantly reduced compared with the existing algorithm, and the optimal reduction is 33.7% and 31.3%, respectively. The capacity value obtained by the proposed method in this paper is lower than that of the compared algorithm, but it is also 11.5% higher than that of the current scheme in this case. The comparisons and discussions demonstrate the effectiveness of the proposed method designed for improving the efficiency of signalized intersections.

A Multiobjective Evolutionary Approach for Solving Large-Scale Network Reconstruction Problems via Logistic Principal Component Analysis

Currently, the problem of uncovering complex network structure and dynamics from time series is prominent in many fields. Despite the recent progress in this area, reconstructing large-scale networks from limited data remains a tough problem. Existing works treat connections of nodes as continuous values, leaving a challenge of setting a proper cut-off value to distinguish whether the connections exist or not. Besides, their performances on large-scale networks are far from satisfactory. Considering the reconstruction error and sparsity as two objectives, this article proposes a subspace learning-based evolutionary multiobjective network reconstruction algorithm, called SLEMO-NR, to solve the aforementioned problems. In the evolutionary process, we assume that binary-coded individuals obey the Bernoulli distribution and can use the probability and natural parameter as alternative representations. Moreover, our approach utilizes the logistic principal component analysis (LPCA) to learn a subspace containing the features of the network structure. The offspring solutions are generated in the learned subspace and then can be mapped back to the original space via LPCA. Benefitting from the alternative representations, a preference-based local search operator (PLSO) is proposed to concentrate on finding solutions approximate to the true sparsity. The experimental results on synthetic networks and six real-world networks demonstrate that, due to the well-learned network structure subspace and the preference-based strategy, our approach is effective in reconstructing large-scale networks compared to six existing methods.

A Stable Large-Scale Multiobjective Optimization Algorithm with Two Alternative Optimization Methods

For large-scale multiobjective evolutionary algorithms based on the grouping of decision variables, the challenge is to design a stable grouping strategy to balance convergence and population diversity. This paper proposes a large-scale multiobjective optimization algorithm with two alternative optimization methods (LSMOEA-TM). In LSMOEA-TM, two alternative optimization methods, which adopt two grouping strategies to divide decision variables, are introduced to efficiently solve large-scale multiobjective optimization problems. Furthermore, this paper introduces a Bayesian-based parameter-adjusting strategy to reduce computational costs by optimizing the parameters in the proposed two alternative optimization methods. The proposed LSMOEA-TM and four efficient large-scale multiobjective evolutionary algorithms have been tested on a set of benchmark large-scale multiobjective problems, and the statistical results demonstrate the effectiveness of the proposed algorithm.

Multiple sparse detection-based evolutionary algorithm for large-scale sparse multiobjective optimization problems

Sparse multiobjective optimization problems are common in practical applications. Such problems are characterized by large-scale decision variables and sparse optimal solutions. General large-scale multiobjective optimization problems (LSMOPs) have been extensively studied for many years. They can be well solved by many excellent custom algorithms. However, when these algorithms are used to deal with sparse LSMOPs, they often encounter difficulties because the sparse nature of the problem is not considered. Therefore, aiming at sparse LSMOPs, an algorithm based on multiple sparse detection is proposed in this paper. The algorithm applies an adaptive sparse genetic operator that can generate sparse solutions by detecting the sparsity of individuals. To improve the deficiency of sparse detection caused by local detection, an enhanced sparse detection (ESD) strategy is proposed in this paper. The strategy uses binary coefficient vectors to integrate the masks of nondominated solutions. Essentially, the mask is globally and deeply optimized by coefficient vectors to enhance the sparsity of the solutions. In addition, the algorithm adopts an improved weighted optimization strategy to fully optimize the key nonzero variables to balance exploration and optimization. Finally, the proposed algorithm is named MOEA-ESD and is compared to the current state-of-the-art algorithm to verify its effectiveness.

