Quality Of Optimal Solution Research Articles

Performance analysis of meta-heuristic optimization techniques for multi-objective VLSI circuit partitioning

Abstract The efficiency of various stages of physical design in the Very Large Scale Integration (VLSI) circuit can be enhanced by using multi-objective optimization techniques. The circuit is partitioned into a set of modules at the beginning of the physical design phase. This step is known as circuit partitioning. All subsequent physical design stages, like floor planning, placement, pin configuration, and routing etc, are influenced by the outcome of the circuit partitioning method being used. The efficiency of the partitioning method controls the quality of ultimate architecture. The efficiency achieved by the final product may be decreased by incorrect partitioning. This study compares the effectiveness of four Meta-heuristic optimization methods include the Genetic Algorithm (GA), Satin Bowered Bird (SBO), Particle Swarm Optimization (PSO), Simulated Annealing (SA) — in terms of number of net cut, duration of sleeping mode, and efficiency in power consumption for addressing the VLSI circuit partitioning problem. This experiment achieves K-way partitioning of the circuit that minimizes net cuts as well as maximizes sleep duration simultaneously, by evaluating optimization function. Solutions developed using GA, SBO and PSO consistently surpass those acquired using SA with respect to quality of optimal solution. The average optimum net cut and sleep duration achieved by this experiment are 10.7 and 9.9 in GA ; 11.5 and 12.3 in SBO, 11.80 and 9.10 in PSO; and 16.8 and 6.7 in SA based method respectively. This research resulted in a considerable reduction in power consumption, with the system’s average power efficiency achieved by 21.6%, 26.84%, 19.85%, and 14.62%, respectively, in GA, SBO , PSO, and SA based optimizations. The experimental results are compared with a recent publication and proposed GA, SBO, and PSO based methods achieve 18.75%, 4.17%, and 1.04% improvement in terms of average net cut respectively. The proposed GA, SBO, PSO and SA based methods also achieve 44.90%, 51.30%, 40.05%, and 18.60% improvement in terms of average power efficiency.

Optimizing the Fixed Number Detector Placement for the Nuclear Reactor Core Using Reinforcement Learning

Monitoring three-dimensional flux distribution in a nuclear reactor core is essential for improving safety and economics, which requires strategically placed in-core detectors. However, the deployment of these sensors is often constrained by physical, industrial, and economic limitations. This study treats optimizing the location of in-core detectors as a Markov decision process and develops a reinforcement learning (RL)–based framework to provide a solution for detector placement given a fixed number of detectors and available detector positions. The RL-based framework contains an environment consisting of a Proper Orthogonal Decomposition–based power reconstruction function paired with a novel reward function based on the power reconstruction error and a well-educated agent that updates the detector placement. Four RL algorithms including Proximal Policy Optimization, Deep Q-Network, Advantage Actor-Critic, and Monte Carlo Tree Search are investigated to optimize the detector placement and are analyzed. Genetic Algorithm (GA), a traditional optimization approach, is applied for comparison. The findings reveal that RL outperforms GA in terms of the quality of optimal solutions, demonstrating an inclination toward locating a global solution. Moreover, the flexible nature of RL enables the integration of developed novel reward functions from a specific reactor core into other reactors, considering the particular engineering requirements within the RL-based framework, thereby enhancing the optimization of in-core detector configurations.

NISQ-Ready Community Detection Based on Separation-Node Identification

The analysis of network structure is essential to many scientific areas ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO-based approach that only needs number-of-nodes qubits and is represented by a QUBO matrix as sparse as the input graph’s adjacency matrix. The substantial improvement in the sparsity of the QUBO matrix, which is typically very dense in related work, is achieved through the novel concept of separation nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which, upon its removal from the graph, yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept by achieving an up to 95% optimal solution quality on three established real-world benchmark datasets. This work hence displays a promising approach to NISQ-ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large-scale, real-world problem instances.

