Global Optimization Strategy Research Articles

Diversified Position Update Equation-Based SSA with Refreshing-Gap Strategy for global optimization

This study, incorporating three improvements into the structure of the original SSA algorithm to increase its exploration and exploitation capabilities, suggests an SSA variant algorithm named ”Diversified Position Update Equation-Based SSA with Refreshing-Gap Strategy (DSSA-R)”. Unlike the original SSA, DSSA-R accepts half of the population as the leader instead of using a single leader salp strategy. Nevertheless, the suggested algorithm includes two different equations to update the positions of the leader salps and follower salps. Furthermore, Refreshing Gap strategy was included in DSSA-R to avoid the algorithm from being stuck in the local optimum. The final improvement made on the original SSA was the addition of ”Linear Population Reduction Strategy” to strengthen the exploitation aspect of the algorithm. The performance of the DSSA-R algorithm was tested using the functions of the CEC 2014 and CEC 2015 benchmark suites and compared with five SSA variants and four state-of-the-art algorithms. Test results show that DSSA-R obtained better and competitive results compared to the algorithms it was compared with.

Inverse Problem in Resonant Ultrasound Spectroscopy With Sampling and Optimization: A Comparative Study on Human Cortical Bone.

The Bayesian inference with prior knowledge has been proposed recently to solve the inverse problem in resonant ultrasound spectroscopy. It allows inferring the elastic properties of high damping materials, such as cortical bone with less dependence on the initial guessed values. In this method, the estimation of the stiffness coefficients is expressed as a probabilistic solution to the inverse problem, which can be achieved by sampling or optimization methods. However, the detailed performance comparison of these two strategies applied to high damping materials has not been fully studied. In this work, the full stiffness tensor of 52 transversely isotropic cortical bone specimens was obtained using Markov chain Monte Carlo (MCMC) sampling and particle swarm optimization (PSO), respectively. Results showed that the local probability distributions of stiffness coefficients estimated by the two methods are consistent. Compared with MCMC, the average calculation speed of PSO is ten times faster [614 s ± 59 s (MCMC) versus 53 s ± 22 s (PSO)]. The mean standard error between theoretical and experimental resonant frequencies was slightly smaller for PSO compared with MCMC. In conclusion, PSO, a global optimization strategy, is suitable to solve the inverse problem for high damping materials.

GREEN: A Global Optimization Scheme for Transportation Efficiency by Mining Taxi Mobility

Taxi business, with its ubiquitous availability, route flexibility and comfortable travel experience, offers a complementary service for the public transportation system. Among the existing methods of doing taxi business, an meaningful issue is to mine efficient seeking strategies for taxi drivers, in order to improve transportation efficiency. Recent efforts have been made mainly on the individual recommendation with respect to shorter seeking time and higher seeking efficiency, whereas the global transportation efficiency will greatly be reduced once each driver only pays attention to his local optimization. Rather than the individual recommendation, in this paper we conduct research on mining the taxis mobility from large-scale taxi data, thereby proposing a novel solution, namely GREEN (short for A Global RoutEs rEcommeNdation), to improve the seeking strategies and optimize the global transportation situation. Specifically, we first investigate how the drop-off information affects seeking strategies and conduct quantitive analysis, revealing the impact of seeking efficiency, passenger density and top drivers’ experience. Moreover, to deal with the conflict between local optimization and global optimization, we dynamically adjust the weights of road segments based on the number of vacant taxis passing through each road segment. Also, to well evaluate the transportation efficiency, we define the seeking efficiency, net revenue and operation efficiency. Extensive experiments on the real-world dataset demonstrate that our scheme can work well, which not only improves the overall seeking efficiency by reducing total vacant driving time, but also increases the global operation efficiency, thereby optimizing the global transportation efficiency.

Multi-Hop Task Offloading With On-the-Fly Computation for Multi-UAV Remote Edge Computing

The dramatic growth in computing capability and the inherent mobility of the unmanned aerial vehicles (UAVs) foster the recent surge of interests in incorporating UAVs into edge computing systems to facilitate on-demand deployment and extended coverage. Nonetheless, due to the limited communication capability of the UAVs, single-UAV edge computing systems may still be incompetent when serving remote users. Although the traditional multi-UAV relay network can be a viable solution, it fails to exploit the computing capability of the UAVs. With this consideration, a multi-hop task offloading with on-the-fly computation scheme is proposed in this work to enable a more powerful multi-UAV remote edge computing network. To solve the corresponding joint resource allocation and deployment problem, two efficient algorithms are proposed. One of them can find the global optimal strategy in a special case, while the other can obtain a good local optimal strategy in the general cases. Both algorithms have a complexity only linear in the number of UAVs and admit distributed implementation. In addition to analysis, numerical results are provided to corroborate the effectiveness of the proposed scheme.

