Complicated Optimization Problem Research Articles

Photonic Ising machines for combinatorial optimization problems

The demand for efficient solvers of complicated combinatorial optimization problems, especially those classified as NP-complete or NP-hard, has recently led to increased exploration of novel computing architectures. One prominent collective state computing paradigm embodied in the so-called Ising machines has recently attracted considerable research attention due to its ability to optimize complex problems with large numbers of interacting variables. Ising model-inspired solvers, thus named due to mathematical similarities to the well-known model from solid-state physics, represent a promising alternative to traditional von Neumann computer architectures due to their high degree of inherent parallelism. While there are many possible physical realizations of Ising solvers, just as there are many possible implementations of any binary computer, photonic Ising machines (PIMs) use primarily optical components for computation, taking advantage of features like lower power consumption, fast calculation speeds, the leveraging of physical optics to perform the calculations themselves, possessing decent scalability and noise tolerance. Photonic computing in the form of PIMs may offer certain computational advantages that are not easily achieved with non-photonic approaches and is nonetheless an altogether fascinating application of photonics to computing. In this review, we provide an overview of Ising machines generally, introducing why they are useful, what types of problems they can tackle, and how different Ising solvers can be compared and benchmarked. We delineate their various operational mechanisms, advantages, and limitations vis-à-vis non-photonic Ising machines. We describe their scalability, interconnectivity, performance, and physical dimensions. As research in PIMs continues to progress, there is a potential that photonic computing could well emerge as a way to handle large and challenging optimization problems across diverse domains. This review serves as a comprehensive resource for researchers and practitioners interested in understanding capabilities and potential of PIMs in addressing such complex optimization problems.

Heuristic Optimization Algorithm of Black-Winged Kite Fused with Osprey and Its Engineering Application.

Swarm intelligence optimization methods have steadily gained popularity as a solution to multi-objective optimization issues in recent years. Their study has garnered a lot of attention since multi-objective optimization problems have a hard high-dimensional goal space. The black-winged kite optimization algorithm still suffers from the imbalance between global search and local development capabilities, and it is prone to local optimization even though it combines Cauchy mutation to enhance the algorithm's optimization ability. The heuristic optimization algorithm of the black-winged kite fused with osprey (OCBKA), which initializes the population by logistic chaotic mapping and fuses the osprey optimization algorithm to improve the search performance of the algorithm, is proposed as a means of enhancing the search ability of the black-winged kite algorithm (BKA). By using numerical comparisons between the CEC2005 and CEC2021 benchmark functions, along with other swarm intelligence optimization methods and the solutions to three engineering optimization problems, the upgraded strategy's efficacy is confirmed. Based on numerical experiment findings, the revised OCBKA is very competitive because it can handle complicated engineering optimization problems with a high convergence accuracy and quick convergence time when compared to other comparable algorithms.

A two-phase algorithm for the dynamic time-dependent green vehicle routing problem in decoration waste collection

Transportation activities associated with construction waste generate substantial carbon emissions, an issue that is attracting increasing environmental concern. To raise construction waste transportation efficiency and reduce carbon emission, we address the dynamic time-dependent green vehicle routing problem for decoration waste collection (DTDGVRP-DWC). In the existing literature, many deterministic approaches to the dynamic vehicle routing problem are myopic, as they only react to already arrived requests. In this paper, we propose a stochastic sampling method to tackle with uncertain customer request in the real world. The DTDGVRP-DWC is formulated as an 0-1 programming. In the new model, we consider urban traffic congestion and variable speeds over time, and factors that significantly influence both carbon emissions and fuel costs. To quickly solve the complicated optimization problem, we develop a two-phase algorithm. In the first phase, we embed a competitive simulated annealing algorithm to determine visitation schedules for anticipated and early-request customers. In the second phase, we propose an event-trigger mechanism to decompose the dynamic problem into a series of static sub-problems, and an effective heuristic to solve each sub-problem. Computational results show that as long as the prediction accuracy exceeds a threshold, the forecast routing method consistently performs better than reactive routing. A real-world case demonstrates that an early commitment waiting time strategy benefits timely service requirements, whereas a late or hybrid waiting time strategy takes overall efficiency and customer satisfaction into account.

Nature-inspired optimization prey–predator algorithm for soil slope stability analysis with physically informed initial population generation

In soil slope stability, locating the critical slip surface with the minimum safety factor is a difficult and complicated optimization problem. Most methods fail when proper bounds are not applied to the decision variable. For the first time, the paper uses the prey–predator algorithm to analyze slopes stability with circular slip surfaces making use of meaningful rules, from an engineering point of view, to define these bounds. The Fellenius method based on limit equilibrium technique also serves as the constraint of the mathematical problem adopted to solve the task. A pseudo-analytical study is also carried out on four benchmark literature problems to test the performance and to certify the accuracy of the results obtained with the new application of the prey–predator algorithm. We show that the solutions obtained are accurate and should be assumed as a reference comparing to other methods.