Variable neighborhood search for weighted total domination problem and its application in social network information spreading

The weighted total domination problem (WTDP) is a practical extension of the well-known total domination problem. The most efficient literature approaches to tackle this problem are based on branch and cut or genetic algorithm. In this work, we propose a different strategy to solve WTDP that relies on the popular variable neighborhood search (VNS) metaheuristic. VNS is equipped with a carefully designed fitness function that allows for evaluation of both feasible and infeasible solutions, which further allows for a thorough search of the promising regions of the solution space. The method also utilizes two effective first-improvement local search procedures. The effectiveness of VNS is demonstrated on a wide range of benchmark sets compared to all three competing methods from the literature. For small-to-middle-sized instances (up to 100 nodes), VNS can obtain solutions that match the quality of optimal solutions in almost all cases (134 out of 135). For middle-to-large-sized instances, VNS can outperform all comparison algorithms in terms of solution quality, which is verified by statistical hypothesis tests. Another key aspect of this paper is presenting a potential application of the WTDP for boosting information spreading across social networks. Experiments confirmed that information spreading is accelerated when informed nodes (spreaders) are set to be solutions of the WTDP obtained by VNS. Although our method has been successfully applied to samples of real social networks of up to approximately 81 thousand nodes and 1.34 million edges, further research might enhance the method to be used on various (unsampled) social network datasets.

Intelligent vehicle pedestrian light (IVPL): A deep reinforcement learning approach for traffic signal control

Deep reinforcement learning (RL) has been widely studied in traffic signal control. Despite the promising results that indicate the superiority of deep RL in terms of the quality of solution and optimality over fixed time signal control, the real-world multi-modal traffic flows, especially pedestrians, are not properly considered nor sufficiently investigated. This study presents a novel deep RL-based adaptive traffic signal model to control the vehicles and pedestrian flows by allocating an equitable green time to each, aiming at minimizing “total user delays” as opposed to “total vehicle delays” dominantly being used in the literature. Our proposed intelligent vehicle pedestrian light (IVPL) method can perform in the absence or presence of pedestrians, especially when there is jaywalking at the intersection, interrupting vehicle flows. To this end, an extended reward function is designed to capture delays due to vehicle-to-vehicle, vehicle-to-pedestrian, and pedestrian-to-pedestrian interactions, as well as red-light delays for vehicles and pedestrians. To evaluate the performance of IVPL, a microsimulation model of an intersection in city of Melbourne is used as a case-study. The real traffic signal parameters of an existing operation system (SCATS) are employed, and the simulation is calibrated using video-based camera data and loop detectors data collected at intersection. The experimental results demonstrate the superiority of the proposed model over fully actuated traffic signal, not only in terms of the quality of optimal solution, but also considering the fact that the proposed model can minimize the “total user delays”.

Coalition Structure Generation in Edge Computing Environment With Multitasking Concurrency

Edge computing (EC) is a distributed computing paradigm that brings computation and data storage closer to the data sources. With the rapid development of EC, offloading scientific computing and data processing tasks from end devices to edge nodes (ENs) can satisfy these tasks’ requirements. However, a single EN with limited computing capacity is usually insufficient to handle these tasks. Hence, using a coalition structure (CS) of many ENs to handle multiple concurrent tasks in an EC environment becomes a feasible scheme. Still, many existing methods cannot be used directly in this scenario because of enormous CS solution space, low search speed, long-running time, poor optimal solution quality, etc. In response, we propose an arbitrary discrete political optimizer (ADPO) algorithm with a discrete recent-past position updating strategy to explore the potential CS space. Unlike other heuristic algorithms, ADPO further improves the better solutions by interacting with each other in the parliamentary affairs phase. After that, we formulate an integer programming (IP) optimization model to alleviate the low search speed or long time consuming. Finally, extensive experiments demonstrate that ADPO is superior to the existing heuristic algorithm. In addition, the IP model excels in exiting algorithms at the running time (milliseconds level) and resource occupied ratio.

