The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of the method to combinatorial optimization problems is challenging but very important for analyzing the algorithm’s behavior. This paper provides a straightforward theoretical derivation showing that the NBN network essentially functions as the maximum probability transition network for algorithms. This paper also presents an efficient NBN computation method with logarithmic linear time complexity to address the time-consuming issue. By applying this efficient NBN algorithm to the OneMax problem and the Traveling Salesman Problem (TSP), we have made several remarkable discoveries for the first time: The fitness landscape of OneMax exhibits neutrality, ruggedness, and modality features. The primary challenges of TSP problems are ruggedness, modality, and deception. Three state-of-the-art TSP algorithms (EAX, LKH, and NLKH) have limitations when addressing challenges related to modality and deception, respectively. LKH, based on local search operators, fails when there are deceptive solutions near global optima. EAX, which is based on a single population, can efficiently maintain diversity. However, when multiple attraction basins exist, EAX retains individuals within multiple basins simultaneously, reducing inter-basin interaction efficiency and leading to algorithm’s stagnation. NLKH improves over LKH by leveraging learned edge weights to increase the chance of reaching the global basin, but it remains vulnerable to deceptive funnels due to biased learning from underrepresented complex instances.

Dynamic optimization focuses on solving problems where the search space changes over time. The multi-population method is the most widely used approach for addressing such problems. Traditional multi-population methods often lack a deep understanding of the problem’s structural characteristics, such as the boundaries of basins of attraction (BoAs), which leads to redundant searches in less promising regions. Without guidance from these structural features, most populations are regenerated randomly, resulting in inefficient exploration. Furthermore, the search range for each population remains fixed and does not adapt to the BoAs, leading to the loss of tracking for certain peaks. To address these challenges, this paper proposes a solution space partitioning based multi-population method. The algorithm partitions the solution space into subspaces and leverages historical population data to assign an uncertainty property to each subspace. It further learns the problem’s BoAs to guide populations in exploiting within the BoAs while exploring outside them. A dual-layer exclusion mechanism dynamically adjusts the search and exclusion ranges based on the BoAs, ensuring precise control, preventing overlaps, and preserving diversity. Experimental results demonstrate that the proposed algorithm significantly outperforms state-of-the-art algorithms on moving peaks benchmark, generalized moving peaks benchmark, and a real-world problem: marine magnetic compensation problem.

Template update is essential for improving the adaptability of tracking algorithms to target appearance variations. While previous methods have leveraged the spatio-temporal complementarity of multi-modal templates for RGBT tracking, a comprehensive analysis of the template update mechanism remains underexplored. In this work, we propose a novel prototype-based framework that decomposes the multi-modal template update process from the perspective of prototype learning into four key components: multi-modal prototype, prototype integration, prototype evaluation, and prototype update algorithm. Our findings highlight that the multi-modal prototype is the most critical factor in enhancing tracking adaptability to appearance variations, leading to more robust target representations. While prototype integration is less crucial when the target representation is already robust, it still contributes to learning a more discriminative representation. Additionally, the accuracy of template updates is strongly influenced by prototype evaluation, which controls the accuracy of the update process. Finally, the prototype update algorithm, which determines when and how template updates occur, is key to maintaining tracking robustness. Building on these insights, we introduce the Multi-modal Prototype RGBT Tracker (MPTrack), which adapts dynamically to appearance variations through prototype learning. MPTrack combines a fixed template from the first frame with both modality-shared and modality-specific templates, forming a robust multi-modal prototype representation. It incorporates a prototype evaluation module that guides updates based on template reliability, and an adaptive update algorithm to manage templates effectively. Additionally, a prototype-guided cross-modal integration module enhances the discriminative power of multi-modal relation modeling. Experimental results on five challenging RGBT tracking benchmarks demonstrate that MPTrack consistently outperforms state-of-the-art methods, setting new performance records. The experimental data and source code will be made publicly available at: https://github.com/mmic-lcl/Datasets-and-benchmark-code.

