High-quality Optimal Solutions Research Articles

Two efficient logarithmic formulations to solve nonconvex economic dispatch

To solve economic dispatch (ED) with nonconvex nonlinear generation cost functions, this paper adopts a global optimization technique where piecewise linear approximation (PLA) functions replace the nonlinear functions. However, a problem with this technique is that the PLA model requires incorporating many discrete variables into the optimization model, which may render the model computationally expensive. This paper presents two efficient representation techniques of the PLAs, which scale logarithmically, including binary zig-zag (ZZB) and general integer zig-zag (ZZI). We replace the nonconvex cost functions in the ED with their PLAs and obtain an alternative ED formulation where two logarithmic techniques model the PLAs. Then, one can efficiently solve the alternative ED model with the standard branch-and-cut/bound-based algorithms to the desired optimality gap. To verify the techniques’ efficacy, we consider test systems having 13, 38, 40, 80, and 160 units. The numerical evaluations show that the logarithmic techniques presented can yield high-quality optimal solutions in less than 2 seconds in the considered cases, illustrating the techniques’ efficiency.

Optimization of micro-perforated panel absorber backed with parallel-arranged cavities of different depths

Micro-perforated panel absorber (MPA) is one of the most effective materials in noise control. For the MPA backed with parallel-arranged cavities of different depths (PCD-MPA), the panel thickness, perforation diameter, perforation rate, and cavity depth are essential parameters for absorption performance. In this study, a Genetic Algorithm (GA)-based optimization design method for PCD-MPA is proposed to achieve specific performance objectives. Firstly, a prediction model for absorption performance of PCD-MPA is proposed. Secondly, a GA optimization method suitable for PCD-MPA is established, taking into account interactive parameters and generating multi-objective and high-quality optimal solutions through iterative adjustments. Finally, an acoustic standard sample was fabricated for experimental validation and compared with analytical results. The findings demonstrate that the proposed optimization method can achieve nearly perfect absorption with a well-selected combination of parameters that meet specific absorption requirements.

Integrated Energy Station Optimal Dispatching Using a Novel Many-Objective Optimization Algorithm Based on Multiple Update Strategies

Regarding the need to decrease carbon emissions, the electric vehicle (EV) industry is growing rapidly in China; the charging needs of EVs require the number of EV charging stations to grow significantly. Therefore, many refueling stations have been modified to integrated energy stations, which contain photovoltaic systems. The key issue in current times is to figure out how to operate these integrated energy stations in an efficient way. Therefore, an effective scheduling model is needed to operate an integrated energy station. Photovoltaic (PV) and energy storage systems are integrated into EV charging stations to transform them into integrated energy stations (PE-IES). Considering the demand for EV charging during different time periods, the PV output, the loss rate of energy storage systems, the load status of regional grids, and the dynamic electricity prices, a multi-objective optimization scheduling model was established for operating integrated energy stations that are connected to a regional grid. The model aims to simultaneously maximize the daily profits of the PE-IES, minimize the daily loss rate of the energy storage system, and minimize the peak-to-valley difference of the load in the regional grid. To validate the effectiveness of the model, simulation experiments under three different scenarios for the PE-IES were conducted in this research. Each object weight was determined using the entropy weight method, and the optimal solution was selected from the Pareto solution set using an order-preference technique according to the similarity to an ideal solution (TOPSIS). The results demonstrate that, compared to traditional charging stations, the daily revenue of the PE-IES stations increases by 26.61%, and the peak-to-valley difference of the power load in the regional grid decreases by 30.54%, respectively. The effectiveness of PE-IES is therefore demonstrated. Furthermore, to solve the complex optimization problem for PE-IES, a novel multi-objective optimization algorithm based on multiple update strategies (MOMUS) was proposed in this paper. To evaluate the performance of the MOMUS, a detailed comparison with seven other algorithms was demonstrated. These results indicate that our algorithm exhibits an outstanding performance in solving this optimization problem, and that it is capable of generating high-quality optimal solutions.