Multi-objective intelligent algorithm model design for housing environment optimization

With the improvement of the national living standard, the buyers have higher and higher requirements for the rationality and aesthetics of the spatial planning and layout of the residential area. The traditional residential space planning method is purely manual design, which is inefficient, and the design effect will be greatly affected by the designer’s work experience and personal aesthetics. Therefore, this research attempts to combine Pareto solution set and piecewise prediction idea into genetic algorithm, propose an algorithm for solving multi-objective optimization problems, and build an intelligent housing environment planning system based on this. The statistical results of simulation experiments show that the system can output more design schemes with better overall quality than the comparison system and manual planning results, and the stability of multiple operations is higher. When the number of iterations reaches 200, the average value of Pareto optimal solution number and optimal solution quality index QPS of the former is 44 and 0.41, respectively. The expert group analyzed the design results of this method and the manual method for an actual case, and found that the results designed by this method met the requirements and the calculation efficiency was much faster than manual processing. From the simulation test data and the actual case analysis, it can be seen that the intelligent housing environment planning system designed in this study is helpful to improve the efficiency of residential space design and the stability of residential space scheme style.

Elite levy spreading differential evolution via ABC shrink-wrap for multi-threshold segmentation of breast cancer images

Differential Evolution (DE) is a commonly used metaheuristic algorithm in different optimization scenarios. However, the original DE suffers from stagnation and premature convergence in solving complex problems. In this study, an Artificial Bee Colony (ABC)-inspired Shrink-wrap (SW) strategy is proposed by combining the idea of a restart operator in ABC. Furthermore, an Elite Levy Spreading (ELS) strategy is proposed, inspired by the ideas of dimensional variation in cuckoo search and linear reduction of the number of flames in the moth-flame optimization. Based on these two strategies, an Enhanced DE (EDE) is proposed, where the ABC-inspired SW strategy is used to enhance the global exploration capability, and the ELS strategy is dedicated to improving the optimal solution quality even further. Based on CEC 2017 test, scalability experiments were conducted on EDE, and performance was compared with state-of-the-art and champion algorithms. The results were analyzed using the Wilcoxon signed rank, Friedman test, and post-hoc statistical tests. Finally, Image Segmentation experiments were performed with some peers on nine breast cancer images to validate the performance of EDE. The above experimental results show that EDE performs satisfactorily in optimization cases and multi-threshold segmentation of breast cancer images.

Research on Global Ship Path Planning Method Based on Improved Ant Colony Algorithm

To solve the global path planning problem of the ship in the static and dynamic environment, we propose an improved ant colony algorithm to plan the ship’s navigation path. We use the artificial potential field method to compute the force direction of the ship at the initial iteration stage. The attraction potential field function is modified to improve the iteration efficiency of the hybrid ant colony algorithm. We design the pseudo-random state transition rule and improve the convergence of the hybrid algorithm by strengthening the selection of good paths. When updating the pheromone, we consider the path’s length, safety, and smoothness to plan a safer navigation path. The simulation results show that the improved ant colony algorithm has a faster convergence speed than the original ant colony algorithm. The optimal solution quality is higher, which can realize global ship path planning in static and dynamic environments.

Multi-Fidelity Surrogate-Based Process Mapping with Uncertainty Quantification in Laser Directed Energy Deposition.

A multi-fidelity (MF) surrogate involving Gaussian processes (GPs) is used for designing temporal process maps in laser directed energy deposition (L-DED) additive manufacturing (AM). Process maps are used to establish relationships between the melt pool properties (e.g., melt pool depth) and process parameters (e.g., laser power and scan velocity). The MFGP surrogate involves a high-fidelity (HF) and a low-fidelity (LF) model. The Autodesk Netfabb finite element model (FEM) is selected as the HF model, while an analytical model developed by Eagar-Tsai is chosen as the LF one. The results show that the MFGP surrogate is capable of successfully blending the information present in different fidelity models for designing the temporal forward process maps (e.g., given a set of process parameters for which the true depth is not known, what would be the melt pool depth?). To expand the newly-developed formulation for establishing the temporal inverse process maps (e.g., to achieve the desired melt pool depth for which the true process parameters are not known, what would be the optimal prediction of the process parameters as a function of time?), a case study is performed by coupling the MFGP surrogate with Bayesian Optimization (BO) under computational budget constraints. The results demonstrate that MFGP-BO can significantly improve the optimization solution quality compared to the single-fidelity (SF) GP-BO, along with incurring a lower computational budget. As opposed to the existing methods that are limited to developing steady-state forward process maps, the current work successfully demonstrates the realization of temporal forward and inverse process maps in L-DED incorporating uncertainty quantification (UQ).

