Generative answer engines expose content through selective citation rather than ranked retrieval, fundamentally altering how visibility is determined.This shift calls for new optimization methods beyond traditional search engine optimization.Existing generative engine optimization (GEO) approaches primarily rely on token-level text rewriting, offering limited interpretability and weak control over the trade-off between citation visibility and content quality.We propose FeatGEO, a featurelevel, multi-objective optimization framework that abstracts webpages into interpretable structural, content, and linguistic properties.Instead of directly editing text, FeatGEO optimizes over this feature space and uses a language model to realize feature configurations into natural language, decoupling high-level optimization from surface-level generation.Experiments on GEO-Bench across three generative engines demonstrate that FeatGEO consistently improves citation visibility while maintaining or improving content quality, substantially outperforming token-level baselines.Further analyses show that citation behavior is more strongly influenced by document-level content properties than by isolated lexical edits, and that the learned feature configurations generalize across language models of different scales.Code is available at https://github. com/EvoNexusX/2026LiuFeatGEO.git.

Dynamic Multimodal Optimization Problems (DMMOPs) demand algorithms capable of swiftly locating and tracking multiple optimal solutions over time. The primary challenge lies in controlling the population diversity to facilitate effective exploration, all within the limitation of computational resources between consecutive environmental changes. In this article, we study the utilization of density information derived from both current and historical populations to enhance exploration. First, for each active sub-population, we construct a density landscape based on the distribution of concurrently active sub-populations and establish dominance relationships between candidate solutions in the sub-population based on density and fitness values, directing this sub-population toward exploring low-density promising areas. Then, for each converged sub-population, we construct a density landscape based on the distribution of sub-populations that have historically become extinct, guiding the restart of this sub-population in low-density unexploited areas. Finally, we develop a comprehensive framework of Density-Assisted Evolutionary Algorithm (DAEA), which encompasses density-assisted search and restart, also combined with initialization. Moreover, we employ prediction and memory strategies to enhance the performance of DAEA in dynamic environments. Notably, the algorithm relies on an external monitor to detect environmental changes and trigger the dynamic response strategy. DAEA is tested on the CEC’2022 dynamic multimodal optimization benchmark suite and is compared against several state-of-the-art dynamic multimodal optimization algorithms. The experimental results demonstrate the competitiveness of DAEA in handling DMMOPs. Additionally, experimental results from the berth allocation problem further confirm the applicability of DAEA to real-world dynamic multimodal optimization tasks.

Leading exemplars play significant roles in updating particles to seek optimal solutions for Particle Swarm Optimization (PSO). Along this road, this paper devises an Individual-level Dominant Exemplar Selection (IDES) framework for PSO, giving rise to a new PSO variant named IDESPSO. Specifically, instead of using their own personally best positions and the globally best position of the entire swarm to update particles, IDES first randomly chooses two different exemplars for each particle from all personally best positions. Then, it compares the two selected exemplars with the personally best position of this particle. Based on the comparison results, different updating strategies are utilized to update different particles. This method notably enriches the variety among the chosen leading exemplars, thereby substantially bolstering the updating diversity of particles. Under IDES, this paper further develops seven selection strategies to help IDESPSO pick up promising exemplars for particles to evolve. Specifically, the seven selection schemes are the roulette wheel selection, the tournament selection, and five hybridizations of two basic models. A series of experiments have been undertaken on the universally used CEC2014 problem suite to compare IDESPSO with the seven selection schemes and two classic PSOs. The empirical results show that IDESPSO paired with anyone of the seven selection methods, markedly outperforms the two classical PSO variants, highlighting its significant performance.

Ant Colony Optimization (ACO) has shown very promising performance in solving Traveling Salesman Problem (TSP). However, most existing ACO algorithms utilize either the absolutely best ants or all ants to update the pheromone matrix. This leads to either serious diversity loss or slow convergence. To alleviate these predicaments, this paper designs a random pairwise competition based ant selection for pheromone updating. Specifically, a number of ants are randomly selected from the ant colony and then are randomly paired together. Subsequently the better one in each pair is selected to update the pheromone matrix. In this way, a good balance between search diversity and search convergence is potentially maintained. Integrating this selection strategy along with a local search scheme into the ACO framework, a new ACO algorithm called random pairwise competition based ACO (RPCACO) is developed. Experiments conducted on 8 TSP instances from the TSPLIB benchmark set demonstrate that RPCACO is more effective and efficient than the five classical ACO algorithms in solving TSP.

