Parallel Differential Evolution Research Articles

Integrated relief pre-positioning and procurement planning considering non-governmental organizations support and perishable relief items in a humanitarian supply chain network

The escalating frequency and severity of disasters on a global scale have sparked inquiries into the efficacy of current disaster planning strategies in various scenarios. Despite the pivotal role of humanitarian supply chain planning in aiding impacted populations, much of the existing research is grounded in simplistic assumptions that limit their practicality. Addressing this gap, our proposed bi-objective model aligns response time and total cost, while also accommodating the collaboration between non-governmental organizations and governmental organizations to mirror real-world intricacies. This study comprehensively delves into various logistics aspects, encompassing pre- and post-disaster phases, including location, allocation, supplier selection, fleet size, supply contract, inventory, distribution, and transportation. This multifaceted approach enhances the model's suitability for managing genuine real-world emergencies. To mitigate disruption risks and unforeseen events, the model introduces pre-positioning, quantity flexibility contract, backup suppliers, and a multi-sourcing policy, thus enhancing the resilience and reliability of the logistics network. We present solutions for diverse scenarios through a scaled weighted sum method, while tackling uncertainty via a heuristic approach known as the backward scenario reduction method. Furthermore, to manage large-scale problems within an acceptable time frame, we propose an advanced hybrid algorithm. This algorithm synergizes a parallel differential evolution framework with reinforcement learning-enhanced local search mechanisms, aiming to improve both computational efficiency and solution accuracy. Finally, we validate the model's applicability through a real case study focusing on a flood scenario in Iran.

Accelerating Asteroidal Period and Pole Inversion from Multiple Lightcurves Using Parallel Differential Evolution and Cellinoid Shape Model

Determining asteroid properties provides valuable physical insights but inverting them from photometric lightcurves remains computationally intensive. This paper presents a new approach that combines a simplified Cellinoid shape model with the Parallel Differential Evolution (PDE) algorithm to accelerate inversion. The PDE algorithm is more efficient than the Differential Evolution algorithm, achieving an extraordinary speedup of 37.983 with 64 workers on multicore CPUs. The PDE algorithm accurately derives period and pole values from simulated data. The analysis of real asteroid lightcurves validates the method’s reliability: in comparison with results published elsewhere, the PDE algorithm accurately recovers the rotational periods and, given adequate viewing geometries, closely matches the pole orientations. The PDE approach converges to solutions within 20,000 iterations and under one hour, demonstrating its potential for large-scale data analysis. This work provides a promising new tool for unveiling asteroid physical properties by overcoming key computational bottlenecks.

Parallel differential evolution paradigm for multilayer electromechanical device optimization

Design optimization of multilayer piezoelectric transducers is intended for efficient and practical usage of wideband transducers for fault diagnosis, biomedical, and underwater applications through adjusting layer thicknesses and volume fraction of piezoelectric material in each layer. In this context, we propose a parallel differential evolution (PDE) algorithm to mitigate the complexities of multivariate optimization as well as the computation time to achieve an optimized wideband transducer for the particular application. For lead magnesium niobate-lead titanate (PMN PT)- and PZT5h-based piezoelectric materials, the fitness function is formulated based on uniformity of mechanical pressure at the first three harmonics to achieve wide bandwidth in the required functional frequency range. It is carried out using a one-dimensional model (ODM), while input layer thicknesses and volume fractions of active material are evaluated using PDE. The simulation is performed on a parallel computing platform utilizing three different host machines to reduce computational time. Results of the proposed methodology for PDE are statistically represented in the form of minimum, maximum, mean, and standard deviation of fitness value, while graphically represented in terms of speedup and time. It can be observed that the execution time for parallel DE decreases with the increasing number of cores.

