Adaptive Gradient Multiobjective Particle Swarm Optimization

Inverse-Designed Ultra-Compact Passive Phase Shifters for High-Performance Beam Steering

Ultra-compact passive phase shifters are inversely designed by the multi-objective particle swarm optimization algorithm. The wavelength-dependent phase difference between two output beams originates from the different distances of the input light passing through the 4 μm × 3.2 μm rectangular waveguide with random-distributed air-hole arrays. As the wavelength changes from 1535 to 1565 nm, a phase difference tuning range of 6.26 rad and 6.95 rad is obtained for TE and TM modes, respectively. Compared with the array waveguide grating counterpart, the phase shifters exhibit higher transmission with a much smaller footprint. By combining the inverse-designed phase shifter and random-grating emitter together, integrated beam-steering structures are built, which show a large scanning range of ±25.47° and ±27.85° in the lateral direction for TE and TM mode, respectively. This work may pave the way for the development of ultra-compact high-performance optical phased array LiDARs.

Knowledge-Data Driven Optimal Control for Nonlinear Systems and Its Application to Wastewater Treatment Process

Optimal control is developed to guarantee nonlinear systems run in an optimum operating state. However, since the operation demands of systems are dynamically changeable, it is difficult for optimal control to obtain reliable optimal solutions to achieve satisfying operation performance. To overcome this problem, a knowledge-data driven optimal control (KDDOC) for nonlinear systems is designed in this article. First, an adaptive initialization strategy, using the knowledge from historical operation information of nonlinear systems, is employed to dynamically preset parameters of KDDOC. Then, the initial performance of KDDOC can be enhanced for nonlinear systems. Second, a knowledge guide-based global best selection mechanism is used to assist KDDOC in searching for the optimal solutions under different operation demands. Then, dynamic optimal solutions of KDDOC can be obtained to adapt to flexible changes in nonlinear systems. Third, a knowledge direct-based exploitation mechanism is presented to accelerate the solving process of KDDOC. Then, the demand response speed of KDDOC can be improved to ensure nonlinear systems with optimal operation performance in different states. Finally, the performance of KDDOC is validated on a simulation and a practical process. Several experimental results illustrate the effectiveness of the proposed optimal control for nonlinear systems.

Domain Adaptation Multitask Optimization

Multitask optimization (MTO) is a new optimization paradigm that leverages useful information contained in multiple tasks to help solve each other. It attracts increasing attention in recent years and gains significant performance improvements. However, the solutions of distinct tasks usually obey different distributions. To avoid that individuals after intertask learning are not suitable for the original task due to the distribution differences and even impede overall solution efficiency, we propose a novel multitask evolutionary framework that enables knowledge aggregation and online learning among distinct tasks to solve MTO problems. Our proposal designs a domain adaptation-based mapping strategy to reduce the difference across solution domains and find more genetic traits to improve the effectiveness of information interactions. To further improve the algorithm performance, we propose a smart way to divide initial population into different subpopulations and choose suitable individuals to learn. By ranking individuals in target subpopulation, worse-performing individuals can learn from other tasks. The significant advantage of our proposed paradigm over the state of the art is verified via a series of MTO benchmark studies.

A Dynamic Neighborhood-Based Switching Particle Swarm Optimization Algorithm

In this article, a dynamic-neighborhood-based switching PSO (DNSPSO) algorithm is proposed, where a new velocity updating mechanism is designed to adjust the personal best position and the global best position according to a distance-based dynamic neighborhood to make full use of the population evolution information among the entire swarm. In addition, a novel switching learning strategy is introduced to adaptively select the acceleration coefficients and update the velocity model according to the searching state at each iteration, thereby contributing to a thorough search of the problem space. Furthermore, the differential evolution algorithm is successfully hybridized with the particle swarm optimization (PSO) algorithm to alleviate premature convergence. A series of commonly used benchmark functions (including unimodal, multimodal, and rotated multimodal cases) is utilized to comprehensively evaluate the performance of the DNSPSO algorithm. The experimental results demonstrate that the developed DNSPSO algorithm outperforms a number of existing PSO algorithms in terms of the solution accuracy and convergence performance, especially for complicated multimodal optimization problems.