Optimizing Truss Structures Using Composite Materials under Natural Frequency Constraints with a New Hybrid Algorithm Based on Cuckoo Search and Stochastic Paint Optimizer (CSSPO)

This article highlights the absence of published paradigms hybridized by The Cuckoo Search (CS) and Stochastic Paint Optimizer (SPO) for optimizing truss structures using composite materials under natural frequency constraints. The article proposes a novel optimization algorithm called CSSPO for optimizing truss structures made of composite materials, known as fiber-reinforced polymer (FRP) composites, to address this gap. Optimization problems of truss structures under frequency constraints are recognized as challenging due to their non-linear and non-convex search spaces that contain numerous local optima. The proposed methodology produces high-quality optimal solutions with less computational effort than the original methods. The aim of this work is to compare the performance of carbon FRP (CFRP), glass FRP (GFRP), and steel using a novel hybrid algorithm to provide valuable insights and inform decision-making processes in material selection and design. Four benchmark structure trusses with natural frequency constraints were utilized to demonstrate the efficiency and robustness of the CSSPO. The numerical analysis findings indicate that the CSSPO outperforms the classical SPO and exhibits comparable or superior performance when compared to the SPO. The study highlights that implementing CFRP and GFRP composites in truss construction leads to a notable reduction in weight compared to using steel.

Transmission Expansion Planning Considering Wind Power and Load Uncertainties

Due to the rapidly increasing power demand worldwide, the development of power systems occupies a significant position in modern society. Furthermore, a high proportion of renewable energy resources (RESs) is an inevitable trend in further power system planning, due to traditional energy shortages and environmental pollution problems. However, as RESs are variable, intermittent, and uncontrollable, more challenges will be introduced in transmission expansion planning (TEP). Therefore, in order to guarantee the security and reliability of the power system, research related to TEP with the integration of RESs is of great significance. In this paper, to solve the TEP problem considering load and wind power uncertainties, an AC TEP model solved by a mixed integer non-linear programming (MINLP) is proposed, the high-quality optimal solutions of which demonstrate the accuracy and efficiency of the method. Latin hypercube sampling (LHS) is employed for the scenario generation, while a simultaneous backward reduction algorithm is applied for the scenario reduction, thus reducing the computational burden. Through this method, the reserved scenarios can effectively reflect the overall trends of the original distributions. Based on a novel worst-case scenario analysis method, the obtained optimal solutions are shown to be more robust and effective.

Multiobjective Optimal Power Flow Using Multiobjective Search Group Algorithm

This paper proposes a new multi-objective method that efficiently solves the multi-objective optimal power flow (MOOPF) problem in power systems. The objective of solving the MOOPF problem is to concurrently optimize the fuel cost, emissions, and active power loss. The proposed multi-objective search group algorithm (MOSGA) is an effective method that combines the merits of the original search group algorithm with fast nondominated sorting, crowding distance, and archive selection strategies to acquire a nondominated set in a single run. The MOSGA is employed on IEEE 30-bus and 57-bus systems to validate its robustness and efficiency. It was found that implementing MOSGA to solve the MOOPF significantly enhanced the performance of power systems in terms of economic, environmental, and technical benefits. As for Case 6, the fuel cost, emissions, and active power loss were reduced by 16.5707%, 52.0605%, and 60.9443%, respectively. The simulation results were analyzed and compared with those of previously reported studies based on the best individual solutions, compromise solutions, and performance indicators. The comparative results confirmed the potential and advantage of MOSGA when solving the MOOPF problem efficiently and MOSGA had high-quality optimal solutions.

Enhanced Atom Search Optimization Based Optimal Control Parameter Tunning of PMSG for MPPT

For the past few years, wind energy is the most popular non-traditional resource among renewable energy resources and it’s significant to make full use of wind energy to realize a high level of generating power. Moreover, diverse maximum power point tracking (MPPT) methods have been designed for varying speed operation of wind energy conversion system (WECS) applications to obtain optimal power extraction. Hence, a novel and meta-heuristic technique, named enhanced atom search optimization (EASO), is designed for a permanent magnet synchronous generator (PMSG) based WECS, which can be employed to track the maximum power point. One of the most promising benefits of this technique is powerful global search capability that leads to fast response and high-quality optimal solution. Besides, in contrast with other conventional meta-heuristic techniques, EASO is extremely not relying on the original solution, which can avoid sinking into a low-quality local maximum power point (LMPP) by realizing an appropriate trade-off between global exploration and local exploitation. At last, simulations employing two case studies through Matlab/Simulink validate the practicability and effectiveness of the proposed techniques for optimal proportional-integral-derivative (PID) control parameters tuning of PMSG based WECS under a variety of wind conditions.

