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Convolutional neural networks (CNNs) have surpassed humans in many computer vision areas. However, the redundancy of CNNs inhibits its application in the embedded device. In this paper, a simple shared channel weight convolution (SCWC) approach is proposed to reduce the number of parameters. Multiplication is much more complex than accumulation, so reducing multiplication is more significant than reducing accumulation in CNNs. The proposed SCWC can reduce the number of multiplications by the distributive property due to the structured channel parameter sharing. Furthermore, the fully trained CNN can be directly compressed without tedious training from scratch. To evaluate the performance of the proposed SCWC, five competitive benchmark datasets for image classification and object detection, CIFAR-10, CIFAR-100, ImageNet, CUB-200–2011 and PASCAL VOC are adopted. Experiments demonstrate that the proposed SCWC can reduce about 50% of parameters and multiplications for ResNet50 with only 0.13% accuracy loss, and reduce about 70% of parameters and multiplications for VGG16 with 1.64% accuracy loss on ImageNet, which is better than many other pruning methods for CNNs. The accuracy loss is very small because of the soft parameter sharing. Moreover, the proposed SCWC is also effective for object detection and fine-grained image classification tasks. [ABSTRACT FROM AUTHOR]

Constrained multimodal multi-objective optimization problems (CMMOPs) consist of multiple equivalent constrained Pareto sets (CPSs) that have the identical constrained Pareto front (CPF). It is challenging for primary multimodal multi-objective evolutionary algorithms (MMEAs) to solve CMMOPs since they do not consider constraints. To tackle this challenge, a dynamic speciation-based differential evolution with ring topology, termed DSRDE, for solving CMMOPs is developed in this paper. To search for multiple equivalent CPSs in CMMOPs, the dynamic speciation-based niche strategy is developed. The dynamic speciation-based niche strategy divides the population into multiple species, each of which searches for diverse and equivalent CPSs in different regions. Particularly, the species number is dynamically decreased to explore the equivalent CPSs with good convergence. Then, a ring topology is constructed among multiple species and their neighbors to balance the diversity, convergence, and feasibility of solutions. Continuously, each species interacts information with its neighbors and searches for equivalent CPSs. DSRDE adopts the popular constrained dominance principle to handle constraints and uses the differential evolutionary algorithm to locate diverse CPSs in the ring topology. It is compared with several state-of-the-art algorithms in two CMMOPs test suites for evaluating the performance of the proposed DSRDE. The experimental results confirm that DSRDE is competitive and has the ability to find multiple CPSs when tackling CMMOPs. DSRDE is also implemented in a real-world CMMOP and obtains superior performance. [ABSTRACT FROM AUTHOR]

Multimodal multi-objective optimization problems (MMOPs) involve locating equivalent Pareto optimal solutions in decision space with the same objective values. The key to handling MMOPs is finding all equivalent Pareto optimal solutions and maintaining a promising balance between the convergence and diversity of solutions in both decision space and objective space. To tackle this issue, a self-organizing quantum-inspired particle swarm optimization algorithm (MMO_SO_QPSO) is proposed in this paper for handling MMOPs. In the proposed MMO_SO_QPSO, a self-organizing map is used to find the best neighbor leader of particles. With the aid of neighbor leader particles, a special zone searching method is adopted to update the position of particles and locate equivalent Pareto optimal solutions in decision space. To maintain diversity and convergence of Pareto optimal solutions, a special archive mechanism that relies on the maximum-minimum distance among solutions is introduced into MMO_SO_QPSO. And some outstanding Pareto optimal solutions are maintained in the special archive. In addition, a new performance indicator is developed to estimate properly the similarity between obtained Pareto optimal solutions and true Pareto optimal solutions. The performance of the proposed MMO_SO_QPSO is compared with six state-of-the-art multimodal multi-objective evolutionary algorithms on two well-known benchmark problems. Experimental results demonstrate the superior performance of MMO_SO_QPSO for solving MMOPs. The effectiveness of several strategies is also discussed. [ABSTRACT FROM AUTHOR]

