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Large-scale multiobjective optimization problems (LSMOPs), which optimize multiple conflicting objectives with hundreds or even thousands of decision variables, demand increasing computational resources to assure satisfactory performance as the decision variables increase. Multiobjective evolutionary algorithms are naturally scalable, but as the dimension increases, the conflict between analyzing enough solutions and the limited number of function evaluations has hindered further improvements in scalability. In this paper, we first define the scalability of multiobjective evolutionary algorithms and design an indicator to quantitatively measure the scalability. Second, to boost scalability when solving LSMOPs, we propose a scalable multiobjective optimization algorithm by transferring weights between solutions to reduce dependency on ever-increasing computational resources as the problem dimension increases. The proposed framework entails constructing a latent decision space to determine evolutionary weights for chosen representative solutions. These computed weights are then transferred to the remaining solutions, enabling evolutionary optimization to proceed without requiring additional evaluations, even as the dimensionality increases. By utilizing the knowledge gained from the source solutions, each solution is customized with an evolutionary weight scheme that not only preserves computational resources but also enhances optimization performance, thereby boosting scalability. We have conducted experiments on LSMOPs to verify the effectiveness and scalability of the proposed algorithm. The proposed method outperforms selected state-of-the-art algorithms and gains scalability boosts in situations where the dimensions increase while the function evaluation remains constant. • This paper defines the scalability of large-scale multiobjective evolutionary algorithms and introduces a novel performance indicator to measure. • We propose a scalable algorithm for LSMOPs to ensure consistent performance within specified function evaluations, regardless of dimensionality. • We design a technique to transfer learned weights between solutions without additional evaluations to enhance scalability while conserving resources. [ABSTRACT FROM AUTHOR]

Dynamic multiobjective optimization problems (DMOPs) vary over time, requiring an optimization algorithm to track the position of Pareto-optimal front (PF) in a dynamic environment. To achieve that, a novel co-evolutionary algorithm based on problem analysis (CAPA) is proposed in this paper. CAPA is designed to solve DMOPs from decision space and objective space simultaneously, which is achieved by the combination of adjustable prediction (AP) and precise mapping strategy (PM). In decision space, the proposed multi-model prediction can estimate the location of new population based on the historical median points. In objective space, a novel sampling method is developed to search for sample points with better convergence or diversity. Then, mapping these sample points back to decision space based on inverse model. Through the problem analysis mechanism, the proportion of the new solutions produced by each strategy changes adaptively. CAPA is incorporated into the dynamic multiobjective evolutionary algorithm (DMOEA) based on decomposition (MOEA/D) to construct a novel algorithm. The efficacy of CAPA is validated by comparison with five state-of-the-art algorithms on 28 benchmarks. Experimental results show that CAPA has the ability to generate high quality population uniformly along PF. [ABSTRACT FROM AUTHOR]

An optimization spiking neural P (OSN P) system is a discrete optimization model without the aid of evolutionary operators of evolutionary algorithms or swarm intelligence algorithms. However, since the processing object of OSN P systems is a spike, where information is encoded by the timing of spikes or the number of spikes in neurons, OSN P systems are limited for solving continuous optimization problems. To break this limitation, an extended numerical spiking neural (ENSN P) system is proposed based on numerical spiking neural P (NSN P) systems and multiple (ENSN P) systems, called optimization numerical spiking neural P systems (ONSN P systems or ONSNPS), are designed to solve continuous constrained optimization problems. More specifically, in ENSN P systems, the production functions are selected by probability to achieve updated parameters. In OSN P systems, a guider algorithm is introduced to finish individuals' crossover and selection. The extensively experimental results in five benchmarks, thirty-two optimization problems including five benchmark problems, seventeen manufacturing design optimization problems and ten benchmarks from CEC show that ONSN P systems in this paper outperform or are competitive to twenty-eight optimization algorithms. Finally, algorithm complexity and Holm-Bonferroni procedure based on statistical results is used to test the complexity changing when we use different dimensionality of the search space and the difference in terms of statistical performance. The testing results indicate that the time complexity of ONSN P systems grows linearly with problem dimensions and ONSN P systems are better performance than the most algorithms. [ABSTRACT FROM AUTHOR]

