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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Two single-handed helical tetraphenylethylene–silica nanotubes with circularly polarized luminescence (CPL) properties and enhanced fluorescence efficiency were fabricated through a supramolecular templating approach using the self-assemblies of chiral gelators as templates. This work provides a facile strategy for constructing CPL-active organic–inorganic hybrid nanomaterials with single-handed helical morphologies. [ABSTRACT FROM AUTHOR]

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 ($\epsilon $ -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. [ABSTRACT FROM AUTHOR]

Byline: Xinye Cai, Praveen Koduru, Sanjoy Das, Stephen M. Welch This paper presents a hybrid algorithm based on Genetic Programming (GP) and Particle Swarm Optimisation (PSO) for the automated recovery of gene network structure. It uses gene expression time series data as well as phenotypic data pertaining to plant flowering time as its input data. The algorithm then attempts to discover simple structures to approximate the plant gene regulatory networks that produce model gene expressions and flowering times that closely resemble the input data. To show the efficacy of the proposed approach, simulation results applied to flowering time control in Arabidopsis thaliana are demonstrated and discussed.

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. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]