Multiple traveling salesmen problem (MTSP) is an extension of traditional traveling salesman problem (TSP). It involves both the city assignment optimization and the route optimization of each salesman. Genetic algorithms (GA) have been widely used to solve MTSP thanks to its easiness in implementation and good global search ability. To help GA effectively solve MTSP, researchers have developed various encoding schemes. However, there is no systematic and comparative study on the effectiveness of these encoding strategies. To fill this gap, this paper conducts investigations to compare four popular encoding strategies for MTSP, namely the one-chromosome encoding, the two-chromosome encoding, the two-part-chromosome encoding and the multi-chromosome encoding. Experimental results on different MTSP instances with different numbers of cities and salesmen show that the multi-chromosome encoding is far better than the other encoding strategies.

Mutation plays a crucial role in assisting differential evolution (DE) to effectively solve optimization problems. The key to mutation lies in the selection of parent individuals participating in the mutation. Along this road, this paper devises a binomial distribution-assisted individual selection strategy for DE. Specifically, this paper takes advantage of the probability distribution function of the binomial distribution to assign weights to individuals based on their fitness rankings. In this way, the selection of individuals focuses more on medium better individuals instead of the top best ones. Therefore, high mutation diversity can be preserved and thus it is likely that falling into local regions can be effectively avoided. Embedding this selection strategy into DE, a novel DE variant called binomial distribution assisted DE (BDDE) is developed. Experiments conducted on the CEC2017 benchmark suite have verified the effectiveness of BDDE in solving optimization problems. Particularly, BDDE gains much better performance against the well-known and representative mutation strategies.

Expensive optimization problems (EOPs) are becoming more and more ubiquitous nowadays. To effectively solve such problems, surrogate-assisted evolutionary algorithms (SAEAs) have been developed. Specifically, a SAEA usually maintains a surrogate model to simulate the real objective function of an EOP. Such a surrogate model is trained based on real-evaluated solutions. Then, it is utilized to evaluate the fitness of individuals in the EA instead of the real expensive fitness evaluation. Though many SAEAs have been designed, they mainly concentrate on dealing with low-dimensional EOPs with fewer than 300 dimensions. Their performance on large-scale EOPs with more than 300 dimensions is unknown. To fill this gap, this paper conducts a comparative study on two types of state-of-the-art SAEAs with a total of four algorithms on four classical EOPs. To make comprehensive comparisons, we range the dimension size from 50 to 1000. As far as we know, this is the first time to assess SAEAs on EOPs with such a wide range of dimension sizes and such high dimensionality. The comparison results show that the optimization performance of the compared four SAEAs on high-dimensional EOPs with more than 500 dimensions is not as satisfactory as their performance on low-dimensional EOPs because of their slow convergence. Therefore, research on large-scale SAEAs for high-dimensional EOPs still deserves intensive attention.

Cooperative coevolution (CC) is a paradigm equipped with the divide-and-conquer strategy for solving large-scale optimization problems (LSOPs). Currently, the computational resource allocation schemes of most CC could be divided into two categories, namely, equal allocation to all subproblems and preference allocation to the subproblems with a large contribution. However, the difficult subproblems are not carefully considered by the existing computational resource allocation schemes. For these subproblems, the investment of computational resources cannot quickly improve the fitness value, which leads to their small early contribution and being neglected. In this article, we comprehensively analyze the imbalanced nature of the subproblems from their difficulty and contribution in LSOPs. First, we propose a method to quantify the optimization difficulty of the problems during the evolution process, which considers both the difficulty of the fitness landscape and the behaviors of the optimization algorithm. Then, we propose a novel both difficulty and contribution-based CC framework, called DCCC, which encourages the allocation of the computational resources to more contributing and more difficult subproblems. DCCC is tested on the CEC’2010 and CEC’2013 large-scale optimization benchmarks, and is compared with several typical CC frameworks and state-of-the-art large-scale optimization algorithms. The experimental results demonstrate that DCCC is very competitive.

Multimodal optimization problems (MMOPs) are common problems with multiple optimal solutions. In this article, a novel method of population division, called nearest-better-neighbor clustering (NBNC), is proposed, which can reduce the risk of more than one species locating the same peak. The key idea of NBNC is to construct the raw species by linking each individual to the better individual within the neighborhood, and the final species of the population is formulated by merging the dominated raw species. Furthermore, a novel algorithm is proposed called NBNC-PSO-ES, which combines the advantages of better exploration in particle swarm optimization (PSO) and stronger exploitation in the covariance matrix adaption evolution strategy (CMA-ES). For the purpose of demonstrating the performance of NBNC-PSO-ES, several state-of-the-art algorithms are adopted for comparisons and tested using typical benchmark problems. The experimental results show that NBNC-PSO-ES performs better than other algorithms.