Adaptive Estimation Distribution Distributed Differential Evolution for Multimodal Optimization Problems

Multimodal optimization problems (MMOPs) require algorithms to locate multiple optima simultaneously. When using evolutionary algorithms (EAs) to deal with MMOPs, an intuitive idea is to divide the population into several small "niches," where different niches focus on locating different optima. These population partition strategies are called "niching" techniques, which have been frequently used for MMOPs. The algorithms for simultaneously locating multiple optima of MMOPs are called multimodal algorithms. However, many multimodal algorithms still face the difficulty of population partition since most of the niching techniques involve the sensitive niching parameters. Considering this issue, in this article, we propose a parameter-free niching method based on adaptive estimation distribution (AED) and develop a distributed differential evolution (DDE) algorithm, which is called AED-DDE, for solving MMOPs. In AED-DDE, each individual finds its own appropriate niche size to form a niche and acts as an independent unit to find a global optimum. Therefore, we can avoid the difficulty of population partition and the sensitivity of niching parameters. Different niches are co-evolved by using the master-slave multiniche distributed model. The multiniche co-evolution mechanism can improve the population diversity for fully exploring the search space and finding more global optima. Moreover, the AED-DDE algorithm is further enhanced by a probabilistic local search (PLS) to refine the solution accuracy. Compared with other multimodal algorithms, even the winner of CEC2015 multimodal competition, the comparison results fully demonstrate the superiority of AED-DDE.

A competitive swarm optimizer with probabilistic criteria for many-objective optimization problems

Although multiobjective particle swarm optimizers (MOPSOs) have performed well on multiobjective optimization problems (MOPs) in recent years, there are still several noticeable challenges. For example, the traditional particle swarm optimizers are incapable of correctly discriminating between the personal and global best particles in MOPs, possibly leading to the MOPSOs lacking sufficient selection pressure toward the true Pareto front (PF). In addition, some particles will be far from the PF after updating, this may lead to invalid search and weaken the convergence efficiency. To address the abovementioned issues, we propose a competitive swarm optimizer with probabilistic criteria for many-objective optimization problems (MaOPs). First, we exploit a probability estimation method to select the leaders via the probability space, which ensures the search direction to be correct. Second, we design a novel competition mechanism that uses winner pool instead of the global and personal best particles to guide the entire population toward the true PF. Third, we construct an environment selection scheme with the mixed probability criterion to maintain population diversity. Finally, we present a swarm update strategy to ensure that the next generation particles are valid and the invalid search is avoided. We employ various benchmark problems with 3–15 objectives to conduct a comprehensive comparison between the presented method and several state-of-the-art approaches. The comparison results demonstrate that the proposed method performs well in terms of searching efficiency and population diversity, and especially shows promising potential for large-scale multiobjective optimization problems.

Performance-driven X-architecture Routing Algorithm for Artificial Intelligence Chip Design in Smart Manufacturing

The new 7nm Artificial Intelligence (AI) chip is an important milestone recently announced by the IBM research team, with a very important optimization goal of performance. This chip technology can be extended to various business scenarios in the Internet of Things. As the basic model for Very Large Scale Integration (VLSI) routing, the Steiner minimal tree can be used in various practical problems, such as wirelength optimization and timing closure. Further considering the X-architecture and the routing resources within obstacles, an effective performance-driven X-architecture routing algorithm for AI chip design in smart manufacturing is proposed to improve the delay performance of the chip. Firstly, a special particle swarm optimization algorithm is presented to solve the discrete length-restricted X-architecture Steiner minimum tree problem in combination with genetic operations, and a particle encoding scheme is presented to encode each particle into an initial routing tree. Secondly, two look-up tables based on pins and obstacles are established to provide a fast information query for the whole algorithm flow. Thirdly, a strategy of candidate point selection is designed to make the particles satisfy the constraints. Finally, a refinement strategy is implemented to further improve the quality of the final routing tree. Compared with other state-of-the-art algorithms, the proposed algorithm achieves a better total wirelength, which is an important index of performance, thus better satisfying the demand for delay performance of AI chip design in smart manufacturing.