Optimization and simultaneous heat integration design of a coal-based ethylene glycol refining process by a parallel differential evolution algorithm

Optimization and simultaneous heat integration design of a coal-based ethylene glycol refining process by a parallel differential evolution algorithm

Model parameter identification for lithium-ion batteries using adaptive multi-context cooperatively co-evolutionary parallel differential evolution algorithm

Lithium-ion battery (LIB) has a polarization phenomenon during charging and discharging processes, and the internal chemistry of LIB is characterized by severe time-varying nonlinearity. Therefore, the equivalent circuit model (ECM) is usually used for LIB research. To address the problems of low identification accuracy and local optimization in the offline identification of battery parameters, this paper proposes a novel adaptive multi-context cooperatively co-evolutionary parallel differential evolution (AMCC-PDE) algorithm to identify parameters of LIB. Firstly, the data segment to be identified is divided into a plurality of segments according to the state of charge (SOC), and each segment is called a unit data segment (UDS). In addition, the UDS has a parameter group (PG) for the first-order RC model. Secondly, according to the differential equation of the first-order RC model, the PG (R0+,R0−, D1, R1, U1, init) of each UDS and the open-circuit voltage (UOCV) at each sampling point are considered as variables to be optimized. Then, such an optimization problem is transformed into a large-scale global optimization (LSGO) problem. In addition, to trade off the relationship between population diversity and convergence speed, a novel parallel mutation strategy is proposed. Finally, an AMCC-PDE algorithm is proposed to solve the above LSGO parameters identification model. In both of the DST and FUDS datasets, the identification error at each point obtained by AMCC-PDE is lower than 2 mV, which shows the effectiveness of AMCC-PDE and indicates that the algorithm can avoid destroying the variable-coupling relationship.

A parallel differential evolution with cooperative multi-search strategy for sizing truss optimization

The increasing complexity of modern structural design problems requires optimization algorithms to have an acceptable completion time regarding the huge number of design variables. This paper proposes a parallel differential evolution with cooperative multi-search strategies (PDECMS) and the implementation with Compute Unified Device Architecture (CUDA) for improving execution time by leveraging the Graphical Processing Unit (GPU). Three sub-populations with dedicated mutation schemes are used to establish island models, which start searching at distinct initial points. As the evolution process begins, the exchange of knowledge between islands is synchronously conducted via the migration of elite individuals. The PDECMS is used to solve five discrete sizing optimization problems of a truss structure to demonstrate the achieved solution quality, convergence speed, and scalability. It has been found that the computing time of PDECMS was at least two times faster than its serial implementation for the large population size and the attained solution quality was generally agreeable with other methods despite the sacrifice for the enhancement of performance. Numerical results reveal that the accomplishment of optimal solutions with fewer iterations and a shorter time comes from the cooperative multi-search strategy and the use of GPU. This outcome, therefore, shows that the PDECMS is capable of optimally solving multi-variable problems with a large search space.

Design and implementation of parallel self-adaptive differential evolution for global optimization

Abstract The results of evolutionary algorithms depend on population diversity that normally decreases by increasing the selection pressure from generation to generation. Usually, this can lead the evolution process to get stuck in local optima. This study is focused on mechanisms to avoid this undesired phenomenon by introducing parallel self-adapted differential evolution that decomposes a monolithic population into more variable-sized sub-populations and combining this with the characteristics of evolutionary multi-agent systems into a hybrid algorithm. The proposed hybrid algorithm operates with individuals having some characteristics of agents, e.g. they act autonomously by selecting actions, with which they affect the state of the environment. Additionally, this algorithm incorporates two additional mechanisms: ageing and adaptive population growth, which help the individuals by decision-making. The proposed parallel differential evolution was applied to the CEC’18 benchmark function suite, while the produced results were compared with some traditional stochastic nature-inspired population-based and state-of-the-art algorithms.

A local surrogate-based parallel optimization for analog circuits

Computationally expensive simulations make challenges for analog/RF circuit and electromagnetic device design automation, where efficiency is a key issue. Both surrogate-based optimization and parallel computing play an important role in addressing this challenge. However, most surrogate-based parallel optimizations use global surrogate models for the entire database or multiple local surrogate models for individuals. Under the condition of limited computing capability, multi-constraints and the curse of dimensionality creates great difficulty in building such accurate surrogate models for large-scale analog/RF circuits. In order to address this problem, a Local Surrogate-based Parallel Optimization (LSPO) for analog/RF circuits is proposed. The state-of-the-art surrogate model-aware evolutionary search (SMAS) framework is used as the foundation of LSPO. The combination of three differential evolution mutation strategies and its self-adaptive adoption mechanism helps SMAS search for the optimal design in a parallel computing environment. Through experiments on a two-stage operational amplifier, a biased-based two-stage operational amplifier, and three benchmark problems with different complexity, it is proved that the LSPO can give a comparative solution in a shorter time, and show better optimization ability than the parallel differential evolution algorithm and state-of-the-art surrogate-based optimization method.