Video action recognition is a fundamental task for video understanding. Action recognition in complex spatio-temporal contexts generally requires fusing of different multi-granularity action information. However, existing works do not consider spatio-temporal information modeling and fusion from the perspective of action granularity. To address this problem, this paper proposes an Action Granularity Pyramid Network (AGPN) for action recognition, which can be flexibly integrated into 2D backbone networks. The core module is the Action Granularity Pyramid Module (AGPM), a hierarchical pyramid structure with residual connections, which is established to fuse multi-granularity action spatio-temporal information. From top to bottom level in the designed pyramid structure, the receptive field decreases and action granularity becomes more refined. To enrich temporal information of the inputs, a Multiple Frame Rate Module (MFM) is proposed to mix different frame rates at a fine-grained pixel-wise level. Moreover, a Spatio-temporal Anchor Module (SAM) is employed to fix spatio-temporal feature anchors to promote the effectiveness of feature extraction. We conduct extensive experiments on three large-scale action recognition datasets, Something-Something V1 & V2 and Kinetics-400. The results demonstrate that our proposed AGPN outperforms the state-of-the-art methods for the tasks of video action recognition.

The multi/many-objective traveling salesman problem (MOTSP), which is NP-hard, can be found in many real-world applications. The Lin–Kernighan (LK) algorithm, as one of the most successful local search (LS) methods for the single-objective traveling salesman problem, adopts a variable neighborhood LS. However, LK cannot be directly applied to the decomposition-based multiobjective optimization framework due to its incapability of effective knowledge transfer among different subproblems, especially for problems with more than two objectives. In this article, we propose an algorithm, called decomposition-based multiobjective LK heuristic with neighborhood structure transfer (NST-MOLK) for MOTSP. In NST-MOLK, the knowledge of a neighborhood structure has been transferred to enhance the efficiency and effectiveness of LK. The experimental studies have been conducted on both benchmark and real-world instances constructed based on the flight prices of seven airlines and 266 airports of different cities in China. Experimental results show that NST-MOLK outperforms both classical and state-of-the-art algorithms significantly. It has also been verified that neighborhood structure transfer can effectively improve the performance of NST-MOLK.

Many practical multiobjective optimization problems have a nested bilevel structure in variables, which can be modeled as bilevel multiobjective optimization problems (BLMOPs). In this article, a cooperative coevolution (CC) with knowledge-based variable decomposition, called bilevel multiobjective CC (BLMOCC), is proposed for BLMOPs. In BLMOCC, the variable interactions are represented by an interaction matrix. The perturbation-based variable decomposition combined with the matrix completion approach has been designed for dynamically discovering the correlation among the bilevel variables, based on which the variables are divided into different groups. To further handle possible weak correlations among various groups of variables, a CC has been adopted for optimizing them in a collaborative way. In experimental studies, BLMOCC is compared with a nested method (NS) and a state-of-the-art algorithm (H-BLEMO) on a set of benchmark problems. The effects of each component in BLMOCC have also been verified by comparing it with its three variants. The experimental results demonstrate that BLMOCC has the best performance among all the compared algorithms. In addition, BLMOCC has also been applied to a real-world management decision-making problem, which further validates its efficiency and effectiveness.

How to evaluate Pareto front approximations generated by multi/many-objective optimizers is a critical issue in the field of multiobjective optimization. Currently, there exist two types of comprehensive quality indicators (i.e., volume-based and distance-based indicators). Distance-based indicators, such as inverted generational distance (IGD), are usually computed by summing up the distance of each reference point to its nearest solution. Their high computational efficiency leads to their prevalence in many-objective optimization. However, in the existing distance-based indicators, the distributions of the solution sets are usually neglected, leading to their lack of ability to well distinguish between different solution sets. This phenomenon may become even more severe in high-dimensional space. To address such an issue, a kernel-based indicator (KBI) is proposed as a comprehensive indicator. Different from other distance-based indicators, a kernel-based maximum mean discrepancy is adopted in KBI for directly measuring the difference that can characterize the convergence, spread, and uniformity of two sets, i.e., the solution set and reference set, by embedding them in reproducing kernel Hilbert space (RKHS). As a result, KBI not only reflects the distance between the solution set and the reference set but also can reflect the distribution of the solution set itself. In addition, to maintain the desirable weak Pareto compliance property of KBI, a nondominated set reconstruction approach is also proposed to shift the original solution set. The detailed theoretical and experimental analysis of KBI is provided in this article. The properties of KBI have also been analyzed by the optimal$\mu $-distribution.