In the realm of practical problem-solving, multi-objective optimisation problems with redundant variables and indefinite objective functions (MOPRVIF) are becoming increasingly prevalent. MOPRVIF involve determining the optimal decision variables that optimise multiple objectives, leveraging the relational data of a set of variables and multiple objectives. For these problems, this paper focuses on the following two issues: one is the demand for a unified computational model to solve this problem; the other is how to improve the algorithm's deep intelligent search capability. In this regard, this paper designs a dual data-driven multi-objective optimisation method. The method used consisted of four parts: elimination of redundant variables (ERV), objective function construction (OFC), selection evolution operator (SEO), and multi-objective evolutionary algorithm (MOEA). MOEA was the main focus of the method. ERV is data preparation and variable selection according to multiple objectives. OFC involves constructing the relationship model between variables and objectives, and a high-accuracy model is important for guaranteeing reliable results. Furthermore, SEO can adjust the evolution operator during a deep search. This is an important guarantee for deep, intelligent search. MOEA combined OFC and SEO to form the final solution algorithm—Dual Data Driven Multi-Objective Evolutionary Algorithm (DDMOEA). DDMOEA was explored using two different disciplinary problems of drug compound optimisation and wild blueberry cultivation and benchmarks were selected. The first two problem domains are distinct. The first problem is more complex than the second; however, both encompass redundant variables and indefinite objective functions. Benchmarks are utilised independently to gauge the profound intelligent search capability. The experiments affirm that the dual data-driven optimization approach proposed in this paper is effective, practical, and scalable. • Provide a unified solution for optimisation problems with redundant variables and indefinite objective functions. • Propose a data-driven multi-objective optimisation algorithm. • Designing an adaptive optimiser to enhance the algorithm's depth search capability. [ABSTRACT FROM AUTHOR]

As a new technology for model compression, self-knowledge distillation (SKD) avoids the large computational overhead of training the teacher model seen with traditional knowledge distillation. However, existing SKD methods pay attention to the knowledge transfer between deep and shallow layers of the network but ignore the mutual learning between shallow branches. This paper proposes a many-objective evolutionary self-knowledge distillation framework (MaOESKD) to guide the knowledge fusion between branches in the SKD neural network. This framework embeds an optimization module and a temporary branch into the multi-branch SKD network. The optimization module includes a many-objective adaptive weight optimization model (MaAWOM) and an many evolutionary optimization algorithm based on multi-strategy consensus mechanism (MaOEA-MCM); meanwhile, the temporary branch performs linear weighted fusion. In the MOBWOM, the weight of different branches in knowledge fusion is taken as the decision variable, and the mutual information, covariance, KL divergence between branch output features, and the total information of each branch are taken as the optimization objective. The MSCMEA integrates several state-of-the-art individual selection strategies in the field of evolutionary algorithms. It includes shift density estimation (SDE), penalized boundary intersection (PBI), balanced fitness estimation (BFE), and adaptive position transformation (APT). The accuracy of MOESKD achieves 99.70, 95.74 and 78.21 in MNIST, CIFAR-10 and CIFAR-100. [ABSTRACT FROM AUTHOR]