Sliding Differential Evolution Scheduling for Federated Learning in Bandwidth-Limited Networks

Federated learning (FL) in a bandwidth-limited network with energy-limited user equipments (UEs) is under-explored. In this article, to jointly save energy consumed by the battery-limited UEs and accelerate the convergence of the global model in FL for the bandwidth-limited network, we propose the sliding differential evolution-based scheduling (SDES) policy. To this end, we first formulate an optimization that aims to minimize a weighted sum of energy consumption and model training convergence. Then, we apply the SDES with parallel differential evolution (DE) operations in several small-scale windows, to address the above proposed problem effectively. Compared with existing scheduling policies, the proposed SDES performs well in reducing energy consumption and the model convergence with lower computational complexity.

Efficient parallel surrogate optimization algorithm and framework with application to parameter calibration of computationally expensive three-dimensional hydrodynamic lake PDE models

Parameter calibration for computationally expensive environmental models (e.g., hydrodynamic models) is challenging because of limits on computing budget and on human time for analysis and because the optimization problem can have multiple local minima and no available derivatives. We present a new general-purpose parallel surrogate global optimization method Parallel Optimization with Dynamic coordinate search using Surrogates (PODS) that reduces the number of model simulations as well as the human time needed for proper calibration of these multimodal problems without derivatives. PODS outperforms state-of-art parallel surrogate algorithms and a heuristic method, Parallel Differential Evolution (P-DE), on all eight well-known test problems. We further apply PODS to the parameter calibration of two expensive (5 h per simulation), three-dimensional hydrodynamic models with the assistant of High-Performance Computing (HPC). Results indicate that PODS outperforms the popularly used P-DE algorithm in speed (about twice faster) and accuracy with 24 parallel processors.

Model calibration using a parallel differential evolution algorithm in computational neuroscience: Simulation of stretch induced nerve deficit

Neuronal damage, in the form of both brain and spinal cord injuries, is one of the major causes of disability and death in young adults worldwide. One way to assess the direct damage occurring after a mechanical insult is the simulation of the neuronal cells functional deficits following the mechanical event. In this study, we use a coupled electrophysiological-mechanical model with several free parameters that are required to be calibrated against experimental results. The calibration is carried out by means of an evolutionary algorithm (differential evolution, DE) that needs to evaluate each configuration of parameters on six different damage cases, each of them taking several minutes to compute. To minimise the simulation time of the parameter tuning for the DE, the stretch of one unique fixed-diameter axon with a simplified triggering process is used to speed up the calculations. The model is then leveraged for the parameter optimization of the more realistic bundle of independent axons, an impractical configuration to run on a single processor computer. To this end, we have developed a parallel implementation based on OpenMP that runs on a multi-processor taking advantage of all the available computational power. The parallel DE algorithm obtains good results, outperforming the best effort achieved by published manual calibration, in a fraction of the time. While not being able to fully capture the experimental results, the resulting nerve model provides a complex averaging framework for nerve damage simulation able to simulate gradual axonal functional alteration in a bundle.

Solution of Linear and Non-Linear Boundary Value Problems Using Population-Distributed Parallel Differential Evolution

Abstract Cases where the derivative of a boundary value problem does not exist or is constantly changing, traditional derivative can easily get stuck in the local optima or does not factually represent a constantly changing solution. Hence the need for evolutionary algorithms becomes evident. However, evolutionary algorithms are compute-intensive since they scan the entire solution space for an optimal solution. Larger populations and smaller step sizes allow for improved quality solution but results in an increase in the complexity of the optimization process. In this research a population-distributed implementation for differential evolution algorithm is presented for solving systems of 2 nd -order, 2-point boundary value problems (BVPs). In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraint boundary conditions and is then solved using differential evolution in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. Four benchmark BVPs are solved using the proposed parallel framework for differential evolution to observe the speedup in the execution time. Meanwhile, the statistical analysis is provided to discover the effect of parametric changes such as an increase in population individuals and nodes representing features on the quality and behavior of the solutions found by differential evolution. The numerical results demonstrate that the algorithm is quite accurate and efficient for solving 2 nd -order, 2-point BVPs.