Generative Adversarial Construction of Parallel Portfolios

Since automatic algorithm configuration methods have been very effective, recently there is increasing research interest in utilizing them for automatic solver construction, resulting in several notable approaches. For these approaches, a basic assumption is that the given training set could sufficiently represent the target use cases such that the constructed solvers can generalize well. However, such an assumption does not always hold in practice since in some cases, we might only have scarce and biased training data. This article studies effective construction approaches for the parallel algorithm portfolios that are less affected in these cases. Unlike previous approaches, the proposed approach simultaneously considers instance generation and portfolio construction in an adversarial process, in which the aim of the former is to generate instances that are challenging for the current portfolio, while the aim of the latter is to find a new component solver for the portfolio to better solve the newly generated instances. Applied to two widely studied problem domains, that is, the Boolean satisfiability problems (SAT) and the traveling salesman problems (TSPs), the proposed approach identified parallel portfolios with much better generalization than the ones generated by the existing approaches when the training data were scarce and biased. Moreover, it was further demonstrated that the generated portfolios could even rival the state-of-the-art manually designed parallel solvers.

An evolving ensemble model of multi-stream convolutional neural networks for human action recognition in still images

Still image human action recognition (HAR) is a challenging problem owing to limited sources of information and large intra-class and small inter-class variations which requires highly discriminative features. Transfer learning offers the necessary capabilities in producing such features by preserving prior knowledge while learning new representations. However, optimally identifying dynamic numbers of re-trainable layers in the transfer learning process poses a challenge. In this study, we aim to automate the process of optimal configuration identification. Specifically, we propose a novel particle swarm optimisation (PSO) variant, denoted as EnvPSO, for optimal hyper-parameter selection in the transfer learning process with respect to HAR tasks with still images. It incorporates Gaussian fitness surface prediction and exponential search coefficients to overcome stagnation. It optimises the learning rate, batch size, and number of re-trained layers of a pre-trained convolutional neural network (CNN). To overcome bias of single optimised networks, an ensemble model with three optimised CNN streams is introduced. The first and second streams employ raw images and segmentation masks yielded by mask R-CNN as inputs, while the third stream fuses a pair of networks with raw image and saliency maps as inputs, respectively. The final prediction results are obtained by computing the average of class predictions from all three streams. By leveraging differences between learned representations within optimised streams, our ensemble model outperforms counterparts devised by PSO and other state-of-the-art methods for HAR. In addition, evaluated using diverse artificial landscape functions, EnvPSO performs better than other search methods with statistically significant difference in performance.

Self-Regulated Particle Swarm Multi-Task Optimization

Population based search techniques have been developed and applied to wide applications for their good performance, such as the optimization of the unmanned aerial vehicle (UAV) path planning problems. However, the search for optimal solutions for an optimization problem is usually expensive. For example, the UAV problem is a large-scale optimization problem with many constraints, which makes it hard to get exact solutions. Especially, it will be time-consuming when multiple UAV problems are waiting to be optimized at the same time. Evolutionary multi-task optimization (EMTO) studies the problem of utilizing the population-based characteristics of evolutionary computation techniques to optimize multiple optimization problems simultaneously, for the purpose of further improving the overall performance of resolving all these problems. EMTO has great potential in solving real-world problems more efficiently. Therefore, in this paper, we develop a novel EMTO algorithm using a classical PSO algorithm, in which the developed knowledge transfer strategy achieves knowledge transfer between task by synthesizing the transferred knowledges from a selected set of component tasks during the updating of the velocities of population. Two knowledge transfer strategies are developed along with two versions of the proposed algorithm. The proposed algorithm is compared with the multifactorial PSO algorithm, the SREMTO algorithm, the popular multifactorial evolutionary algorithm and a classical PSO algorithm on nine popular single-objective MTO problems and six five-task MTO problems, which demonstrates its superiority.