In this article, we consider the dynamic allocation of bursty requests stochastically arriving at heterogeneous servers with uncertain setup times. Lower expected response time and less power consumption are desirable objectives of users and service providers respectively. However, sudden increase and decrease of cloud servers caused by bursty requests are rather challenging to get an appropriate trade-off between the two conflicting objectives which are closely related to the launched servers. The heterogeneity of the cloud servers further makes it more difficult to decide how to switch on and off servers and effectively and efficiently allocate bursty requests with balanced objectives. Based on a Markov decision process, a real-time bilevel decision-making model is constructed for unallocated requests which includes: whether to launch a server and which type of server to launch. A learn-and-deploy algorithm framework is proposed which contains two complementary stages. In the first stage, an effective offline bi-objective optimization algorithm is proposed to learn a set of policies, which provides helpful trade-off information for a decision-maker to choose a preferred policya posteriori. In terms of the system status, a policy decides whether to launch a server according to a state-action table and which server to launch using a server priority sequence. In the second stage, a computationally efficient policy deployment method is proposed to search the corresponding action in the selected policy based on the current system status and apply it to the real-time system. Experimental studies over a large number of random and real instances have been conducted to validate the effectiveness of the proposed bilevel model and algorithm. Compared to the most recent existing method, the performance of the proposed approach can at most achieve an 80% improvement on power consumption and 20% improvement on response time.

Feature selection has been considered as an effective method to solve imbalanced classification problems. It can be formulated as a multiobjective optimization problem (MOP) aiming to find a small feature subset while achieving a high classification accuracy. With traditional MOP, the focus is on deriving an optimal solution (i.e., a feature subset), while ignoring the diversity in solution space (e.g., there could exist multiple feature subsets achieving the same accuracy). Providing more options for feature selection would be beneficial since some features can be more difficult to obtain than others. In this work, we treat feature selection as a multimodal MOP (MMOP) whose goals are to find an excellent Pareto front in objective space and as many equivalent Pareto optimal solutions (feature subsets) as possible in feature space. Note that though several multimodal multiobjective evolutionary algorithms (MMEAs) have been proposed, their use of a convergence-first selection criterion could cause the loss of solution diversity in an objective and feature space. To address the issue, a novel competition-driven mechanism is designed to assist the existing multimodal MMEAs in locating more equivalent feature subsets and a desired Pareto front. The effectiveness of the proposed mechanism is first verified on all 22 MMOPs from CEC2019. Then, the proposed method is applied to feature selection in imbalanced classification problems and a real-world application, i.e., credit card fraud detection. Experimental results show that the proposed mechanism can not only provide more equivalent feature subsets but also improve classification accuracy.

Optimization modeling of real-world application problems usually involves noise from various sources. Noisy optimization imposes challenges to optimization methods since the objective values can be different for multiple evaluations. In this article, we propose a novel online population size learning (OPL) technique of evolution strategies for handling noisy optimization problems. By re-evaluating a fraction of the candidates, we measure the strength of noise level of the re-evaluated candidate solutions and adapt the population size according to the noise level. The proposed OPL combines the advantages of both explicit averaging by re-evaluations and the implicit averaging by large population size and overcomes their limitations. We incorporate it with the covariance matrix adaptation evolution strategy (CMA-ES) and obtain OPL-CMA-ES. Compared with the existing noise handling technique, the proposed OPL is much simpler in both concepts and computation. We conduct comprehensive experiments to evaluate the algorithm’s performance on standard problems with Gaussian noise. We further evaluate the performance of OPL-CMA-ES on the black-box optimization benchmarks (BBOBs) noisy testbed, which is a standard platform for comparing black-box optimization algorithms, compared with the state-of-the-art noise-handling algorithms. The experimental results show that OPL-CMA-ES achieves remarkable performance and outperforms the compared variants.

Different from multiobjective optimization problems (MOPs), multimodal MOPs (MMOPs) focus on both decision and objective spaces rather than only objective one. Thus, finding a good Pareto front approximation and finding the maximal number of equivalent Pareto optimal solutions for each objective vector in the Pareto front are two core tasks for them. Although some multimodal multiobjective evolutionary algorithms have been proposed to handle them, they can quickly converge to the easy-to-find equivalent Pareto optimal solutions, thereby losing their ability to improve solution diversity in decision space and performance in objective space. To address the above issues, this work proposes a new information utilization method. Its core idea is to randomly extract a certain amount of decision variable information from the current optimal solutions to construct an information vector, which is, in turn, used to assist the generation of elite solutions. The proposed method can assist any available intelligent optimizers to improve their performance in solving MMOPs. This is confirmed by experimental results obtained from solving 22 such problems from CEC2019 and 12 scalable imbalanced distance minimization problems through a number of optimizers. Finally, we apply the proposed method to credit card fraud detection problems to show its practical significance.