A direct collocation framework for optimal control simulation of pedaling using OpenSim.

The direct collocation (DC) method has shown low computational costs in solving optimization problems in human movements, but it has rarely been used for solving optimal control pedaling problems. Thus, the aim of this study was to develop a DC framework for optimal control simulation of human pedaling within the OpenSim modeling environment. A planar bicycle-rider model was developed in OpenSim. The DC method was formulated in MATLAB to solve an optimal control pedaling problem using a data tracking approach. Using the developed DC framework, the optimal control pedaling problem was successfully solved in 24 minutes to ten hours with different objective function weightings and number of nodes from two different initial conditions. The optimal solutions for equal objective function weightings were successful in terms of tracking, with the model simulated pedal angles and pedal forces within ±1 standard deviation of the experimental data. With these weightings, muscle tendon unit (MTU) excitation patterns generally matched with burst timings and shapes observed in the experimental EMG data. Tracking quality and MTU excitation patterns were changed little by selection of node density above 31, and the optimal solution quality was not affected by initial guess used. The proposed DC framework could easily be turned into a predictive simulation with other objective functions such as fastest pedaling rate. This flexible and computationally efficient framework should facilitate the use of optimal control methods to study the biomechanics, energetics, and control of human pedaling.

Horizontal and vertical search artificial bee colony for image segmentation of COVID-19 X-ray images

The artificial bee colony algorithm (ABC) has been successfully applied to various optimization problems, but the algorithm still suffers from slow convergence and poor quality of optimal solutions in the optimization process. Therefore, in this paper, an improved ABC (CCABC) based on a horizontal search mechanism and a vertical search mechanism is proposed to improve the algorithm's performance. In addition, this paper also presents a multilevel thresholding image segmentation (MTIS) method based on CCABC to enhance the effectiveness of the multilevel thresholding image segmentation method. To verify the performance of the proposed CCABC algorithm and the performance of the improved image segmentation method. First, this paper demonstrates the performance of the CCABC algorithm itself by comparing CCABC with 15 algorithms of the same type using 30 benchmark functions. Then, this paper uses the improved multi-threshold segmentation method for the segmentation of COVID-19 X-ray images and compares it with other similar plans in detail. Finally, this paper confirms that the incorporation of CCABC in MTIS is very effective by analyzing appropriate evaluation criteria and affirms that the new MTIS method has a strong segmentation performance.

Wireless Sensor Network Node Localization Algorithm Based on PSO-MA

Aiming at the large error and low accuracy of wireless sensor node location, this paper proposes a node location method based on the fusion of Particle Swarm Optimization and Monkey Algorithm (PSO-MA). Firstly, this article describes the node location model based on DV-HOP algorithm; secondly, this article uses PSO in node location, uses place Laplace distribution for population initialization, improves population diversity, and optimizes particle weights to avoid algorithm falling into local optimality. In this paper, dynamic guidance factors are used to update individual positions to improve individual optimization capabilities, and Monkey Algorithm is used to select individuals to improve the quality of optimal solutions. In the simulation experiment, the algorithm PSO and MA of this paper are compared to achieve better positioning results in the reference node ratio, node density and communication radius indicators.

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.