Intelligent Reflecting Surface Enhanced Secure Transmission Against Both Jamming and Eavesdropping Attacks

Both the jammer and the eavesdropper pose severe threat to wireless communications due to the broadcast nature of wireless channels. In this paper, an intelligent reflecting surface (IRS) assisted secure communication system is considered, where a base station (BS) wishes to reliably convey information to a user, in the presence of both a jammer and an eavesdropper whose transmit informations are not completely known. Specifically, with the imperfect third-party node's channel state information (CSI) and no knowledge of the jammer's transmit beamforming, we aim to maximize the system achievable rate by jointly designing the BS's transmit beamforming and the IRS's reflect beamforming, while limiting the information leakage to the potential eavesdropper. Due to the non-convexity and intractability of the original problem induced by the incompleted information, we utilize the auxiliary variables, Cauchy-Schwarz inequality, and General Sign-Definiteness transformation to convert the original optimization problem into a tractable convex optimization problem, and then obtain the high-quality optimal solution by using the successive convex approximation and penalty convex concave procedure. Numerical simulations demonstrate the superiority of our proposed optimization algorithm compared with existing approaches, and also reveal the impact of key parameters on the achievable system performance.

An evolutionary symbiotic organisms search for multiconstraint truss optimization under free vibration and transient behavior

In this paper, an evolutionary symbiotic organisms search algorithm as a hybridization of differential evolution and symbiotic organisms search is developed for shape and size optimization of truss structures with free vibration and transient behavior under multiple constraints. For that aim, a mutation operator combined by two global differential evolution operators and a novel symbiotic organisms search operator is proposed to reinforce the exploration ability of the proposed algorithm. This newly suggested symbiotic organisms search operator is relied upon the symbiotic relationship in such a way that an arbitrary organism can receive benefits from both mutualisms and commensalisms. A threshold is automatically integrated into the mutation step to switch from the exploration capability to the exploitation one. In addition, an elitist scheme is applied to the selection phase to purify the most potential candidates for the next symbiotic ecosystem. Accordingly, the present algorithm can result in a high-quality optimal solution with a better convergence evolution. 26 mathematical functions and 7 well-known benchmark problems regarding size and shape truss optimization under multiple constraints are tested to verify the effectiveness of the proposed methodology. Obtained outcomes have indicated that the developed algorithm outperforms both original algorithms and many existing approaches in the literature. To further illustrate the ability of the proposed paradigm, two among the above five examples under transient excitations with strength, displacement, and buckling constraints are then optimized.

A novel hybrid differential evolution and symbiotic organisms search algorithm for size and shape optimization of truss structures under multiple frequency constraints

Although a large number of metaheuristic algorithms and their variants have been proposed for many engineering optimization problems, no paradigms hybridized by differential evolution (DE) and symbiotic organisms search (SOS) to concurrently improve the optimal solution quality and the convergence speed have been published thus far, especially for size and shape optimization of truss structures with multiple frequency constraints. Therefore, this article aims to propose a novel optimization algorithm as a cross-breed of the DE and the SOS, named HDS, for such problems. This algorithm can simultaneously and effectively enhance both global and local searching abilities by utilizing newly developed operators hybridized from the DE and SOS. An automatically adapted parameter is suggested for a better trade-off between those two capabilities. Furthermore, an elitist scheme is used in the selection phase to extract the best solutions for the next generation. As a consequence, the proposed methodology results in high-quality optimal solutions with a lower computational effort in comparison with two original methods, even many other optimization paradigms available in the literature. 26 benchmark mathematical functions are examined first. 5 numerical examples of shape and size optimization of truss structures are then investigated to validate the feasibility of the current paradigm.

A Hybrid Rao-NM Algorithm for Image Template Matching.

This paper proposes a hybrid Rao-Nelder–Mead (Rao-NM) algorithm for image template matching is proposed. The developed algorithm incorporates the Rao-1 algorithm and NM algorithm serially. Thus, the powerful global search capability of the Rao-1 algorithm and local search capability of NM algorithm is fully exploited. It can quickly and accurately search for the high-quality optimal solution on the basis of ensuring global convergence. The computing time is highly reduced, while the matching accuracy is significantly improved. Four commonly applied optimization problems and three image datasets are employed to assess the performance of the proposed method. Meanwhile, three commonly used algorithms, including generic Rao-1 algorithm, particle swarm optimization (PSO), genetic algorithm (GA), are considered as benchmarking algorithms. The experiment results demonstrate that the proposed method is effective and efficient in solving image matching problems.