The gate assignment problem (GAP) aims at assigning gates to aircraft considering operational efficiency of airport and satisfaction of passengers. Unlike the existing works, we model the GAP as a bi-objective constrained optimization problem. The total walking distance of passengers and the total robust cost of the gate assignment are the two objectives to be optimized, while satisfying the constraints regarding the limited number of flights assigned to apron, as well as three types of compatibility. A set of real instances is then constructed based on the data obtained from the Baiyun airport (CAN) in Guangzhou, China. A two-phase large neighborhood search (2PLNS) is proposed, which accommodates a greedy and stochastic strategy (GSS) for the large neighborhood search; both to speed up its convergence and to avoid local optima. The empirical analysis and results on both the synthetic instances and the constructed real-world instances show a better performance for the proposed 2PLNS as compared to many state-of-the-art algorithms in literature. An efficient way of choosing the tradeoff from a large number of nondominated solutions is also discussed in this article.

The decomposition-based algorithms [e.g., multiobjective evolutionary algorithm based on decomposition (MOEA/D)] transform a multiobjective optimization problem (MOP) into a number of single-objective optimization subproblems and solve them in a collaborative manner. It is a natural framework for using single-objective local search (LS) to solve combinatorial MOPs. However, commonly used decomposition methods, such as weighted sum (WS), Tchebycheff (TCH), and penalty-based boundary intersection (PBI) may not be good at maintaining the population diversity while providing diverse initial solutions for different LS procedures in a collaborative way. Based on our previous work on the constrained decomposition with grids (CDG), this article proposes a dynamic CDG (DCDG) framework used to design a multiobjective memetic algorithm (DCDG-MOMA). DCDG uses grids for maintaining diversity, supporting the collaborative LS. In addition, DCDG dynamically increases the number of grids for obtaining more nondominated solutions as well as the better collaborative search among them. DCDG-MOMA has been compared with several classical and state-of-the-art algorithms on multiobjective traveling salesman problem (MOTSP), multiobjective quadratic assignment problem (MOQAP), and multiobjective capacitated arc routing problem (MOCARP).

Assessing the performance of Pareto front (PF) approximations is a key issue in the field of evolutionary multi/many-objective optimization. Inverted generational distance (IGD) has been widely accepted as a performance indicator for evaluating the comprehensive quality for a PF approximation. However, IGD usually becomes infeasible when facing a real-world optimization problem as it needs to know the true PF a priori. In addition, the time complexity of IGD grows quadratically with the size of the solution/reference set. To address the aforementioned issues, a grid-based IGD (Grid-IGD) is proposed to estimate both convergence and diversity of PF approximations for multi/many-objective optimization. In Grid-IGD, a set of reference points is generated by estimating PFs of the problem in question, based on the representative nondominated solutions of all the approximations in a grid environment. To reduce the time complexity, Grid-IGD only considers the closest solution within the grid neighborhood in the approximation for every reference point. Grid-IGD also possesses other desirable properties, such as Pareto compliance, immunity to dominated/duplicate solutions, and no need of normalization. In the experimental studies, Grid-IGD is verified on both the artificial and real PF approximations obtained by five many-objective optimizers. Effects of the grid specification on the behavior of Grid-IGD are also discussed in detail theoretically and experimentally.

Multiobjective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multiobjective optimization problems. In fact, many real-world multiobjective problems contain a number of constraints. To promote research on constrained multiobjective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multiobjective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness, and diversity-hardness. We then develop a general toolkit to construct difficulty adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. In fact, the combination of the three primary constraint functions with different parameters allows the construction of a large variety of CMOPs, with difficulty that can be defined by a triplet, with each of its parameters specifying the level of one of the types of primary difficulty. Furthermore, the number of objectives in this toolkit can be scaled beyond three. Based on this toolkit, we suggest nine difficulty adjustable and scalable CMOPs and nine CMaOPs, to be called DAS-CMOP1-9 and DAS-CMaOP1-9, respectively. To evaluate the proposed test problems, two popular CMOEAs-MOEA/D-CDP (MOEA/D with constraint dominance principle) and NSGA-II-CDP (NSGA-II with constraint dominance principle) and two popular constrained many-objective evolutionary algorithms (CMaOEAs)-C-MOEA/DD and C-NSGA-III-are used to compare performance on DAS-CMOP1-9 and DAS-CMaOP1-9 with a variety of difficulty triplets, respectively. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility-, and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