Particle Swarm Optimization Algorithm With Self-Organizing Mapping for Nash Equilibrium Strategy in Application of Multiobjective Optimization

In this article, the Nash equilibrium strategy is used to solve the multiobjective optimization problems (MOPs) with the aid of an integrated algorithm combining the particle swarm optimization (PSO) algorithm and the self-organizing mapping (SOM) neural network. The Nash equilibrium strategy addresses the MOPs by comparing decision variables one by one under different objectives. The randomness of the PSO algorithm gives full play to the advantages of parallel computing and improves the rate of comparison calculation. In order to avoid falling into local optimal solutions and increase the diversity of particles, a nonlinear recursive function is introduced to adjust the inertia weight, which is called the adaptive particle swarm optimization (APSO). In addition, the neighborhood relations of current particles are constructed by SOM, and the leading particles are selected from the neighborhood to guide the local and global search, so as to achieve convergence. Compared with several advanced algorithms based on the eight multiobjective standard test functions with different Pareto solution sets and Pareto front characteristics in examples, the proposed algorithm has a better performance.

Cooperative Optimal Controller and Its Application to Activated Sludge Process

With the increasing complexity and scale of activated sludge process (ASP), it is quite challenging to coordinate the performance indices with different time scales. To address this problem, a cooperative optimal controller (COC) is proposed to improve the operation performance in this paper. First, a cooperative optimal scheme is developed for designing the control system, where the different time-scale performance indices are formulated by two levels. Second, a data-driven surrogate-assisted optimization (DDSAO) algorithm is provided to optimize the cooperative objectives, where a surrogate model is established for evaluating the feasibility of optimal solutions based on the minimum squared error. Third, an adaptive predictive control strategy is investigated to derive the control laws for improving the tracking control performance. Finally, the proposed COC is tested on benchmark simulation model No. 1 (BSM1). The results demonstrate that the proposed COC is able to coordinate the multiple time-scale performance indices and achieve the competitive optimal control performance.

A Many-Objective Evolutionary Algorithm Based on a Two-Round Selection Strategy

Balancing population diversity and convergence is critical for evolutionary algorithms to solve many-objective optimization problems (MaOPs). In this paper, a two-round environmental selection strategy is proposed to pursue good tradeoff between population diversity and convergence for many-objective evolutionary algorithms (MaOEAs). Particularly, in the first round, the solutions with small neighborhood density are picked out to form a candidate pool, where the neighborhood density of a solution is calculated based on a novel adaptive position transformation strategy. In the second round, the best solution in terms of convergence is selected from the candidate pool and inserted into the next generation. The procedure is repeated until a new population is generated. The two-round selection strategy is embedded into an MaOEA framework and the resulting algorithm, namely, 2REA, is compared with eight state-of-the-art MaOEAs on various benchmark MaOPs. The experimental results show that 2REA is very competitive with the compared MaOEAs and the two-round selection strategy works well on balancing population diversity and convergence.

Synchronization of Coupled Harmonic Oscillators With Asynchronous Intermittent Communication

This paper adopts two different approaches, the small-gain technique and the integral quadratic constraints (IQCs), to investigate the synchronization problem of coupled harmonic oscillators (CHOs) via an event-triggered control strategy in a directed graph. First, a novel control protocol is proposed such that every state signal of the CHO decides when to exchange information with its neighbors asynchronously. Then, the resulting closed-loop system based on the designed control protocol is converted into a feedback interconnection of a linear system and a bounded operator, and the stable condition of the feedback interconnection is presented by employing the small-gain technique. In order to better describe the relationship between the input and output, the IQCs theorem is applied to derive the stable condition on the basis of the Kalman-Yakubovich-Popov lemma. Finally, a simulation example is provided to verify the proposed new algorithms.