Programmable wavelength filter with double ring loaded MZI

We propose a novel filter circuit that incorporates a double ring resonator with a balanced Mach–Zehnder interferometer (MZI). The circuit has a response equivalent to a conventional ring loaded MZI filter, but with added flexibility in terms of configurability. The second-order filter can also be cascaded to realize higher-order filters. The circuit incorporates a two-stage input and output coupler to further reduce the effect of dispersion. A combination of local and global optimization strategies to program the filter, using tailored objective functions, have been tested in simulation and experiments. To our best knowledge, this is the first time a global optimization strategy is directly used in ARMA filter synthesis and simulation without any additional requirement. We further extend the optimization strategy into experiments and demonstrated its use in practical case for programmable filter circuits.

A robust approach to warped Gaussian process-constrained optimization

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work considers optimization problems with aggregated black-box constraints. Each aggregated black-box constraint sums several draws from the same black-box function with different decision variables as arguments in each individual black-box term. Such constraints are important in applications where, e.g., safety-critical measures are aggregated over multiple time periods. Our approach, which uses robust optimization, reformulates these uncertain constraints into deterministic constraints guaranteed to be satisfied with a specified probability, i.e., deterministic approximations to a chance constraint. While robust optimization typically considers parametric uncertainty, our approach considers uncertain functions modeled by warped Gaussian processes. We analyze convexity conditions and propose a custom global optimization strategy for non-convex cases. A case study derived from production planning and an industrially relevant example from oil well drilling show that the approach effectively mitigates uncertainty in the learned curves. For the drill scheduling example, we develop a custom strategy for globally optimizing integer decisions.

Learning in continuous action space for developing high dimensional potential energy models

Reinforcement learning (RL) approaches that combine a tree search with deep learning have found remarkable success in searching exorbitantly large, albeit discrete action spaces, as in chess, Shogi and Go. Many real-world materials discovery and design applications, however, involve multi-dimensional search problems and learning domains that have continuous action spaces. Exploring high-dimensional potential energy models of materials is an example. Traditionally, these searches are time consuming (often several years for a single bulk system) and driven by human intuition and/or expertise and more recently by global/local optimization searches that have issues with convergence and/or do not scale well with the search dimensionality. Here, in a departure from discrete action and other gradient-based approaches, we introduce a RL strategy based on decision trees that incorporates modified rewards for improved exploration, efficient sampling during playouts and a “window scaling scheme" for enhanced exploitation, to enable efficient and scalable search for continuous action space problems. Using high-dimensional artificial landscapes and control RL problems, we successfully benchmark our approach against popular global optimization schemes and state of the art policy gradient methods, respectively. We demonstrate its efficacy to parameterize potential models (physics based and high-dimensional neural networks) for 54 different elemental systems across the periodic table as well as alloys. We analyze error trends across different elements in the latent space and trace their origin to elemental structural diversity and the smoothness of the element energy surface. Broadly, our RL strategy will be applicable to many other physical science problems involving search over continuous action spaces.

Cooperative particle swarm optimizer with depth first search strategy for global optimization of multimodal functions

Cooperative particle swarm optimizer with depth first search strategy for global optimization of multimodal functions

A Complex-Valued Encoding Multichain Seeker Optimization Algorithm for Engineering Problems

This article comes up with a complex-valued encoding multichain seeker optimization algorithm (CMSOA) for the engineering optimization problems. The complex-valued encoding strategy and the multichain strategy are leaded in the seeker optimization algorithm (SOA). These strategies enhance the individuals’ diversity, enhance the local search, avert falling into the local optimum, and are the influential global optimization strategies. This article chooses fifteen benchmark functions, four proportional integral derivative (PID) control parameter models, and six constrained engineering problems to test. According to the experimental results, the CMSOA can be used in the benchmark functions, in the PID control parameter optimization, and in the optimization of constrained engineering problems. Compared to the particle swarm optimization (PSO), simulated annealing based on genetic algorithm (SA_GA), gravitational search algorithm (GSA), sine cosine algorithm (SCA), multiverse optimizer (MVO), and seeker optimization algorithm (SOA), the optimization ability and robustness of the CMSOA are better than those of others algorithms.