Multi-objective power distribution optimization using NSGA-II

Power distribution is one of the major areas of electrical engineering. The issue of optimized power distribution is of great concern and here it is dealt with as a single- and multi-objective problem. We know that evolutionary algorithms have better efficiency in solving such problems. In this paper, we have applied heuristics non-dominated sorting genetic algorithm II (NSGA-II, multiple objective optimization algorithm) to optimize functions such as corona loss, efficiency, potential drop, resistive loss, and volume of the conductor. The NSGA-II has outperformed other algorithms involving the optimal solution. NSGA-II is not only simple in terms of programming but also achieves the desired high-quality optimal solutions in fewer iterations. After our experiment, we have optimized the various functions presented in this paper.

Automated process design and integration of precooling for energy-efficient BOG (boil-off gas) liquefaction processes

As awareness on air pollution in marine environment increases, transition of ship fuel to natural gas has been recognized as a practical solution for emission minimization. It is realized with LNG-fueled ship, whose implementation in practice demands cost-effective and energy-efficient re-liquefaction of BOG. The purpose of this study is to introduce precooling cycle to BOG re-liquefaction process to enhance energy efficiency and explore the most appropriate usage of pre-cooling refrigerants between CO2 and NH3. Three different configurations for precooling are compared, and operating conditions are optimized with an objective function to minimize energy consumption. Pre-screening based on sensitivity analysis, before optimization, is carried out to exclude any potential infeasible solution space. It allows robust optimization, leading to high quality optimal solution. Up to 7.9% reduction in overall energy consumption is achieved with the integration of precooling cycles, illustrated by high dependence on physical properties of saturated refrigerants. The modeling and optimization framework proposed in this study can serve as an effective application to the wide range of refrigeration systems subject to various refrigerants.

Reinforcement learning for optimum design of a plane frame under static loads

A new method is presented for optimum cross-sectional design of planar frame structures combining reinforcement learning (RL) and metaheuristics. The method starts from RL jointly using artificial neural network so that the action taker, or the agent, can choose a proper action on which members to be increased, reduced or kept their size. The size of the neural network is compressed into small numbers of inputs and outputs utilizing story-wise decomposition of the frame. The trained agent is used in the process of generating a neighborhood solution during optimization with simulated annealing (SA) and particle swarm optimization (PSO). Because the proposed method is able to explore the solution space efficiently, better optimal solutions can be found with less computational cost compared with those obtained solely by metaheuristics. Utilization of RL agent also leads to high-quality optimal solutions regardless of variation of parameters of SA and PSO or initial solution. Furthermore, once the agent is trained, it can be applied to optimization of other frames with different numbers of stories and spans.

Multi-Searcher Optimization for the Optimal Energy Dispatch of Combined Heat and Power-Thermal-Wind-Photovoltaic Systems

This paper proposes a novel multi-searcher optimization (MSO) algorithm for the optimal energy dispatch (OED) of combined heat and power-thermal-wind-photovoltaic systems. The available power of wind turbine (WT) units and photovoltaic (PV) units is approximated with the probability density functions of wind speed and solar irradiance, respectively. The chaos theory is used to implement a wide global search, which can effectively avoid a low-quality local optimum for OED. Besides, a double-layer searcher is designed to guarantee fast convergence to a high-quality optimal solution. Finally, three benchmark functions and an energy system with 27 units are used for testing the performance of the MSO compared with nine other frequently used heuristic algorithms. The simulation results demonstrate that the proposed technique not only can solve the highly nonlinear, non-smooth, and non-convex OED problem of an energy system, but can also achieve a superior performance for the convergence speed and the optimum quality.

Ensemble learning for optimal active power control of distributed energy resources and thermostatically controlled loads in an islanded microgrid

To achieve an effective coordination between the secondary control and the tertiary control of load frequency control (LFC), a new optimal active power control (OAPC) is constructed for real-timely changing the operating points of distributed energy resources (DERs) and thermostatically controlled loads (TCLs) in an islanded microgrid. A large number of TCLs are integrated as a load aggregator (LA) for participating the secondary control of LFC, which can enhance the dynamic response performance due to their much faster response speeds compared with that of distributed generators. Since OAPC is a nonsmooth and nonlinear optimization with a quite short implementation period, a novel model-free ensemble learning (EL) is proposed to rapidly obtain a high-quality optimal solution for it. EL based OAPC is composed of multiple sub-optimizers and a learning concentrator, where each sub-optimizer is responsible for providing the exploitation and exploration samples to the learning concentrator, while the reinforcement learning based concentrator is mainly used for knowledge learning and knowledge transfer. Case studies are thoroughly carried out to verify the performance of EL based OAPC in an islanded microgrid with 12 DERs and 900 TCLs.