• Analyze DE algorithm two key issues: parameter sensitivity and search imbalance. • A complementary mutation strategy based on complementary symmetric selection and a Gaussian distribution mutation is proposed. • Data fusion-based parameter adaptation method proposed for parameter rationalization. • A novel variant of DE called DACDE is designed and results shown competitive edge. As an excellent optimization algorithm widely used to solve various practical problems, differential evolution (DE) algorithm has few parameters, yet its performance is significantly affected by these parameters. To address this issue, this paper presents a novel variant of DE called DACDE, which utilizes data fusion-based parameter adaptation and a complementary mutation strategy. Most parameter adaptation methods based on successful history only analyze the mean of parameters and ignore their degree of dispersion. In DACDE, the successful parameter distribution is recorded and described by both the mean and variance. Data fusion is then used to combine records and generate an estimated distribution, which is applied to a Gaussian distribution to generate new parameters. Inspired by opposition-based learning, we introduce a complementary mutation strategy. This strategy employs a symmetric selection mechanism to adapt to the varying search abilities required by the algorithm at different stages. The new variant is verified on 32 single-objective functions from CEC 2011 and 2014 benchmark suites, and the results show that DACDE is competitive compared to other 29 evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Convergence analysis of multi-objective optimization algorithm has been an area of vital interest to the research community. With this regard, a number of approaches have been proposed and studied. However, these studies and developed proposals cannot cope with more than 3-dimensional optimization problems. Generally speaking, interpolation planes are formed by 3-dimension data. So, when the dimensionality of the Pareto front is more than 3, the dimensionality of Pareto front will be reduced to 3 by involving principal component analysis. This may lead to some important data being missed. Due to missing data, the formed interpolation plane is usually inaccurate and uneven. This will give rise to difficulties to evaluate the distance between the Pareto front and the optimal Pareto front. Subsequently, it is not easy to evaluate exact convergence time and with this regard the existing solutions lack general. Having this in mind, this paper develops a general convergence analysis (GCAM) for evolutionary multi-objective optimization algorithm (EMOA). In this approach, two originality aspects come to existence: one associates with the interpolation plane convergence analysis while the second concerns the improved drift analysis of evolutionary algorithm. Firstly, for more than 3-dimensional space, the dimensionality of the Pareto front set becomes reduced to 3 through a locally linear embedding. This overcomes the irregular interpolation plane problem and produce a high-quality interpolation. Secondly, this study originally analyzes the convergence of EMOA by engaging an improved drift analysis. Finally, we determine the first stopping time of EMOA by analyzing the convergence metric. The experimental results demonstrate that the proposed method exhibits better performance in comparison with CAD, CAL, and CAC. Specifically, the error proportion of SMS-EMOA, AR-MOEA, SPEA2+SDE, GFM-MOEA has been decreased by 12%, 15%, 21%, 19% and 17%, respectively. [ABSTRACT FROM AUTHOR]

The application of semantic technologies, particularly ontologies, in the realm of multi-objective evolutionary algorithms is overlook despite their effectiveness in knowledge representation. In this paper, we introduce MOODY, an ontology specifically tailored to formalize these kinds of algorithms, encompassing their respective parameters, and multi-objective optimization problems based on a characterization of their search space landscapes. MOODY is designed to be particularly applicable in automatic algorithm configuration, which involves the search of the parameters of an optimization algorithm to optimize its performance. In this context, we observe a notable absence of standardized components, parameters, and related considerations, such as problem characteristics and algorithm configurations. This lack of standardization introduces difficulties in the selection of valid component combinations and in the re-use of algorithmic configurations between different algorithm implementations. MOODY offers a means to infuse semantic annotations into the configurations found by automatic tools, enabling efficient querying of the results and seamless integration across diverse sources through their incorporation into a knowledge graph. We validate our proposal by presenting four case studies. • A semantic model is proposed for consolidating multi-objective optimization knowledge. • A knowledge graph is presented, as well as the tools to include new RDF data. • The model allows for semantic reasoning on evolutionary algorithm configurations. • The proposal is validated on three use cases with data from experiments. • Moody enables knowledge-based recommendations of configurations for algorithms. [ABSTRACT FROM AUTHOR]