Improved Slime Mould Algorithm Hybridizing Chaotic Maps and Differential Evolution Strategy for Global Optimization

Slime Mould Algorithm (SMA) is a new meta-heuristics algorithm that is inspired by the behaviors of slime mould from nature. Due to its effective performance, SMA has shown its competitive performance among other meta-heuristics algorithms and has been used in many mathematical optimization and real-world problems. However, SMA tends to sink into local optimality and lacks the diversity of the population. Therefore, to cope with the drawbacks of the classical SMA, this paper proposes an improved SMA algorithm named CHDESMA. First of all, the chaotic maps methods have the characteristics of ergodicity and randomness, and we used chaotic maps methods to replace the original random initialization to improve the diversity of the algorithm, which is more suitable for exploring the potential areas in the early stage. Then, based on the superior searching ability of the differential evolution algorithm (DE), the crossover and selection operations of DE are applied to CHDESMA, and the position is updated by the combination of the original SMA operator and the mutation strategy of DE, which effectively avoids the algorithm falling into local optimum. CHDESMA was evaluated using CEC2014 and CEC2017 test suits and four real-world engineering problems. CHDESMA was compared with advanced algorithms and DE variants. The experimental results and statistical analysis indicate that CHDESMA has competitive performance compared with the state-of-the-art algorithms.

An Improved Lion Swarm Optimization Algorithm With Chaotic Mutation Strategy and Boundary Mutation Strategy for Global Optimization

Lion swarm optimization (LSO) inspired by the natural division of labor among lion king, lionesses and lion cubs in a lion group, i.e., lion king guarding, lionesses hunting and lion cubs following, is a relatively novel swarm intelligent optimization technique. Due to its remarkable performance, the canonical LSO has been extensively researched. However, how to balance contradictions between the exploration and the exploitation and alleviate the premature convergence are two critical concerns that need to be dealt with in the LSO study. To address these two drawbacks, enhance the optimization performance, and broaden its application domain, an improved lion swarm optimization algorithm with chaotic mutation strategy and a boundary mutation strategy (CBLSO) is proposed in this paper. In the proposed algorithm, a chaotic mutation strategy based on chaotic cubic mapping is designed to enhance the exploration ability of the algorithm, while the boundary mutation strategy based on the concept of multilevel parallel is adopted to manage boundary constraint violations, which is beneficial for improving the exploitation ability of the algorithm. The proposed CBLSO is evaluated on 56 classic test functions and 30 CEC2014 benchmark functions, and is compared with quite a few state-of-the-art algorithms regarding often-used performance metrics. The experimental results demonstrate the superior performance of the embedded strategies on balancing the exploration and the exploitation. Furthermore, the proposed CBLSO is applied to the optimal dispatch problem of cascade hydropower stations based on a novel constraints handling method designed in this paper to validate its good practicability and performance. The experimental results of a case study on the optimal dispatch problem of China’s Wujiang cascade hydropower stations indicate that the proposed CBLSO can produce better and more reliable optimal results than the canonical LSO and other comparison algorithms with competitive speed. Thus, we can conclude that the proposed CBLSO is a competitive and effective alterative tool to solve complex numerical optimization problems and real-world optimization with complicated constraints.

An Efficiency Based Approach for the Energy Management in HEVs

A proper Energy Management Strategy (EMS) is a cornerstone for Hybrid Electric Vehicles consumption minimization. In general, to find the global optimal strategy, the knowledge of the entire mission profile of the vehicle is needed, making the real-time implementation impossible. A well-known solution to this problem is the Equivalent Consumption Minimization Strategy (ECMS) that optimizes at each time instant an equivalent fuel consumption, which combines the real fuel rate and a virtual fuel associated to the use of the battery energy. This virtual fuel is the actual battery power weighted by an equivalence factor, that implicitly accounts for the battery recharge efficiency during the vehicle mission. In this work, we propose an effciency based EMS, rather than a fuel consumption based one. Despite the two approaches are proven to be identical under some assumptions, in the efficiency based solution the defnition of the equivalence factor results easier. An offline estimation of this quantity is firstly proposed, eventually extended with a real-time adaptation. Simulation results show the effectiveness of the proposed approach, in particular when the adaptive strategy is used.