Pharmacological, Non-Pharmacological Policies and Mutation: An Artificial Intelligence Based Multi-Dimensional Policy Making Algorithm for Controlling the Casualties of the Pandemic Diseases

Fighting against the pandemic diseases with unique characters requires new sophisticated approaches like the artificial intelligence. This paper develops an artificial intelligence algorithm to produce multi-dimensional policies for controlling and minimizing the pandemic casualties under the limited pharmacological resources. In this respect, a comprehensive parametric model with a priority and age-specific vaccination policy and a variety of non-pharmacological policies are introduced. This parametric model is utilized for constructing an artificial intelligence algorithm by following the exact analogy of the model-based solution. Also, this parametric model is manipulated by the artificial intelligence algorithm to seek for the best multi-dimensional non-pharmacological policies that minimize the future pandemic casualties as desired. The role of the pharmacological and non-pharmacological policies on the uncertain future casualties are extensively addressed on the real data. It is shown that the developed artificial intelligence algorithm is able to produce efficient policies which satisfy the particular optimization targets such as focusing on minimization of the death casualties more than the infected casualties or considering the curfews on the people age over 65 rather than the other non-pharmacological policies. The paper finally analyses a variety of the mutant virus cases and the corresponding non-pharmacological policies aiming to reduce the morbidity and mortality rates.

Evolutionary Multitasking Multilayer Network Reconstruction

Due to the multilayer nature of real-world systems, the problem of inferring multilayer network structures from nonlinear and complex dynamical systems is prominent in many fields, including engineering, biological, physical, and computer sciences. Many network reconstruction methods have been proposed to address this problem, but none of them consider the similarities among network reconstruction tasks at different component layers, which are inspired by topology correlations and dynamic couplings among different component layers. This article develops an evolutionary multitasking multilayer network reconstruction framework to make use of the correlations among different component layers to improve the reconstruction performance; we refer to this framework as EM2MNR. In EM2MNR, the multilayer network reconstruction problem is first established as a multitasking multilayer network reconstruction problem, where the goal of each task is to reconstruct the network structure of a component layer. In addition, multitasking multilayer network reconstruction problems are high dimensional, but existing evolutionary multitasking algorithms may have poor performance when dealing with optimization problems with a high-dimensional search space. Inspired by the sparsity of multilayer networks, EM2MNR employs the restricted Boltzmann machine to extract low effective features from the original decision space and then decides whether to conduct knowledge transfer on these features. To verify the performance of EM2MNR, this article also designs a test suite for multilayer network reconstruction problems. The experimental results demonstrate the significant improvement obtained by the proposed EM2MNR framework on 96 multilayer network reconstruction problems.

A Variable Importance-Based Differential Evolution for Large-Scale Multiobjective Optimization

Large-scale multiobjective optimization problems (LMOPs) bring significant challenges for traditional evolutionary operators, as their search capability cannot efficiently handle the huge decision space. Some newly designed search methods for LMOPs usually classify all variables into different groups and then optimize the variables in the same group with the same manner, which can speed up the population's convergence. Following this research direction, this article suggests a differential evolution (DE) algorithm that favors searching the variables with higher importance to the solving of LMOPs. The importance of each variable to the target LMOP is quantized and then all variables are categorized into different groups based on their importance. The variable groups with higher importance are allocated with more computational resources using DE. In this way, the proposed method can efficiently generate offspring in a low-dimensional search subspace formed by more important variables, which can significantly speed up the convergence. During the evolutionary process, this search subspace for DE will be expanded gradually, which can strike a good balance between exploration and exploitation in tackling LMOPs. Finally, the experiments validate that our proposed algorithm can perform better than several state-of-the-art evolutionary algorithms for solving various benchmark LMOPs.

The Influence of Genetic Algorithms on Learning Possibilities of Artificial Neural Networks

The presented research study focuses on demonstrating the learning ability of a neural network using a genetic algorithm and finding the most suitable neural network topology for solving a demonstration problem. The network topology is significantly dependent on the level of generalization. More robust topology of a neural network is usually more suitable for particular details in the training set and it loses the ability to abstract general information. Therefore, we often design the network topology by taking into the account the required generalization, rather than the aspect of theoretical calculations. The next part of the article presents research whether a modification of the parameters of the genetic algorithm can achieve optimization and acceleration of the neural network learning process. The function of the neural network and its learning by using the genetic algorithm is demonstrated in a program for solving a computer game. The research focuses mainly on the assessment of the influence of changes in neural networks’ topology and changes in parameters in genetic algorithm on the achieved results and speed of neural network training. The achieved results are statistically presented and compared depending on the network topology and changes in the learning algorithm.