Balancing multiple objectives and various constraints is crucial for effectively solving constrained multi-objective optimization problems (CMOPs). Excessive focus on either convergence or feasibility may not result in favorable outcomes of the algorithm. To confront this challenge, this paper proposes a cooperative evolutionary algorithm named SaE-CMO, which aims to achieve a harmonious balance between convergence and feasibility by extracting valuable information from both feasible and infeasible regions. To achieve this, SaE-CMO employs a dual-population approach to enhance search progress, consisting of a main population, Population1, and an auxiliary population, Population2. These two populations complement each other to achieve optimal results. A newly proposed self-adaptive epsilon method is employed in both Population1 and Population2, using different comparison criteria to select next population from mating pools, respectively. Population2 can retain some solutions that are well-constrained but poorly converged, thereby preserving information about both the constrained and the unconstrained Pareto front. This property enables Population2 to assist Population1 in maintaining diversity in certain complex CMOPs. To verify the effectiveness of SaE-CMO, we conduct experiments on three benchmark test instances and four real-world CMOPs with some related state-of-the-art constrained multi-objective optimization algorithms, experimental results prove that the proposed algorithm outperforms the compared algorithms. [ABSTRACT FROM AUTHOR]

Dynamic multi-objective optimization problems (DMOPs) are multi-objective problems that are influenced by dynamically changing environmental parameters. Most current algorithms for solving DMOPs only respond to dynamic changes in the decision space or objective space and also ignore the impact of the type of DMOPs on the algorithm. The changes in the Pareto-optimal solution (POS) and Pareto-optimal front (POF) may affect the type of change in DMOPs. Therefore, this paper proposed an adaptive dynamic multi-objective evolutionary algorithm for type detection (TDA-DMOEA). First, the dynamic detection operator is designed to identify the types of dynamic problems. The Wilcoxon signed-rank test and Hyper Volume (HV) are used to detect the difference of POS and POF in two adjacent environments respectively. Then, different response strategies are designed to cope with different types of changes in DMOP. In particular, a multi-angle-based transfer learning method (MA-TL) with a closed kernel function is derived when faced with simultaneous changes in POS and POF. Finally, a comprehensive study of the commonly used benchmark set of DMOPs is presented, and the proposed algorithm achieves better performance in optimizing DMOPs. [ABSTRACT FROM AUTHOR]

Multi-objective optimization problems with interval parameter (IMOPs) are among the most critical optimization problems in practical applications. However, in contrast to deterministic multi-objective optimization, few studies have addressed IMOPs. Moreover, the uncertainty in such problems makes the convergence and diversity of the algorithm more challenging. Therefore, this paper proposes an interval multi-objective optimization algorithm based on elite genetic strategy (EG-IMOEA). First, existing interval dominance relations cannot comprehensively determine which of the two intervals is better when their midpoints are equal but their upper and lower limits are unequal. Therefore, a conditional-based interval confidence dominance relation is proposed that considers both the average level of convergence and value of the minimum lower limit of intervals. The interval crowding distance (ICD) applied to multiple objectives is then defined to evaluate the solutions more completely. Furthermore, an elite genetic strategy for crossover and mutation is proposed to generate better offspring. The proposed algorithm was evaluated on nine benchmark test problems and compared with the typical algorithm as well as state-of-the-art algorithms. The results showed that this algorithm outperformed the comparison algorithms in terms of convergence, diversity, imprecision, and uniform distribution. [ABSTRACT FROM AUTHOR]

More and more studies have demonstrated that circRNAs can be used as markers of various diseases due to their inherent stability. Numerous computational methods, especially artificial intelligence approaches, have been applied to the prediction of circRNA-disease associations. However, the objective functions of these prediction methods are usually single and standard. The single objective function hardly reflects the characteristics of the prediction problem, and leads to low prediction accuracy. There has never been a method to design a set of objective functions for the circRNA-disease prediction problem and solve it by using intelligent optimization algorithms. In this paper, a method ICDMOE is proposed to identify circRNA-disease associations via a multi-objective evolutionary algorithm. A solution space is defined and four objective functions are designed based on matrix factorization and modularity of similarity networks. An improved decomposition-based multi-objective evolutionary algorithm (MOEA/D) is also employed to solve these objective functions. In the MOEA/D, an adaptive penalty-based boundary intersection strategy is proposed, which not only ensures convergence, but also guarantees the diversity of solutions in the Pareto front. Finally, the experimental results show that ICDMOE has better performance than pure matrix factorization-based methods, non-adaptive MOEA/D-based methods and other prediction methods. Furthermore, we find that the predicted disease-circRNAs can be confirmed by existing studies, miRNA regulations and expression profiles, etc. These indicate that ICDMOE can provide good candidates for biomedical experiments. [ABSTRACT FROM AUTHOR]