Collaboration and Resource Sharing in the Multidepot Multiperiod Vehicle Routing Problem with Pickups and Deliveries

In this work, a multidepot multiperiod vehicle routing problem with pickups and deliveries (MDPVRPPD) is solved by optimizing logistics networks with collaboration and resource sharing among logistics service providers. The optimal solution can satisfy customer demands with periodic time characteristics and incorporate pickup and delivery services with maximum resource utilization. A collaborative mechanism is developed to rearrange both the open and closed vehicle routes among multiple pickup and delivery centers with improved transportation efficiency and reduced operational costs. The effects of resource sharing strategies combining customer information sharing, facility service sharing, and vehicle sharing are investigated across multiple service periods to maximize resource utilization and refine the resource configuration. A multiobjective optimization model is developed to formulate the MDPVRPPD so that the minimum total operational costs, waiting time, and the number of vehicles are obtained. A hybrid heuristic algorithm incorporating a 3D clustering and an improved multiobjective particle swarm optimization (IMOPSO) algorithm is introduced to solve the MDPVRPPD and find Pareto optimal solutions. The proposed hybrid heuristic algorithm is based on a selective exchange mechanism that enhances local and global searching capabilities. Results demonstrate that the proposed IMOPSO outperforms other existing algorithms. We also study profit allocation issues to quantify the stability and sustainability of long-term collaboration among logistics participants, using the minimum costs remaining savings method. The proposed model and solution methods are validated by conducting an empirical study of a real system in Chongqing City, China. This study contributes to the development of efficient urban logistics distribution systems, and facilitates the expansion of intelligent and sustainable supply chains.

Multi-objective particle swarm optimization with random immigrants

Complex problems of the current business world need new approaches and new computational algorithms for solution. Majority of the issues need analysis from different angles, and hence, multi-objective solutions are more widely used. One of the recently well-accepted computational algorithms is Multi-objective Particle Swarm Optimization (MOPSO). This is an easily implemented and high time performance nature-inspired approach; however, the best solutions are not found for archiving, solution updating, and fast convergence problems faced in certain cases. This study investigates the previously proposed solutions for creating diversity in using MOPSO and proposes using random immigrants approach. Application of the proposed solution is tested in four different sets using Generational Distance, Spacing, Error Ratio, and Run Time performance measures. The achieved results are statistically tested against mutation-based diversity for all four performance metrics. Advantages of this new approach will support the metaheuristic researchers.

Dynamic Group Learning Distributed Particle Swarm Optimization for Large-Scale Optimization and Its Application in Cloud Workflow Scheduling

Cloud workflow scheduling is a significant topic in both commercial and industrial applications. However, the growing scale of workflow has made such a scheduling problem increasingly challenging. Many current algorithms often deal with small- or medium-scale problems (e.g., less than 1000 tasks) and face difficulties in providing satisfactory solutions when dealing with the large-scale problems, due to the curse of dimensionality. To this aim, this article proposes a dynamic group learning distributed particle swarm optimization (DGLDPSO) for large-scale optimization and extends it for the large-scale cloud workflow scheduling. DGLDPSO is efficient for large-scale optimization due to its following two advantages. First, the entire population is divided into many groups, and these groups are coevolved by using the master-slave multigroup distributed model, forming a distributed PSO (DPSO) to enhance the algorithm diversity. Second, a dynamic group learning (DGL) strategy is adopted for DPSO to balance diversity and convergence. When applied DGLDPSO into the large-scale cloud workflow scheduling, an adaptive renumber strategy (ARS) is further developed to make solutions relate to the resource characteristic and to make the searching behavior meaningful rather than aimless. Experiments are conducted on the large-scale benchmark functions set and the large-scale cloud workflow scheduling instances to further investigate the performance of DGLDPSO. The comparison results show that DGLDPSO is better than or at least comparable to other state-of-the-art large-scale optimization algorithms and workflow scheduling algorithms.