Several distinctive Pareto Sets (PSs) with an identical Pareto Front (PF) and local PSs with acceptable quality are comprised in multimodal multi-objective optimization problems (MMOPs). Recently, many multimodal multi-objective evolutionary algorithms (MMEAs) have been proposed. However, even though most of MMEAs have the ability to discover equivalent global PSs, these methods encounter failures in developing local PSs. The main reasons are that local PSs are dominated by global PSs and are removed from the population during the evolutionary process. To tackle this matter, a two-stage adaptive differential evolution with a dynamic dual-populations strategy, termed TADE_DDS, is developed. In TADE_DDS, a dynamic population strategy is put forward to divide the population into a global population that locates equivalent global PSs and a local population that aims to locate local PSs. Subsequently, the whole procedure is completed by two evolutionary stages associated with a dynamic population strategy, and an adaptive differential evolution algorithm is adopted for both global and local populations. The first-stage evolution aims to find more favorable local PSs and the second-stage evolution concentrates on finding a variety of global PSs. Additionally, a local environmental selection and a global environmental selection are performed for developing the diversity of local PSs and improving the convergence of global PSs and local PSs, respectively. TADE_DDS and several popular MMEAs are implemented on standard test problems. Experimental results demonstrate that TADE_DDS is equipped to locate both global and local PSs, and is superior to its competing algorithms. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) require a delicate balance between satisfying constraints and optimizing objectives. Existing constrained multi-objective evolutionary algorithms (CMOEAs) often struggle to balance convergence, diversity, and feasibility, especially when dealing with CMOPs that have complex feasible regions. This paper proposes a multi-task-based self-organizing mapping evolutionary algorithm (MTSOM) to tackle this challenge, which includes a main and auxiliary task. Two populations independently optimize two tasks without considering constraints in the early stage. Subsequently, in the middle stage, both tasks explore the distribution structure of the population in parallel by employing a novel constraint-to-constraint self-organizing mapping (SOM) approach. In the late stage, the main task fully considers feasibility, while the auxiliary task focuses solely on the highest priority constraints. This approach enables rapid convergence toward feasible regions. To evaluate MTSOM's effectiveness, we conducted a series of experiments on five benchmark suites. Results indicate that MTSOM is competitive when compared to other state-of-the-art CMOEAs. Additionally, our proposed constraint-to-constraint SOM is superior in handling complex CMOPs. [ABSTRACT FROM AUTHOR]

This paper proposes a spherical evolution algorithm with two-stage search. Spherical search and hypercube search are combined to achieve individuals' evolution. A self-adaptive Gaussian scale factor and a variable scale factor are designed to adaptively control individuals' spherical and hypercube search area according to their search situations. Two search stages frequently switch with four search cases to enhance the balance between exploration and exploitation processes. A directed adjacency matrix is devised to analyze the relationship among individuals from the perspective of graph theory. Experiments compare the proposed algorithm with five algorithms with distinctive search patterns on twenty nine CEC2017 benchmark functions. The diversity analysis and graph theory analysis show the good population diversity and effective information spreading of the proposed algorithm. Twenty two real-world problems evaluate the practicality and optimization ability of the proposed algorithm. Finally, the computational time complexity demonstrates that the proposed algorithm is more efficient than the original spherical evolution algorithm. • A spherical evolution algorithm with two-stage search is proposed. • Spherical search and hypercube search are combined to adaptively guide individuals' evolution. • A directed adjacency matrix is firstly introduced to analyze the relationship among individuals. • Functions and real-world problems verify the superior search performance of the proposed algorithm. • The computational efficiency of the proposed algorithm is enhanced. [ABSTRACT FROM AUTHOR]

Both problem characteristics in multimodality and multi-objective are involved in multimodal multi-objective optimization problems (MMOPs). How to locate diverse Pareto sets and approximate Pareto front simultaneously is a challenging research topic. To address this issue, a cluster-based immune-inspired algorithm using manifold learning is proposed in this paper for solving MMOPs. First of all, the population is partitioned into multiple subpopulations, and each of them is expected to find equivalent Pareto solutions in different regions. Subsequently, the immune-inspired algorithm with proportional cloning and hypermutation is developed for improving the diversity of the population and obtaining high-quality Pareto solutions in the decision space. Additionally, principal component analysis is adopted to learn the manifold of the Pareto set, further improve the convergence, and enhance interaction among subpopulations. The proposed algorithm is compared with six state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm is capable of locating equivalent Pareto optimal solutions in the decision space and maintaining the diversity and convergence of solutions in both decision space and objective space, simultaneously. [ABSTRACT FROM AUTHOR]

There are two major challenges when handling the multimodal multi-objective optimization (MMO) problems. One is the loss of diversity since most of the evolutionary algorithms designed for MMO prefer the base algorithm with rapid convergence. Therefore, the extra niching or other diversity preserving mechanism is inevitable. The other is the distribution of the Pareto optimal solutions with imbalanced density. Since the Pareto optimal sets may show different characteristics in the decision space, it is tough to converge the solutions to the Pareto front uniformly. To address these issues, subset selection and manifold learning based competitive swarm optimization algorithm, namely MMO_CSO, is proposed. Competitive swarm optimizer which has well balance on both diversity and convergence is adopted. Moreover, a subset selection strategy is applied to select diversified individuals for learning the manifold structure of the Pareto set. Thereby, the subset selection based manifold learning mechanism is designed to generate the promising solutions which could approach the real Pareto solutions and fill the sparse Pareto subregion. Compared against six state-of-the-art peer algorithms, the proposed MMO_CSO has a better performance to search for the Pareto optimal solutions both in decision space and objective space on CEC2019 MMO benchmarks. [ABSTRACT FROM AUTHOR]