A New Many-Objective Evolutionary Algorithm Based on Generalized Pareto Dominance.

In the past several years, it has become apparent that the effectiveness of Pareto-dominance-based multiobjective evolutionary algorithms deteriorates progressively as the number of objectives in the problem, given by M , grows. This is mainly due to the poor discriminability of Pareto optimality in many-objective spaces (typically M ≥ 4 ). As a consequence, research efforts have been driven in the general direction of developing solution ranking methods that do not rely on Pareto dominance (e.g., decomposition-based techniques), which can provide sufficient selection pressure. However, it is still a nontrivial issue for many existing non-Pareto-dominance-based evolutionary algorithms to deal with unknown irregular Pareto front shapes. In this article, a new many-objective evolutionary algorithm based on the generalization of Pareto optimality (GPO) is proposed, which is simple, yet effective, in addressing many-objective optimization problems. The proposed algorithm used an "( M-1 ) + 1" framework of GPO dominance, ( M-1 )-GPD for short, to rank solutions in the environmental selection step, in order to promote convergence and diversity simultaneously. To be specific, we apply M symmetrical cases of ( M-1 )-GPD, where each enhances the selection pressure of M-1 objectives by expanding the dominance area of solutions, while remaining unchanged for the one objective left out of that process. Experiments demonstrate that the proposed algorithm is very competitive with the state-of-the-art methods to which it is compared, on a variety of scalable benchmark problems. Moreover, experiments on three real-world problems have verified that the proposed algorithm can outperform the others on each of these problems.

Hybrid Surrogate-Based Constrained Optimization With a New Constraint-Handling Method.

Surrogate-based-constrained optimization for some optimization problems involving computationally expensive objective functions and constraints is still a great challenge in the optimization field. Its difficulties are of two primary types. One is how to handle the constraints, especially, equality constraints; another is how to sample a good point to improve the prediction of the surrogates in the feasible region. Overcoming these difficulties requires a reliable constraint-handling method and an efficient infill-sampling strategy. To perform inequality- and equality-constrained optimization of expensive black-box systems, this work proposes a hybrid surrogate-based-constrained optimization method (HSBCO), and the main innovation is that a new constraint-handling method is proposed to map the feasible region into the origin of the Euclidean subspace. Thus, if the constraint violation of an infeasible solution is large, then it is far from the origin in the Euclidean subspace. Therefore, all constraints of the problem can be transformed into an equivalent equality constraint, and the distance between an infeasible point and the origin in the Euclidean subspace represents the constraint violation of the infeasible solution. Based on the distance, the objective function of the problem can be penalized by a Gaussian penalty function, and the original constrained optimization problem becomes an unconstrained optimization problem. Thus, the feasible solutions of the original minimization problem always have a lower objective function value than any infeasible solution in the penalized objective space. To improve the optimization performance, kriging-based efficient global optimization (EGO) is used to find a locally optimal solution in the first phase of HSBCO, and starting from this locally optimal solution, RBF-model-based global search and local search strategies are introduced to seek global optimal solutions. Such a hybrid optimization strategy can help the optimization process converge to the global optimal solution within a given maximum number of function evaluations, as demonstrated in the experimental results on 23 test problems. The method is shown to achieve the global optimum more closely and efficiently than other leading methods.

Hierarchical Topology-Based Cluster Representation for Scalable Evolutionary Multiobjective Clustering.

Evolutionary multiobjective clustering (MOC) algorithms have shown promising potential to outperform conventional single-objective clustering algorithms, especially when the number of clusters k is not set before clustering. However, the computational burden becomes a tricky problem due to the extensive search space and fitness computational time of the evolving population, especially when the data size is large. This article proposes a new, hierarchical, topology-based cluster representation for scalable MOC, which can simplify the search procedure and decrease computational overhead. A coarse-to-fine-trained topological structure that fits the spatial distribution of the data is utilized to identify a set of seed points/nodes, then a tree-based graph is built to represent clusters. During optimization, a bipartite graph partitioning strategy incorporated with the graph nodes helps in performing a cluster ensemble operation to generate offspring solutions more effectively. For the determination of the final result, which is underexplored in the existing methods, the usage of a cluster ensemble strategy is also presented, whether k is provided or not. Comparison experiments are conducted on a series of different data distributions, revealing the superiority of the proposed algorithm in terms of both clustering performance and computing efficiency.