Hybrid Differential Evolution Algorithm and Adaptive Large Neighborhood Search to Solve Parallel Machine Scheduling to Minimize Energy Consumption in Consideration of Machine-Load Balance Problems

Environmental and economic considerations create a challenge for manufacturers. The main priorities for production planning in environmentally friendly manufacturing industries are reducing energy consumption and improving productivity by balancing machine load. This paper focuses on parallel machine scheduling to minimize energy consumption (PMS_ENER), which is an indicator of environmental sustainability when considering machine-load balance problems. A mathematical model was formulated to solve the proposed problem and tested using a set of problem groups. The findings indicated that the mathematical model could find an optimal solution within a limited calculation time for small problems. For medium and large problems, the mathematical model could also find the optimal solution within a limited calculation time, but worse than all metaheuristics. However, finding an optimal solution for a larger problem is time-consuming. Thus, a novel method, a hybrid differential evolution algorithm with adaptive large neighborhood search (HyDE-ALNS), is presented to solve large-scale PMS_ENER. The new mutation and recombination formula for the differential evolution (DE) algorithm proposed in this article obtained promising results. By using the HyDE-ALNS, we improved the solution quality by 0.22%, 7.21%, and 12.01% compared with a modified DE (MDE-3) for small, medium, and large problems respectively. In addition, five new removal methods were designed to implement in ALNS and achieve optimal solution quality.

Multifidelity Genetic Transfer: An Efficient Framework for Production Optimization

Summary Production optimization led by computing intelligence can greatly improve oilfield economic effectiveness. However, it is confronted with huge computational challenge because of the expensive black-box objective function and the high-dimensional design variables. Many low-fidelity methods based on simplified physical models or data-driven models have been proposed to reduce evaluation costs. These methods can approximate the global fitness landscape to a certain extent, but it is difficult to ensure accuracy and correlation in local areas. Multifidelity methods have been proposed to balance the advantages of the two, but most of the current methods rely on complex computational models. Through a simple but efficient shortcut, our work aims to establish a novel production-optimization framework using genetic transfer learning to accelerate convergence and improve the quality of optimal solution using results from different fidelities. Net present value (NPV) is a widely used standard to comprehensively evaluate the economic value of a strategy in production optimization. On the basis of NPV, we first established a multifidelity optimization model that can synthesize the reference information from high-fidelity tasks and the approximate results from low-fidelity tasks. Then, we introduce the concept of relative fidelity as an indicator for quantifying the dynamic reliability of low-fidelity methods, and further propose a two-mode multifidelity genetic transfer learning framework that balances computing resources for tasks with different fidelity levels. The multitasking mode takes the elite solution as the transfer medium and forms a closed-loop feedback system through the information exchange between low- and high-fidelity tasks in parallel. Sequential transfer mode, a one-way algorithm, transfers the elite solutions archived in the previous mode as the population to high-fidelity domain for further optimization. This framework is suitable for population-based optimization algorithms with variable search direction and step size. The core work of this paper is to realize the framework by means of differential evolution (DE), for which we propose the multifidelity transfer differential evolution (MTDE). Corresponding to multitasking and sequential transfer in the framework, MTDE includes two modes, transfer based on base vector (b-transfer) and transfer based on population (p-transfer). The b-transfer mode incorporates the unique advantages of DE into fidelity switching, whereas the p-transfer mode adaptively conducts population for further high-fidelity local search. Finally, the production-optimization performance of MTDE is validated with the egg model and two real field cases, in which the black-oil and streamline models are used to obtain high- and low-fidelity results, respectively. We also compared the convergence curves and optimization results with the single-fidelity method and the greedy multifidelity method. The results show that the proposed algorithm has a faster convergence rate and a higher-quality well-control strategy. The adaptive capacity of p-transfer is also demonstrated in three distinct cases. At the end of the paper, we discuss the generalization potential of the proposed framework.