Design cost minimization of a reinforced concrete column section using overnew swarm-based optimization algorithms

It is very tiresome for a practiser to detect the best feasible sizing design of structural members including reinforced concrete columns that is a highly nonlinear and complicated structural engineering optimization problem. This is due to such a design is practically conducted via conventional trial-and-error computing methods in which resistance to external loads, cost efficiency, and aesthetic factors, etc. have to be considered. This study focuses on minimizing the design cost of primarily proposed reinforced concrete column design problem via three overnew swarm-based optimizers such as Coati Optimization Algorithm, Fox Optimizer and Pelican Optimization Algorithm (POA) that are firstly utilized for this purpose. In this regard, the type of steel rebar distribution, the characteristic strength of the concrete, the height and width of the column section, and the number and diameter of the rebars are treated as discrete design variables of the newly proposed complex reinforced concrete column design cost optimization problem. In solution, the design requirements specified in practice code provisions should also be met. Here, Turkish Building Earthquake Code 2018 specifications are considered as practice structural design constraints. Consequently, the algorithmic performances of three overnew swarm-based metaheuristic optimization algorithms are compared and evaluated in detail. Amongst them, the POA shows most fruitful algorithmic design solution performance.

Improved Snake Optimizer Using Sobol Sequential Nonlinear Factors and Different Learning Strategies and Its Applications

The Snake Optimizer (SO) is an advanced metaheuristic algorithm for solving complicated real-world optimization problems. However, despite its advantages, the SO faces certain challenges, such as susceptibility to local optima and suboptimal convergence performance in cases involving discretized, high-dimensional, and multi-constraint problems. To address these problems, this paper presents an improved version of the SO, known as the Snake Optimizer using Sobol sequential nonlinear factors and different learning strategies (SNDSO). Firstly, using Sobol sequences to generate better distributed initial populations helps to locate the global optimum solution faster. Secondly, the use of nonlinear factors based on the inverse tangent function to control the exploration and exploitation phases effectively improves the exploitation capability of the algorithm. Finally, introducing learning strategies improves the population diversity and reduces the probability of the algorithm falling into the local optimum trap. The effectiveness of the proposed SNDSO in solving discretized, high-dimensional, and multi-constraint problems is validated through a series of experiments. The performance of the SNDSO in tackling high-dimensional numerical optimization problems is first confirmed by using the Congress on Evolutionary Computation (CEC) 2015 and CEC2017 test sets. Then, twelve feature selection problems are used to evaluate the effectiveness of the SNDSO in discretized scenarios. Finally, five real-world technical multi-constraint optimization problems are employed to evaluate the performance of the SNDSO in high-dimensional and multi-constraint domains. The experiments show that the SNDSO effectively overcomes the challenges of discretization, high dimensionality, and multi-constraint problems and outperforms superior algorithms.

A gene-inspired metaheuristic for scheduling workflow tasks in mobile edge computing-supported cyber–physical systems

This paper proposes a cost-minimization scheduling algorithm for the joint optimization of task offloading and resource allocation for workflow applications in a mobile edge computing (MEC)-supported cyber–physical system. We model this scheduling problem as an integer program that minimizes the total communication and computation cost under resources and deadline constraints upon workflow applications. To cope with this complicated optimization problem, we develop an efficient heuristic method to dispatch the workflow tasks onto MEC servers with sufficient resources. By using the task dispatching heuristic to evaluate the quality of each candidate solution, we construct a novel gene-inspired metaheuristic algorithm (GIMA) that incorporates an offspring-production operator and a conditional insertion scheme into the improvement strategy to explore high-quality solutions. Specifically, the offspring-production operator can enhance the scheduling quality by generating improved offspring solutions based on existing solutions. The conditional insertion scheme is further incorporated to reduce the computational overhead involved in solution exploration. We perform extensive simulations to justify the performance of the proposed GIMA in solving the scheduling problem studied in this work. Experimental results on real-world and synthetic workflow applications show that GIMA outperforms other metaheuristics in terms of cost reduction and computational efficiency.