A conjugate gradient-assisted multi-objective evolutionary algorithm for fluence map optimization in radiotherapy treatment

Intensity-modulated radiotherapy (IMRT) is one of the most applied techniques for cancer radiotherapy treatment. The fluence map optimization is an essential part of IMRT plan designing, which has a significant impact on the radiotherapy treatment effect. In fact, the treatment planing of IMRT is an inverse multi-objective optimization problem. Existing approaches of solving the fluence map optimization problem (FMOP) obtain a satisfied treatment plan via trying different coupling weights, the optimization process needs to be conducted many times and the coupling weight setting is completely based on the experience of a radiation physicist. For fast obtaining diverse high-quality radiotherapy plans, this paper formulates the FMOP into a three-objective optimization problem, and proposes a conjugate gradient-assisted multi-objective evolutionary algorithm (CG-MOEA) to solve it. The proposed algorithm does not need to set the coupling weights and can produce the diverse radiotherapy plans within a single run. Moreover, the convergence speed is further accelerated by an adaptive local search strategy based on the conjugate-gradient method. Compared with five state-of-the-art multi-objective evolutionary algorithms (MOEAs), the proposed CG-MOEA can obtain the best hypervolume (HV) values and dose–volume histogram (DVH) performance on five clinical cases in cancer radiotherapy. Moreover, the proposed algorithm not only obtains the more optimal solution than traditional method used to solve the FMOP, but also can find diverse Pareto solution set which can be provided to radiation physicist to select the best treatment plan. The proposed algorithm outperforms dose-volume histogram state-of-the-art multi-objective evolutionary algorithms and traditional method for FMOP on five clinical cases in cancer radiotherapy.

Improved SparseEA for sparse large-scale multi-objective optimization problems

Sparse large-scale multi-objective optimization problems (LSMOPs) widely exist in real-world applications, which have the properties of involving a large number of decision variables and sparse Pareto optimal solutions, i.e., most decision variables of these solutions are zero. In recent years, sparse LSMOPs have attracted increasing attentions in the evolutionary computation community. However, all the recently tailored algorithms for sparse LSMOPs put the sparsity detection and maintenance in the first place, where the nonzero variables can hardly be optimized sufficiently within a limited budget of function evaluations. To address this issue, this paper proposes to enhance the connection between real variables and binary variables within the two-layer encoding scheme with the assistance of variable grouping techniques. In this way, more efforts can be devoted to the real part of nonzero variables, achieving the balance between sparsity maintenance and variable optimization. According to the experimental results on eight benchmark problems and three real-world applications, the proposed algorithm is superior over existing state-of-the-art evolutionary algorithms for sparse LSMOPs.

A responsive ant colony optimization for large-scale dynamic vehicle routing problems via pheromone diversity enhancement

Large-scale dynamic vehicle routing problem (LSDVRP) is exhibiting extensive application prospect with the rapid growth of online logistics, whereas a few approaches have been developed to address LSDVRPs. The difficulty in solving LSDVRPs lies in that it requires quick response and high adaptability to numerous newly appeared customers in LSDVRPs. To overcome this difficulty, in this paper, we propose a responsive ant colony optimization algorithm, termed as RACO, for efficiently addressing LSDVRPs. In the proposed RACO, a pheromone diversity enhancing method is suggested to generate diverse pheromone matrices for quickly responding to newly appeared customer requests in solving LSDVRPs. A pheromone ensemble technique is further designed to produce a high-quality initial population that well adapts to the new customer requests by making use of diverse pheromone matrices. Empirical results on a set of 12 LSDVRP test instances demonstrate the effectiveness of the suggested pheromone diversity enhancing method in quickly responding to newly appeared customer requests for solving LSDVRPs. Moreover, we investigate the computational cost and the traveling cost obtained by the proposed RACO to evaluate responsiveness and adaptability of the proposed RACO, respectively. Comparison with four state-of-the-art approaches to DVRPs validates the superiority of the proposed RACO in addressing LSDVRPs in terms of responsiveness and adaptability.