Efficient global optimisation of microwave antennas based on a parallel surrogate model‐assisted evolutionary algorithm

Computational efficiency is a major challenge for evolutionary algorithm (EA)-based antenna optimisation methods due to the computationally expensive electromagnetic simulations. Surrogate model-assisted EAs considerably improve the optimisation efficiency, but most of them are sequential methods, which cannot benefit from parallel simulation of multiple candidate designs for further speed improvement. To address this problem, a new method, called parallel surrogate model-assisted hybrid differential evolution for antenna optimisation (PSADEA), is proposed. The performance of PSADEA is demonstrated by a dielectric resonator antenna, a Yagi-Uda antenna, and three mathematical benchmark problems. Experimental results show high operational performance in a few hours using a normal desktop 4-core workstation. Comparisons show that PSADEA possesses significant advantages in efficiency compared to a state-of-the-art surrogate model-assisted EA for antenna optimisation, the standard parallel differential evolution algorithm, and parallel particle swarm optimisation. In addition, PSADEA also shows stronger optimisation ability compared to the above reference methods for challenging design cases.

Using synchronous and asynchronous parallel Differential Evolution for calibrating a second-order traffic flow model

Given the importance of the credibility and validity required by macroscopic traffic flow models in performing real-word simulations, the necessity of including an accurate, computationally fast, and reliable constrained optimization scheme appears to be mandatory to ensure that the traffic flow characteristics are accurately represented by such models. To this end, a parallel, synchronous or asynchronous, metamodel-assisted Differential Evolution (DE) algorithm is employed for the calibration of a second-order macroscopic gas-kinetic traffic flow (GKT) model using real traffic data from Attiki Odos freeway in Athens, Greece. Two Artificial Neural Networks, a Multi-layer Perceptron and a Radial Basis Function network, are used as surrogate models to decrease the computation time of the evaluation phase of the DE optimizer. The parallelization of the DE algorithm is performed using the Message Passing Interface (MPI). Numerical simulations are performed, which demonstrate that the DE algorithm can be effectively used for the search of the global optimal model parameters in the GKT model, while appears to be a promising method for the calibration of other similar traffic models.

Research on joint generation scheduling of cascade hydro plants in the dry season

Abstract As more and more reservoirs are built, concentrated water releasing in the dry season will bring about additional flow compensation and the joint operation of cascade hydro plants is quite important. This paper discusses the water level decline strategy of four cascade hydro plants in the Jinsha River and analyses the relationship between guaranteed output and total power generation. Considering stochastic inflows, an implicit stochastic optimization method is employed and a multi-objective parallel differential evolution algorithm is proposed to extract dispatching rules. Finally, a method which combines discriminant method and dispatching rules is proposed for practical operations and achieves good performance. Compared with routine scheduling, the power generations of the proposed method are improved observably in different typical years. The average power generation increases about 3% with the same cascade minimum output.

Glass-like energy and property landscape of Pt nanoclusters

Pt nanoclusters play an important role in catalysis-related applications. Essential to their activities are their geometries and energy landscapes. In this work, we studied the energy landscapes of Pt clusters using a parallel differential evolution optimization algorithm and an accelerated ab initio atomic relaxation method, which allowed us to explore unprecedentedly large numbers of geometry local minima at ab initio level. We found many lower-energy isomers with low symmetry in their geometry. The energy landscapes were demonstrated to be glass-like with a large number of local minimum structures close to the global minimum. The electronic and magnetic properties of most glass-like local minima were dramatically different from the global minimum, and they should be observed in the experimental measurements. The connections between these local minima were further analyzed using data mining techniques.