Global Optimal Cooperative Control of Multiple DC–DC Converter Systems for Dynamic Consensus

To improve the poor dynamic consensus in multiple dc-dc converter systems caused by parameter differences, this article proposes a global optimal cooperative control strategy. The proposed control strategy achieves dynamic consensus of output currents by minimizing a global performance index, which consists of local errors and neighbor synchronization errors. In this system, each converter is regarded as an agent in the communication digraph, so as to construct a cyber-physical model. Accordingly, a cooperative control method based on the linear quadratic regulator (LQR) is proposed, with the help of nonlinear coordinate transformation techniques. Different from conventional LQR, integral action is introduced to eliminate steady-state errors and improve coordinated performance. Meanwhile, the proof of the stability and consensus of the closed-loop system is given using Lyapunov approach. Moreover, the design guidelines to tune the dynamic response are provided through simulations. The experimental results further demonstrate the effectiveness and superiority of the proposed control method in a multiconverter prototype.

Comparative study on fuel saving potential of series-parallel hybrid transmission and series hybrid transmission

The series hybrid transmission (SHT) and series-parallel hybrid transmission (SPHT) have become an important development direction in the field of hybrid electric vehicles (HEVs) in China. The main difference between a SHT and SPHT is that the engine can directly drive the vehicle through the addition of one clutch in the SPHT. The SPHT is thus more complex in structure, but its fuel economy advantages, as compared with the SHT, have remained controversial. Therefore, this study provides a thorough comparison between the SHT and SPHT for different types of vehicles and driving cycles. A global optimal control strategy based on dynamic programming (DP) is developed to evaluate the economic performance of the SHT and SPHT. Particularly, a mode-switching penalty matrix is designed in the control strategy based on the energy consumed during the mode-switching process. To exclude the influence of the configuration parameters and power sources, a large number of simulations are conducted for different parameter combinations. The results show that the SPHT has notable advantages in fuel saving compared with the SHT, especially in high-speed driving cycles for type C vehicles, while there is a negligible difference in the fuel consumption between the two for type A vehicles under urban driving cycles. Under the Worldwide Harmonized Light Vehicles Test Cycle (WLTC), the SPHT has a fuel saving of approximately 7.2% more than the SHT for type B vehicles. This study provides a new theoretical basis on technical path selection for the SHT and SPHT.

Adaptive memetic differential evolution with multi-niche sampling and neighborhood crossover strategies for global optimization

This paper proposes an adaptive memetic differential evolution with multi-niche sampling and neighborhood crossover strategies for global optimization. In the proposed algorithm, a multi-niche sampling strategy is designed to sample a subpopulation for evolution at each generation. In this strategy, the entire population is firstly divided into multiple niches by employing a certain niching strategy at each generation. A subpopulation is then dynamically sampled from the resulting niches such that supporting a diverse search at the early stage of evolution while an intensive search towards the end of evolution. The above strategy will be further coupled with a neighborhood crossover, which is devised to encourage high potential solutions for exploitation while low potential solutions for exploration, thus appropriately searching the solution space. Additionally, an adaptive local search (ALS) scheme along with an adaptive elimination operation (AEO) have been designed. The ALS aims to appropriately fine-tune promising solutions in the sampled subpopulation while the AEO tends to adaptively eliminate unpromising individuals in the population during evolution. The performance of the proposed algorithm has been evaluated on CEC’2015 benchmark functions and compared with related methods. Experimental results show that our algorithm can achieve a superior performance and outperform related methods. The results also confirm the significance of devised strategies in the proposed algorithm.

Decomposition of overlapping peaks in X‐ray fluorescence using improved crow searching algorithm based on opposite learning

AbstractTo overcome the difficulties in overlapping peaks decomposition in X‐ray fluorescence (XRF) spectrum of heavy metal Pb and As, an improved crow searching algorithm (CSA) (ICSA) method was proposed. Compared with the CSA, three main improvements were performed: the opposite learning (OL) mechanism was introduced to expand the diversity of population and the parameter TF was introduced to control the convergence, which could avoid falling into the local minimum during the initialization process. Furthermore, this method has made some adjustments on the global optimization strategy, which can make the convergence more stable. When using the ICSA to decompose the overlapping peaks, the resolution accuracy improved by 2.23%, and the mean square error is better than other four algorithms of the same type, showing the feasibility of ICSA in dealing with the overlapping peaks.