Combinatorial multiobjective optimization problems (CMOPs) are very popular due to their widespread applications in the real world. One common method for CMOPs is Pareto local search (PLS), a natural extension of single-objective local search (LS). However, classical PLS tends to reserve all of the nondominated solutions for LS, which causes the inefficient LS, as well as unbearable computational and space cost. Due to the aforementioned reasons, most PLS approaches can only handle CMOPs with no more than two objectives. In this paper, by combining the Pareto dominance and weighted sum (WS) approach in a grid system, the grid weighted sum dominance (gws-dominance) is proposed and integrated into PLS for CMOPs with multiple objectives. In the grid system, at most one representative solution is maintained in each grid for more efficient LS, thus largely reducing the computational and space complexity. The grid-based WS approach can further guide the LS in different grids for maintaining more widely and uniformly distributed Pareto front approximations. In the experimental studies, the grid WS PLS is compared with the classical PLS, three decomposition-based LS approaches [multiobjective evolutionary algorithm based on decomposition-LS (WS, Tchebycheff, and penalty-based boundary intersection)], a grid-based algorithm ( ϵ -MOEA), and a state-of-the-art hybrid approach (multiobjective memetic algorithm based on decomposition) on two sets of benchmark CMOPs. The experimental results show that the grid weighted sum Pareto local search significantly outperforms the compared algorithms and remains effective and efficient on combinatorial multiobjective and even many-objective optimization problems.

In this paper, a hierarchical image matting model is proposed to extract blood vessels from fundus images. More specifically, a hierarchical strategy is integrated into the image matting model for blood vessel segmentation. Normally the matting models require a user specified trimap, which separates the input image into three regions: the foreground, background and unknown regions. However, creating a user specified trimap is laborious for vessel segmentation tasks. In this paper, we propose a method that first generates trimap automatically by utilizing region features of blood vessels, then applies a hierarchical image matting model to extract the vessel pixels from the unknown regions. The proposed method has low calculation time and outperforms many other state-of-art supervised and unsupervised methods. It achieves a vessel segmentation accuracy of 96.0%, 95.7% and 95.1% in an average time of 10.72s, 15.74s and 50.71s on images from three publicly available fundus image datasets DRIVE, STARE, and CHASE DB1, respectively.

Decomposition-based multiobjective evolutionary algorithm has shown its advantage in addressing many-objective optimization problem (MaOP). To further improve its convergence on MaOPs and its diversity for MaOPs with irregular Pareto fronts (PFs, e.g., degenerate and disconnected ones), we proposed a decomposition-based many-objective evolutionary algorithm with two types of adjustments for the direction vectors (MaOEA/D-2ADV). At the very beginning, search is only conducted along the boundary direction vectors to achieve fast convergence, followed by the increase of the number of the direction vectors for approximating a more complete PF. After that, a Pareto-dominance-based mechanism is used to detect the effectiveness of each direction vector and the positions of ineffective direction vectors are adjusted to better fit the shape of irregular PFs. The extensive experimental studies have been conducted to validate the efficiency of MaOEA/D-2ADV on many-objective optimization benchmark problems. The effects of each component in MaOEA/D-2ADV are also investigated in detail.

Decomposition-based multiobjective evolutionary algorithms (MOEAs) decompose a multiobjective optimization problem (MOP) into a set of scalar objective subproblems and solve them in a collaborative way. Commonly used decomposition approaches originate from mathematical programming and the direct use of them may not suit MOEAs due to their population-based property. For instance, these decomposition approaches used in MOEAs may cause the loss of diversity and/or be very sensitive to the shapes of Pareto fronts (PFs). This paper proposes a constrained decomposition with grids (CDG) that can better address these two issues thus more suitable for MOEAs. In addition, different subproblems in CDG defined by the constrained decomposition constitute a grid system. The grids have an inherent property of reflecting the information of neighborhood structures among the solutions, which is a desirable property for restricted mating selection in MOEAs. Based on CDG, a constrained decomposition MOEA with grid (CDG-MOEA) is further proposed. Extensive experiments are conducted to compare CDG-MOEA with the domination-based, indicator-based, and state-of-the-art decomposition-based MOEAs. The experimental results show that CDG-MOEA outperforms the compared algorithms in terms of both the convergence and diversity. More importantly, it is robust to the shapes of PFs and can still be very effective on MOPs with complex PFs (e.g., extremely convex, or with disparately scaled objectives).