Simultaneous optimization of nonsharp distillation sequences and heat integration networks by simulated annealing algorithm

Based on stochastic optimization, a new method is proposed to synthesize heat integrated distillation sequences (HIDiSs), which are basic configurations and allow nonsharp splits with at most two middle components. Distillation sequences and heat integration networks are simultaneously optimized to minimize the total annual cost (TAC) of HIDiSs. First, the synthesis problem is formulated as an implicit mixed-integer nonlinear programming problem. Discrete variables are distillation sequences. Continuous variables include operating pressures, key component recoveries and ratios of the actual reflux ratios to the minimum reflux ratios in columns. Next, solution strategies are presented, including representing distillation sequences through a novel encoding method, randomly generating neighboring distillation sequences, automatically determining heat integration networks by the pinch method, and calculating the TAC based on shortcut design of columns. Then, the optimization problem is solved by an improved simulated annealing algorithm. Finally, correctness verification for the method is made in two case studies. The optimization algorithm is proved to be computationally efficient and capable to obtain high-quality optimal solution. The results demonstrate that heat integration between columns significantly reduces the energy consumption compared to the non-integrated distillation sequences. Moreover, nonsharp HIDiSs can further reduce the TAC compared to those with only sharp splits.

TRUST-TECH-Enhanced Differential Evolution Methodology for Box-Constrained Nonlinear Optimization

The differential evolution algorithm and its variants have been developed to solve box-constrained optimisation problems with encouraging results. However, differential evolution still suffers from its poor ability to zoom in on promising regions to find a high-quality or global optimal solution. The transformation under stability-retraining equilibrium characterisation (TRUST-TECH) methodology is a systematical and deterministic method to find a set of multiple local optimal solutions. This paper presents a TRUST-TECH-enhanced differential evolution methodology (TT-DEM) to improve the performance of differential evolution method. In the TT-DEM framework, a differential evolution method is carried out to identify promising regions containing a set of high-quality solution or even the global optimal solution, while TRUST-TECH exploits the identified promising regions to compute those high-quality optimal solutions. Following this framework, the original differential evolution (DE) and three adaptive DEs are enhanced by TRUST-TECH. Numerical studies are conducted on several benchmark functions with promising results.

TRUST-TECH-enhanced differential evolution methodology for box-constrained nonlinear optimisation

The differential evolution algorithm and its variants have been developed to solve box-constrained optimisation problems with encouraging results. However, differential evolution still suffers from its poor ability to zoom in on promising regions to find a high-quality or global optimal solution. The transformation under stability-retraining equilibrium characterisation (TRUST-TECH) methodology is a systematical and deterministic method to find a set of multiple local optimal solutions. This paper presents a TRUST-TECH-enhanced differential evolution methodology (TT-DEM) to improve the performance of differential evolution method. In the TT-DEM framework, a differential evolution method is carried out to identify promising regions containing a set of high-quality solution or even the global optimal solution, while TRUST-TECH exploits the identified promising regions to compute those high-quality optimal solutions. Following this framework, the original differential evolution (DE) and three adaptive DEs are enhanced by TRUST-TECH. Numerical studies are conducted on several benchmark functions with promising results.

A Novel Consensus-Based Particle Swarm Optimization-Assisted Trust-Tech Methodology for Large-Scale Global Optimization.

A novel three-stage methodology, termed the "consensus-based particle swarm optimization (PSO)-assisted Trust-Tech methodology," to find global optimal solutions for nonlinear optimization problems is presented. It is composed of Trust-Tech methods, consensus-based PSO, and local optimization methods that are integrated to compute a set of high-quality local optimal solutions that can contain the global optimal solution. The proposed methodology compares very favorably with several recently developed PSO algorithms based on a set of small-dimension benchmark optimization problems and 20 large-dimension test functions from the CEC 2010 competition. The analytical basis for the proposed methodology is also provided. Experimental results demonstrate that the proposed methodology can rapidly obtain high-quality optimal solutions that can contain the global optimal solution. The scalability of the proposed methodology is promising.