Preparation of many-body ground states by time evolution with variational microscopic magnetic fields and incomplete interactions

State preparation is of fundamental importance in quantum physics, which can be realized by constructing the quantum circuit as a unitary that transforms the initial state to the target, or implementing a quantum control protocol to evolve to the target state with a designed Hamiltonian. In this work, we study the latter on quantum many-body systems by the time evolution with fixed couplings and variational magnetic fields. In specific, we consider to prepare the ground states of the Hamiltonians containing certain interactions that are missing in the Hamiltonians for the time evolution. An optimization method is proposed to optimize the magnetic fields by "fine-graining" the discretization of time, in order to gain high precision and stability. The back propagation technique is utilized to obtain the gradients of the fields against the logarithmic fidelity. Our method is tested on preparing the ground state of Heisenberg chain with the time evolution by the XY and Ising interactions, and its performance surpasses two baseline methods that use local and global optimization strategies, respectively. Our work can be applied and generalized to other quantum models such as those defined on higher dimensional lattices. It enlightens to reduce the complexity of the required interactions for implementing quantum control or other tasks in quantum information and computation by means of optimizing the magnetic fields.

High-Performance Hybrid-Global-Deflated-Local Optimization with Applications to Active Learning.

Mathematical optimization lies at the core of many science and industry applications. One important issue with many current optimization strategies is a well-known trade-off between the number of function evaluations and the probability to find the global, or at least sufficiently high-quality local optima. In machine learning (ML), and by extension in active learning - for instance for autonomous experimentation - mathematical optimization is often used to find the underlying uncertain surrogate model from which subsequent decisions are made and therefore ML relies on high-quality optima to obtain the most accurate models. Active learning often has the added complexity of missing offline training data; therefore, the training has to be conducted during the data collection which can stall the acquisition if standard methods are used. In this work, we highlight recent efforts to create a high-performance hybrid optimization algorithm (HGDL), combining derivative-free global optimization strategies with local, derivative-based optimization, ultimately yielding an ordered list of unique local optima. Redundancies are avoided by deflating the objective function around earlier encountered optima. HGDL is designed to take full advantage of parallelism by having the most computationally expensive process, the local first and second-order-derivative-based optimizations, run in parallel on separate compute nodes in separate processes. In addition, the algorithm runs asynchronously; as soon as the first solution is found, it can be used while the algorithm continues to find more solutions. We apply the proposed optimization and training strategy to Gaussian-Process-driven stochastic function approximation and active learning.

Global optimization of a vapor compression refrigeration system with a self-adaptive differential evolution algorithm

This paper presents a global optimization strategy for the vapor compression refrigeration system (VCRS) based on self-adaptive differential evolution (SADE) algorithm to minimize the system energy consumption with the indoor cooling requirements fulfilled. The simplified hybrid VCRS model is established based on the thermodynamics and heat transfer theory, together with the parameter regression method, to predict the system performance and energy consumption under different working conditions. Then considering the interactions between components, the influences of varying indoor loads and outdoor air conditions, a global optimization problem with constraints is formulated. The SADE algorithm is used to solve the global optimization problem, and the optimal variables settings are obtained. Simulation results demonstrate that the proposed global optimization strategy can improve the VCRS energy efficiency in different time periods while satisfying the cooling demands. Averagely 15.57% energy saving on the typical testing day can be achieved. Moreover, significant energy savings can be obtained during the morning and evening periods with partial indoor cooling loads. Furthermore, to show the effectiveness of proposed SADE strategy, the DE and classical PSO algorithms are compared, and the results indicate that the SADE algorithm can significantly reduce the calculation time, and can avoid local minimum. This research brings a feasible methodology, to reduce the energy consumption of air conditioning systems effectively.

Hierarchical classification of data with long-tailed distributions via global and local granulation

Automated learning from datasets with a long-tailed distribution has gradually become a research hotspot due to the increasing complexity of large-scale real-world datasets. Existing solutions to long-tailed data classification usually involve re-balancing strategies for global optimization, which can achieve satisfactory results. However, re-balancing strategies tend to alter the original data. In this paper, we propose a knowledge granulation method based on global and local granulation to assist the hierarchical classification of long-tailed data without altering the original data. Firstly, a global classifier is constructed based on the WordNet knowledge organization’s hierarchical structure, which is used to granulate the global data from coarse to fine. Secondly, a local hierarchical classifier adapted to tail data is constructed for tail classes that contain few samples. The hierarchical structure of this local classifier is obtained by granulating the data via spectral clustering rather than by using the semantic hierarchy of classes. Finally, the global classifier is used to preliminarily classify samples, then uncertain samples are further classified by the tail local classifier. Experimental results show that the proposed method outperforms several state-of-the-art models designed for the hierarchical classification of long-tailed data.