Automated optic disk (OD) detection plays an important role in developing a computer aided system for eye diseases. In this paper, we propose an algorithm for the OD detection based on structured learning. A classifier model is trained based on structured learning. Then, we use the model to achieve the edge map of OD. Thresholding is performed on the edge map, thus a binary image of the OD is obtained. Finally, circle Hough transform is carried out to approximate the boundary of OD by a circle. The proposed algorithm has been evaluated on three public datasets and obtained promising results. The results (an area overlap and Dices coefficients of 0.8605 and 0.9181, respectively, an accuracy of 0.9777, and a true positive and false positive fraction of 0.9183 and 0.0102) show that the proposed method is very competitive with the state-of-the-art methods and is a reliable tool for the segmentation of OD.

Solving constrained multi-objective optimization problems is a difficult task, it needs to simultaneously optimize multiple conflicting objectives and a number of constraints. This paper first reviews a number of popular constrained multi-objective evolutionary algorithms (CMOEAs) and twenty-three widely used constrained multi-objective optimization problems (CMOPs) (including CF1-10, CTP1-8, BNH, CONSTR, OSY, SRN and TNK problems). Then eight popular CMOEAs with simulated binary crossover (SBX) and differential evolution (DE) operators are selected to test their performance on the twenty-three CMOPs. The eight CMOEAs can be classified into domination-based CMOEAs (including ATM, IDEA, NSGA-II-CDP and SP) and decomposition-based CMOEAs (including CMOEA/D, MOEA/D-CDP, MOEA/D-SR and MOEA/D-IEpsilon). The comprehensive experimental results indicate that IDEA has the best performance in the domination-based CMOEAs and MOEA/D-IEpsilon has the best performance in the decomposition-based CMOEAs. Among the eight CMOEAs, MOEA/D-IEpsilon with both SBX and DE operators has the best performance on the twenty-three test problems.

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and then solves them in parallel. In many MOEA/D variants, each subproblem is associated with one and only one solution. An underlying assumption is that each subproblem has a different Pareto-optimal solution, which may not be held, for irregular Pareto fronts (PFs), e.g., disconnected and degenerate ones. In this paper, we propose a new variant of MOEA/D with sorting-and-selection (MOEA/D-SAS). Different from other selection schemes, the balance between convergence and diversity is achieved by two distinctive components, decomposition-based-sorting (DBS) and angle-based-selection (ABS). DBS only sorts L closest solutions to each subproblem to control the convergence and reduce the computational cost. The parameter L has been made adaptive based on the evolutionary process. ABS takes use of angle information between solutions in the objective space to maintain a more fine-grained diversity. In MOEA/D-SAS, different solutions can be associated with the same subproblems; and some subproblems are allowed to have no associated solution, more flexible to MOPs or many-objective optimization problems (MaOPs) with different shapes of PFs. Comprehensive experimental studies have shown that MOEA/D-SAS outperforms other approaches; and is especially effective on MOPs or MaOPs with irregular PFs. Moreover, the computational efficiency of DBS and the effects of ABS in MOEA/D-SAS are also investigated and discussed in detail.

This paper proposes a new constraint handling method named Angle-based Constrained Dominance Principle (ACDP). Unlike the original Constrained Dominance Principle (CDP), this approach adopts the angle information of the objective functions to enhance the population's diversity in the infeasible region. To be more specific, given two infeasible solutions, if the angle of the solutions is greater than a given threshold, they are considered to be non-dominated by each other. For a feasible solution and an infeasible solution, if the angle of the solutions is less than a given threshold, the feasible solution is better, otherwise they are non-dominated. To verify the proposed constraint handling approach ACDP, eight test problems CMOP1 to CMOP8 are introduced. The suggested algorithm MOEA/D-ACDP is compared with MOEA/D-CDP and NSGA-II-CDP on CMOP1 to CMOP8. The experimental results demonstrate that ACDP performs better than CDP in the framework of MOEA/D, and MOEA/D-ACDP is significantly better than NSGA-II-CDP, especially on the test instances with the very low ratio of feasible region against the whole objective space.