Studies have shown that deep neural networks (DNNs) are susceptible to adversarial attacks, which can cause misclassification. The adversarial attack problem can be regarded as an optimization problem, then the genetic algorithm (GA) that is problem-independent can naturally be designed to solve the optimization problem to generate effective adversarial examples. Considering the dimensionality curse in the image processing field, traditional genetic algorithms in high-dimensional problems often fall into local optima. Therefore, we propose a GA with multiple fitness functions (MF-GA). Specifically, we divide the evolution process into three stages, i.e., exploration stage, exploitation stage, and stable stage. Besides, different fitness functions are used for different stages, which could help the GA to jump away from the local optimum.Experiments are conducted on three datasets, and four classic algorithms as well as the basic GA are adopted for comparisons. Experimental results demonstrate that MF-GA is an effective black-box attack method. Furthermore, although MF-GA is a black-box attack method, experimental results demonstrate the performance of MF-GA under the black-box environments is competitive when comparing to four classic algorithms under the white-box attack environments. This shows that evolutionary algorithms have great potential in adversarial attacks.

Although followership has been widely studied in sociology and management, the problem of finding followers has not drawn attention in the field of artificial intelligence. We refer to the problem of finding followers of a given object as followers search. In sociology, followers are close to their leaders, and leaders are superior to their followers. In this article, aimed at finding followers of a given object, we formulate followers on the basis of both superiority and closeness. The former means that the given object should be superior to followers, and the latter means that followers should be close to the given object. We present a followers search algorithm to find the followers of the given object. Furthermore, we apply the ideas of followers to the market basket and recommender system datasets. The experimental results demonstrate the rationality of the discovered followers on the market basket dataset and the improved performance of the TrustPMF algorithm by adopting followership on recommender system datasets, which indicate a promising future for followers search.

Multimodal optimization problems (MMOPs) are common in real-world applications and involve identifying multiple optimal solutions for decision makers to choose from. The core requirement for dealing with such problems is to balance the ability of exploration in the global space and exploitation in the multiple optimal areas. In this paper, based on the differential evolution (DE), we propose a novel algorithm focusing on the formulation, balance, and keypoint of species for MMOPs, called FBK-DE. First, nearest-better clustering (NBC) is used to divide the population into multiple species with minimum size limitations. Second, to avoid placing too many individuals into one species, a species balance strategy is proposed to adjust the size of each species. Third, two keypoint-based mutation operators named DE/keypoint/1 and DE/keypoint/2 are proposed to evolve each species together with traditional mutation operators. The experimental results of FBK-DE on 20 benchmark functions are compared with 15 state-of-the-art multimodal optimization algorithms. The comparisons show that the proposed FBK-DE performs competitively with these algorithms.

Large-scale optimization problems and constrained optimization problems have attracted considerable attention in the swarm and evolutionary intelligence communities and exemplify two common features of real problems, i.e., a large scale and constraint limitations. However, only a little work on solving large-scale continuous constrained optimization problems exists. Moreover, the types of benchmarks proposed for large-scale continuous constrained optimization algorithms are not comprehensive at present. In this article, first, a constraint-objective cooperative coevolution (COCC) framework is proposed for large-scale continuous constrained optimization problems, which is based on the dual nature of the objective and constraint functions: modular and imbalanced components. The COCC framework allocates the computing resources to different components according to the impact of objective values and constraint violations. Second, a benchmark for large-scale continuous constrained optimization is presented, which takes into account the modular nature, as well as both imbalanced and overlapping characteristics of components. Finally, three different evolutionary algorithms are embedded into the COCC framework for experiments, and the experimental results show that COCC performs competitively.

Deep neural networks (DNNs) are used in various domains, such as image classification, natural language processing and face recognition, etc. However, the presence of malicious examples, generated by specific methods, could result in DNNs misclassification. Such maliciously modified examples are called adversarial examples. So far, most work about adversarial examples mainly focuses on the multi-class classification tasks, and only a little work has been done in the field of multi-label classification.In this study, we have proposed a novel algorithm that generates effective multi-label adversarial examples by solving a linear programming problem (MLA-LP). We minimize the l∞norm of distortion while constraining the changes in the label loss of the example after being perturbed. Then, we transform this constrained optimization problem into a linear programming problem for reducing the time cost. In comparison to the existing multi-label classification model attack algorithms, the attack performance of the proposed MLA-LP is found to be competitive, and the adversarial examples generated by MLA-LP have significantly smaller distortions.

Both Particle Swarm Optimization (PSO) and Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) exhibit good performance when solving global optimization problems. However, PSO could be misled by historical information and falls into a local optimum. Further, CMA-ES cannot fully utilize global information. Therefore, in this paper, we first propose a time-window PSO (TW-PSO) as an improvement of PSO, which could enhance the exploration ability of the algorithm. Second, we design a hybrid algorithm of TW-PSO, PSO and CMA-ES, i.e., HTPC, which combines the advantages of TW-PSO, PSO, and CMA-ES. We test HTPC on single-objective optimization problems from the CEC-2019 100-Digit Challenge, and the experimental results show that the performance of HTPC is competitive.