A small-population based parallel differential evolution algorithm for short-term hydrothermal scheduling problem considering power flow constraints

Short-term optimal hydrothermal scheduling plays one of the most important roles in the modern power system plan and operation. The problem aims at minimizing the total fuel cost of the thermal units while satisfying various constraints such as power balance, water balance and other constraints on thermal units as well as hydro units. Except for the above various constraints, transmission network topology and valve point effects are also introduced into the mathematical optimizing model of the short-term hydrothermal scheduling (STHS) problem. Then a small-population based parallel differential evolution approach is proposed to solve the STHS problem considering power flow constraints. In the proposed approach, a large population is divided into several subpopulations each with a small population size and several parallel running processes of one or more CPUs are performed synchronously each evolving a certain subpopulation and searching for the optimal solution independently. Two different methods are employed in the proposed parallel DE approach in order to avoid low diversity of the small population in each process. One is implemented through the small population itself and the other through the communication mechanism among different running processes. Four constraint handling rules as well as a lead operation are proposed to enhance the feasibility of solutions. Numerical results for two well-known sample test systems are presented to demonstrate the capabilities of the proposed parallel DE algorithm to generate optimal solutions of STHS problem. Two other test systems with transmission networks of standard IEEE 9-bus and IEEE 39-bus are also employed to test the effectiveness of the proposed parallel DE algorithm. The results demonstrate the superiority of the proposed algorithm.

Real-Time Energy-Saving Optimization for Multiple Trains Based on Multiagent Cooperative Control

Nowadays, the energy-saving optimization problem has gradually become a hot spot in the subject of high-speed train control. Traditional static train trajectory planning is designed offline according to a preplanned timetable, but ignored are the uncertainties of parameters because of line conditions and other factors in the process of operation. Thus, the previous operation strategy may not suit the remaining section. The cooperative control strategy for multiple trains was investigated with the aim of conserving energy between successive stations under the constraints of safety and punctuality. First, combined with the train operation strategy under the quasi-moving block system of the Chinese Train Control System, a train cooperative interaction mechanism based on multiagent input is proposed to obtain the real-time running characteristics of trains on the railway via the Radio Block Center (RBC) agent. In the case of unanticipated events of railway line conditions, train operation is often out of accord with the timetable. Therefore, a resilience set related to trip-time deviation and headway variation is introduced to evaluate the robustness of the railway system and achieve balance in the train group. Also, a multigroup parallel differential evolution algorithm is developed to solve the online optimization problem of a high-speed train group according to real-time information. The proposed approach is analyzed by using operational data from the Wuhan–Changsha highspeed railway line in China to assess energy savings and punctuality. Results of the case study show superior performance and effectiveness of the model, and the methodology is illustrated.

Verification of Dependability on Parallel Differential Evolution Based Voltage and Reactive Power Control

Abstract: This paper evaluates dependability on parallel differential evolution (DE) based voltage and reactive power control (Volt/Var Control: VVC) Considering large penetration of renewable energies and deregulated environment of power systems VVC requires fast computation even for larger-scale problems One solutions to increase the computation speed is to use parallel and distributed computing. Since power system is one of the infrastructures of social community, not only fast computation, but also sustainable control (dependability) is strongly required for VVC. The simulation results with IEEE 14, 30, 57, and 118 bus systems indicate that parallel DE is superior to parallel Particle Swarm Optimization (PSO) especially for dependability on VVC.

Enhanced parallel Differential Evolution algorithm for problems in computational systems biology

Many key problems in computational systems biology and bioinformatics can be formulated and solved using a global optimization framework. The complexity of the underlying mathematical models require the use of efficient solvers in order to obtain satisfactory results in reasonable computation times. Metaheuristics are gaining recognition in this context, with Differential Evolution (DE) as one of the most popular methods. However, for most realistic applications, like those considering parameter estimation in dynamic models, DE still requires excessive computation times.Here we consider this latter class of problems and present several enhancements to DE based on the introduction of additional algorithmic steps and the exploitation of parallelism. In particular, we propose an asynchronous parallel implementation of DE which has been extended with improved heuristics to exploit the specific structure of parameter estimation problems in computational systems biology. The proposed method is evaluated with different types of benchmarks problems: (i) black-box global optimization problems and (ii) calibration of non-linear dynamic models of biological systems, obtaining excellent results both in terms of quality of the solution and regarding speedup and scalability.