• The algorithm named AMSMO is proposed for high-dimensional and computationally expensive problems. • The real-time auto-selection of kernels approach for building the most promising RBF is proposed. • The new distance- and objective-based criterion is proposed for the global search. • The dynamic search criterion is used to make the algorithm explore at the early search stage and exploit at the final stage. • A cluster-based restart criterion that aims at refining the training data for surrogate models is proposed. Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for solving computationally expensive optimization problems. However, the performance of SAEAs deteriorates drastically for high-dimensional problems since the accuracy of surrogates may decrease to an insupportably low level in high dimensions which profoundly affect subsequent evolution optimization. To overcome this issue, this paper proposes an adaptive multi-surrogate and module-based optimization algorithm named AMSMO. Unlike existing algorithms that adopt sole surrogate models, AMSMO develops a real-time autoselection of kernels approach for building the most promising RBF. AMSMO makes use of five modules to promote the optimization quality, including: a. global search module; b. local search module; c. semi-local search module; d. convergence module; e. restart module. Specifically, we provide a novel distance- and objective-value-based criterion for global search. The semi-local search module applies a dynamic search criterion that makes the algorithm explore at the early search stage and exploit at the final stage. A cluster-based restart criterion is proposed to address the stagnation of optimization. Several benchmark functions with dimensions varying from 30 to 100 and computationally intensive practical simulation–optimization problems are adopted to validate the proposed algorithm. The empirical experiments demonstrate that the proposed algorithm outperforms other state-of-the-art algorithms in most cases. [ABSTRACT FROM AUTHOR]

Evolutionary Algorithm is a mature global optimization method with high robustness and wide applicability. It can effectively address complex problems that are difficult to be solved by traditional optimization algorithms. In evolution, it is still uncertain which gene parent can produce offspring through competition and eventually become an excellent individual of the last generation population. Inspired by the fact that gene sequencing can discover biological gene defects, this paper proposes a dynamic multi-objective evolutionary algorithm based on gene sequencing and gene editing (GSGE). The gene sequencing algorithm is designed using support vector machine (SVM), and correlation coefficient, as the result of sequencing, has also been verified. Combining stratified sampling and multi-population strategy, a prediction strategy that can use all chromosome information is designed. The new gene editing strategy edits individual genes to optimize the Pareto optimal front (PF) distribution, for the first time different types of genes can match different optimization strategies, which greatly improves the distribution of the population without affecting the convergence. The comparison experiment between GSGE and the state of the art algorithms is performed on 25 test functions and the Pareto optimal set (PS) curves obtained by dimension reduction fully demonstrate the significant advantages of GSGE. • Gene sequencing using support vector machine was designed for gene classification. • A prediction strategy that can use all chromosome information is designed. • A novel gene editing strategy was designed to achieve direct assign values to genes. [ABSTRACT FROM AUTHOR]

To improve the utilization of infrastructure resources and reduce the cost of operators in the future 6G network construction, a 6G shared base stations optimization model is proposed in this paper, which is a bi-level multiobjective optimization problem (BLMOP). In such a BLMOP, the tower company is responsible for the construction of base stations at the upper level, while operators share the base station resources of the tower company at the lower level. In addition, we also propose two strategies to solve the optimization efficiently. First, we use surrogate models to fit lower-level Pareto fronts (PF), then the degree of lower-level optimality constraint violation is converted to distance between the candidate solutions and the approximate lower level PF. So the BLMOP is transformed to a single-level constrained multi-objective optimization problem. Second, to accelerate the current lower-level optimization, we migrate the modified population from the adjacent lower-level optimization tasks. These two strategies effectively reduce the computational overhead. Compared with three existing works, the proposed method has achieved the best or comparable results on 7 benchmark problems and 5 generated test instances with less computation overhead, whose efficiency has been confirmed. [ABSTRACT FROM AUTHOR]