In this paper, a multi-phase strategy for dynamic resource allocation is proposed for some special optimization problems where the evolutionary process cannot be explicitly divided into two phases, under the decomposition-based multiobjective evolutionary optimization framework. Based on the evolutionary status, a switching mechanism is adopted to adaptively use either convergence or diversity information in the external archive, to guide the evolutionary search in the working population. The proposed algorithm is compared with six well-known multiobjective evolutionary algorithms on multiobjective travelling salesman problem (MOTSP). Experimental results show that our proposed algorithm performs better than other compared algorithms.

In this paper, we proposed a two-phase many-objective evolutionary algorithm to tackle many objective optimization problems. In the first phase, the algorithm focuses on achieving good convergence towards the boundary Pareto optimal solutions. In the second phase, it maintains a good balance between convergence and diversity by using a set of widely spread reference lines. In addition, a penalty based adjustment for reference line has been adopted to handle many objective optimization problems with incomplete PFs. The performance of our proposed algorithm is validated and compared with four state-of-the-art many objective evolutionary algorithms on DTLZ problems. The results show that our proposed algorithm is very competitive with other compared algorithms.

At Intensive Care Unit (ICU), acute hypotensive episode (AHE) can cause serious consequences. It can make the organs broken, or even the patient dead. Generally AHE is predicted by the doctor clinically. In order to forecast the AHE automatically, this paper proposes an algorithm based on the genetic programming (GP) and random forest (RF). The algorithm obtains features of the signal through the Intrinsic Mode Function (IMF) signal produced by applying empirical mode decomposition (EMD) to the arterial blood pressure (MAP) signal. Then the feature sets and the data sets are grouped to evolve decision functions via GP. Finally, a random forest is formed and the classification result is obtained by voting. The achieved accuracy of the proposed method is 77.55%, the sensitivity is 80.55% and specificity is 75.14% after the five-fold cross-validation.

Domination-based sorting and decomposition are two basic strategies used in multiobjective evolutionary optimization. This paper proposes a hybrid multiobjective evolutionary algorithm integrating these two different strategies for combinatorial optimization problems with two or three objectives. The proposed algorithm works with an internal (working) population and an external archive. It uses a decomposition-based strategy for evolving its working population and uses a domination-based sorting for maintaining the external archive. Information extracted from the external archive is used to decide which search regions should be searched at each generation. In such a way, the domination-based sorting and the decomposition strategy can complement each other. In our experimental studies, the proposed algorithm is compared with a domination-based approach, a decomposition-based one, and one of its enhanced variants on two well-known multiobjective combinatorial optimization problems. Experimental results show that our proposed algorithm outperforms other approaches. The effects of the external archive in the proposed algorithm are also investigated and discussed.

In this paper, we propose a decomposition based multiobjective evolutionary algorithm that extracts information from an external archive to guide the evolutionary search for continuous optimization problem. The proposed algorithm used a mechanism to identify the promising regions(subproblems) through learning information from the external archive to guide evolutionary search process. In order to demonstrate the performance of the algorithm, we conduct experiments to compare it with other decomposition based approaches. The results validate that our proposed algorithm is very competitive.

In this paper, a hierarchical Pareto dominance based multi-objective evolutionary approach is proposed for the optimization of gene regulatory network models. The approach is presented based on the neglected observations in GRN optimization that (i) structural dependencies exist among objectives; and (ii) some objectives may be more important than others. The hierarchical Pareto dominance is able to reduce the number of objectives during optimization process and increase the selection pressure to relieve the many objective problem. The proposed hierarchical Pareto dominance based multi-objective approach is verified and compared with classical Pareto dominance based algorithm NSGAII on the gene regulatory network optimization problem. The results obtained indicate that the presented approach has great performance when no noise exist. Also it shows superior results compared to NSGAII.

This paper proposes a new approach for biologically inspired computing on the basis of Gene Regulatory Networks. These networks are models of genes and dynamic interactions that take place between them. The differential equation representations of such networks resemble neural networks as well as idiotypic networks in immune system. Although several potential applications have been outlined, an example, the problem of placing sensors optimally in a distributed environment is considered in detail. A comparison with NSGA-II suggest that the new method is able to accomplish near-optimal coverage of sensors in a network.

In this paper, we describe a Genetic Programming and Particle Swarm Hybrid algorithm for Gene Network discovery.