The Set-Based Hypervolume Newton Method for Bi-Objective Optimization

In this paper, we propagate the use of a set-based Newton method that enables computing a finite size approximation of the Pareto front (PF) of a given twice continuously differentiable bi-objective optimization problem (BOP). To this end, we first derive analytically the Hessian matrix of the hypervolume indicator, a widely used performance indicator for PF approximation sets. Based on this, we propose the hypervolume Newton method (HNM) for hypervolume maximization of a given set of candidate solutions. We first address unconstrained BOPs and focus further on first attempts for the treatment of inequality constrained problems. The resulting method may even converge quadratically to the optimal solution, however, this property is-as for all Newton methods-of local nature. We hence propose as a next step a hybrid of HNM and an evolutionary strategy in order to obtain a fast and reliable algorithm for the treatment of such problems. The strengths of both HNM and hybrid are tested on several benchmark problems and comparisons of the hybrid to state-of-the-art evolutionary algorithms for hypervolume maximization are presented.

A Generic WebLab Control Tuning Experience Using the Ball and Beam Process and Multiobjective Optimization Approach

In control engineering education, the possibility of using a real control system in the learning process motivates professors to improve both students’ knowledge and skills, thus avoiding an approach only based on control theory. While considering that control engineering laboratories are expensive, mainly because educational plants should reproduce classical problems that are found in the industry, the use of virtual laboratories appears as an interesting strategy for reducing costs and improving the diversity of experiments. In this research, remote experimentation was assumed regarding the ball and beam process as an alternative didactic methodology. While assuming a nonlinear and unstable open-loop process, this study presents how students should proceed to control the plant focusing on the topic that is associated with multiobjective optimization. Proportional-Integral-Derivative (PID) controller was tuned considering the Non-dominated Sorting Genetic Algorithm (NSGA-II) to illustrate the WebLab learning procedures described in this research. The proposed strategy was compared to the Åström’s robust loop shaping method to emphasize the performance of the multiobjective optimization technique. Analyzing the feedback provided by the students, remote experimentation can be seen as an interesting approach for the future of engineering learning, once it can be directly associated with industry demand of connected machines and real-time information analysis.

Adaptive Multiobjective Differential Evolution With Reference Axis Vicinity Mechanism

Due to the simple but effective search framework, differential evolution (DE) has achieved successful applications in multiobjective optimization problems. However, most of the previous research on the multiobjective DE (MODE) focused on the design of control strategies of parameters and mutation operators for a given population at each generation, and ignored that the given population might have a bad distribution in the objective space. Therefore, this paper proposes a new variant of MODE in which a reference axis vicinity mechanism (RAVM) is developed to restore the good distribution of the given population and maintain its convergence before the evolution (i.e., mutation, crossover, and selection) starts at each generation. Besides the RAVM, a hybrid control strategy of parameters and mutation operators is also presented to accelerate convergence by integrating both randomness and guided information derived from solutions generated during the search process. Computational results on four series of benchmark problems illustrate that the proposed MODE with the RAVM and hybrid control strategy is competitive or even superior to some state-of-the-art multiobjective evolutionary algorithms in the literature.

A Discrete Multiobjective Particle Swarm Optimizer for Automated Assembly of Parallel Cognitive Diagnosis Tests

Parallel test assembly has long been an important yet challenging topic in educational assessment. Cognitive diagnosis models (CDMs) are a new class of assessment models and have drawn increasing attention for being able to measure examinees' ability in detail. However, few studies have been devoted to the parallel test assembly problem in CDMs (CDM-PTA). To fill the gap, this paper models CDM-PTA as a subset-based bi-objective combinatorial optimization problem. Given an item bank, it aims to find a required number of tests that achieve optimal but balanced diagnostic performance, while satisfying important practical requests in the aspects of test length, item type distribution, and overlapping proportion. A set-based multiobjective particle swarm optimizer based on decomposition (S-MOPSO/D) is proposed to solve the problem. To coordinate with the property of CDM-PTA, S-MOPSO/D utilizes an assignment-based representation scheme and a constructive learning strategy. Through this, promising solutions can be built efficiently based on useful assignment patterns learned from personal and collective search experience on neighboring scalar problems. A heuristic constraint handling strategy is also developed to further enhance the search efficiency. Experimental results in comparison with three representative approaches validate that the proposed algorithm is effective and efficient.