Route Design Model of Multiple Feeder Bus Service Based on Existing Bus Lines

The feeder bus, as an important component of urban public transportation systems, is capable of filling the existing service gap left by urban rail transit to satisfy feeder demand. Two challenges to taking advantage of the feeder bus are identified. The first challenge is to identify the service gap, and the second one is to strengthen the coordination of multilevel urban traffic modes. Given these two challenges, this paper established a route design model that introduced a feeder bus demand coefficient to quantify feeder demand for each bus stop. To assist the design of feeder bus routes, an optimization approach based on the tabu search algorithm was proposed. Considering the sizeable combinational optimization problem, the algorithm decomposed this problem into three phases: feeder area partition, candidate stop selection, and route design problem. In the first phase, the entire area was partitioned into several subareas and the specific boundary nodes were moved into an adjacent subarea. Then, the stops with the minimum overall travel cost from every subarea were chosen as candidate ones under the limit of operating costs. The last step was to find the shortest circular route to visit each candidate stop and determine the operating direction. The proposed optimization had been implemented in a downtown area of Suzhou, China, in order to verify its effectiveness through the performance in terms of the quality of optimal solutions and computing efficiency. In addition, a possibility of simplifying a multiple circular route design problem to a single route design problem utilizing spatial clustering is provided to enhance the computing efficiency in a large-scale network.

Optimization of electric distribution network configuration for power loss reduction based on enhanced binary cuckoo search algorithm

This paper presents a new network reconfiguration (NR) method using enhanced binary cuckoo search algorithm (EBCSA) to reduce power loss in the distribution system. Enhanced binary cuckoo search algorithm (EBCSA) is developed by transferring the continuous cuckoo search algorithm (CSA) to the binary domain and adding a new local search mechanism. Calculation results on different test systems demonstrate that EBCSA has capability for searching the optimal network configuration with greater success rate, better optimal solution quality and smaller number of average convergence iterations than those of binary CSA, binary coyote optimization algorithm, binary genetic algorithm and binary particle swarm optimization. Furthermore, the effect of the transfer function transferring from continuous domain to binary domain and the value of the parameters of EBCSA for the NR problem are also evaluated to choose the suitable values. The results show that EBCSA is a tool worth considering for the NR problem.

Hybridizing salp swarm algorithm with particle swarm optimization algorithm for recent optimization functions

The salp swarm algorithm (SSA) has shown its fast search speed in several challenging problems. Research shows that not every nature-inspired approach is suitable for all applications and functions. Additionally, it does not provide the best exploration and exploitation for each function during the search process. Therefore, there were several researches attempts to improve the exploration and exploitation of the meta-heuristics by developing the newly hybrid approaches. This inspired our current research and therefore, we developed a newly hybrid approach called hybrid salp swarm algorithm with particle swarm optimization for searching the superior quality of optimal solutions of the standard and engineering functions. The hybrid variant integrates the advantages of SSA and PSO to eliminate many disadvantages such as the trapping in local optima and the unbalanced exploitation. We have used the velocity phase of the PSO approach in salp swarm approach in order to avoid the premature convergence of the optimal solutions in the search space, escape from ignoring in local minima and improve the exploitation tendencies. The new approach has been verified on different dimensions of the given functions. Additionally, the proposed technique has been compared with a wide range of algorithms in order to confirm its efficiency in solving standard CEC 2005, CEC 2017 test suits and engineering problems. The simulation results show that the proposed hybrid approach provides competitive, often superior results as compared to other existing algorithms in the research community.

Parallel Gradient-Based EM Optimization for Microwave Components Using Adjoint- Sensitivity-Based Neuro-Transfer Function Surrogate

This article proposes a novel parallel gradient-based electromagnetic (EM) optimization approach to microwave components using adjoint-sensitivity-based neuro-transfer function (neuro-TF) surrogate. In the proposed technique, the surrogate model is trained using not only the input-output behavior but also the adjoint sensitivity information generated from the EM simulation simultaneously. By exploiting adjoint EM sensitivity for surrogate modeling, the proposed technique can obtain accurate surrogate models with larger valid range using the same amount of fine model evaluations compared with the existing gradient-based surrogate optimization without adjoint sensitivity. Furthermore, because the surrogate model is developed using adjoint EM sensitivity, the gradients calculated using the developed surrogate model in the proposed technique are much more accurate. The accurate gradients lead to further speedup of the surrogate optimization and improved quality of surrogate optimal solution in each surrogate optimization iteration. Since the surrogate model is valid in a large neighborhood and the gradients are sufficiently accurate, the proposed technique can achieve the optimal EM solution faster than the existing gradient-based surrogate optimization without adjoint sensitivity. Three examples of EM optimizations of microwave components are used to demonstrate the proposed technique.