A Cooperative Evolutionary Framework Based on an Improved Version of Directed Weight Vectors for Constrained Multiobjective Optimization With Deceptive Constraints.

When solving constrained multiobjective optimization problems (CMOPs), the most commonly used way of measuring constraint violation is to calculate the sum of all constraint violations of a solution as its distance to feasibility. However, this kind of constraint violation measure may not reflect the distance of an infeasible solution from feasibility for some problems, for example, when an infeasible solution closer to a feasible region does not have a smaller constraint violation than the one farther away from a feasible region. Unfortunately, no set of artificial benchmark problems focusing on this area exists. To remedy this issue, a set of CMOPs with deceptive constraints is introduced in this article. It is the first attempt to consider CMOPs with deceptive constraints (DCMOPs). Based on our previous work, which designed a set of directed weight vectors to solve CMOPs, this article proposes a cooperative framework with an improved version of directed weight vectors to solve DCMOPs. Specifically, the cooperative framework consists of two switchable phases. The first phase uses two subpopulations-one to explore feasible regions and the other to explore the entire space. The two subpopulations provide useful information about the optimal direction of objective improvement to each other. The second phase aims mainly at finding Pareto-optimal solutions. Then an infeasibility utilization strategy is used to improve the objective function values. The two phases are switchable based on the information found to date at any time in the evolutionary process. The experimental results show that this method significantly outperforms the algorithms with which it is compared on most of the DCMOPs, in terms of reliability and stability in finding a set of well-distributed optimal solutions.

A Guiding Evolutionary Algorithm with Greedy Strategy for Global Optimization Problems.

A Guiding Evolutionary Algorithm (GEA) with greedy strategy for global optimization problems is proposed. Inspired by Particle Swarm Optimization, the Genetic Algorithm, and the Bat Algorithm, the GEA was designed to retain some advantages of each method while avoiding some disadvantages. In contrast to the usual Genetic Algorithm, each individual in GEA is crossed with the current global best one instead of a randomly selected individual. The current best individual served as a guide to attract offspring to its region of genotype space. Mutation was added to offspring according to a dynamic mutation probability. To increase the capability of exploitation, a local search mechanism was applied to new individuals according to a dynamic probability of local search. Experimental results show that GEA outperformed the other three typical global optimization algorithms with which it was compared.

Digitization and visualization of greenhouse tomato plants in indoor environments.

This paper is concerned with the digitization and visualization of potted greenhouse tomato plants in indoor environments. For the digitization, an inexpensive and efficient commercial stereo sensor-a Microsoft Kinect-is used to separate visual information about tomato plants from background. Based on the Kinect, a 4-step approach that can automatically detect and segment stems of tomato plants is proposed, including acquisition and preprocessing of image data, detection of stem segments, removing false detections and automatic segmentation of stem segments. Correctly segmented texture samples including stems and leaves are then stored in a texture database for further usage. Two types of tomato plants-the cherry tomato variety and the ordinary variety are studied in this paper. The stem detection accuracy (under a simulated greenhouse environment) for the cherry tomato variety is 98.4% at a true positive rate of 78.0%, whereas the detection accuracy for the ordinary variety is 94.5% at a true positive of 72.5%. In visualization, we combine L-system theory and digitized tomato organ texture data to build realistic 3D virtual tomato plant models that are capable of exhibiting various structures and poses in real time. In particular, we also simulate the growth process on virtual tomato plants by exerting controls on two L-systems via parameters concerning the age and the form of lateral branches. This research may provide useful visual cues for improving intelligent greenhouse control systems and meanwhile may facilitate research on artificial organisms.

Epileptic seizure detection using genetically programmed artificial features.

Patient-specific epilepsy seizure detectors were designed based on the genetic programming artificial features algorithm, a general-purpose, methodic algorithm comprised by a genetic programming module and a k-nearest neighbor classifier to create synthetic features. Artificial features are an extension to conventional features, characterized by being computer-coded and may not have a known physical meaning. In this paper, artificial features are constructed from the reconstructed state-space trajectories of the intracranial EEG signals intended to reveal patterns indicative of epileptic seizure onset. The algorithm was evaluated in seven patients and validation experiments were carried out using 730.6 hr of EEG recordings. The results with the artificial features compare favorably with previous benchmark work that used a handcrafted feature. Among other results, 88 out of 92 seizures were detected yielding a low false negative rate of 4.35%.