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

A Unified Design Method for Multi-Source Complementary Heating Systems Based on a Transient Simulation

Combining various sources to create a complementary system plays a key role in utilizing clean energy sources economically and mitigating air pollution during the heating season in Northern China. However, there is a lack of unified and reasonable design methods for such systems, resulting in the excessive capacity of equipment and the waste of energy. In this work, a unified design method is proposed to solve this problem. A generalized structure and its mathematical model are firstly established, enabling transient simulations on the TRNSYS platform. Then, a preliminary screening criterion for the system composition a general operation strategy is proposed. Finally, the system configuration is optimized by using the genetic algorithm. The method is successfully applied in a demonstration project in China. The results show that the coupling system consisting of a biomass boiler (384 kW), an air-source heat pump (430 kW) and a ground-source heat pump (369 kW) is the most economical, and the annual cost is 26.7% lower than that of a single-equipment system. Additionally, the sensitive factors that strongly affect the optimization results are explored. The establishment of the generalized structure and its mathematical model enables the quick calculation and convenient comparison of various schemes, and simplifies the complicated optimization problem of the capacity optimization of each piece of equipment. The proposed design method can reduce the annual cost to a minimum value, and thus it provides a theoretical basis for the large-scale application of clean energy sources for heating.

Adaptive habitat biogeography-based optimizer for optimizing deep CNN hyperparameters in image classification

Deep Convolutional Neural Networks (DCNNs) have shown remarkable success in image classification tasks, but optimizing their hyperparameters can be challenging due to their complex structure. This paper develops the Adaptive Habitat Biogeography-Based Optimizer (AHBBO) for tuning the hyperparameters of DCNNs in image classification tasks. In complicated optimization problems, the BBO suffers from premature convergence and insufficient exploration. In this regard, an adaptable habitat is presented as a solution to these problems; it would permit variable habitat sizes and regulated mutation. Better optimization performance and a greater chance of finding high-quality solutions across a wide range of problem domains are the results of this modification's increased exploration and population diversity. AHBBO is tested on 53 benchmark optimization functions and demonstrates its effectiveness in improving initial stochastic solutions and converging faster to the optimum. Furthermore, DCNN-AHBBO is compared to 23 well-known image classifiers on nine challenging image classification problems and shows superior performance in reducing the error rate by up to 5.14%. Our proposed algorithm outperforms 13 benchmark classifiers in 87 out of 95 evaluations, providing a high-performance and reliable solution for optimizing DNNs in image classification tasks. This research contributes to the field of deep learning by proposing a new optimization algorithm that can improve the efficiency of deep neural networks in image classification.

SHuffled Ant Lion Optimization approach with an exponentially weighted random walk strategy

Ant Lion Optimization (ALO) method is one of the population-based nature-inspired optimization algorithms which mimics the hunting strategy of antlions. ALO is successfully employed for solving many complicated optimization problems. However, it is reported in the literature that the original ALO has some limitations such as the requirement of high number of iterations and possibility of trapping to local optimum solutions, especially for complex or large-scale problems. For this purpose, the SHuffled Ant Lion Optimization (SHALO) approach is proposed by conducting two improvements in the original ALO. Performance of the proposed SHALO approach is evaluated by solving some unconstrained and constrained problems for different conditions. Furthermore, the identified results are statistically compared with the ones obtained by using the original ALO, two improved ALOs which are the self-adaptive ALO (saALO) and the exponentially weighted ALO (EALO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) approaches. Identified results indicated that the proposed SHALO approach significantly improves the solution accuracy with a mean success rate of 76% in terms of finding the global or near-global optimum solutions and provides better results than ALO (22%), saALO (25%), EALO (14%), GA (28%), and PSO (49%) approaches for the same conditions.

Joint resource allocation and beamforming design for RIS-aided symbiotic radio networks: A DRL approach

In this paper, we investigate a Reconfigurable Intelligent Surface (RIS)-assisted secure Symbiosis Radio (SR) network to address the information leakage of the primary transmitter (PTx) to potential eavesdroppers. Specifically, the RIS serves as a secondary transmitter in the SR network to ensure the security of the communication between the PTx and the Primary Receiver (PRx), and simultaneously transmits its information to the PTx concurrently by configuring the phase shifts. Considering the presence of multiple eavesdroppers and uncertain channels in practical scenarios, we jointly optimize the active beamforming of PTx and the phase shifts of RIS to maximize the secrecy energy efficiency of RIS-supported SR networks while satisfying the quality of service requirement and the secure communication rate. To solve this complicated non-convex stochastic optimization problem, we propose a secure beamforming method based on Proximal Policy Optimization (PPO), which is an efficient deep reinforcement learning algorithm, to find the optimal beamforming strategy against eavesdroppers. Simulation results show that the proposed PPO-based method is able to achieve fast convergence and realize the secrecy energy efficiency gain by up to 22% when compared to the considered benchmarks.

NH3 Emissions and Lifetime Estimated by Satellite Observations with Differential Evolution Algorithm

As an important irritant trace gas in the atmosphere, ammonia (NH3) significantly impacts human health and environment. Bottom-up emission inventories are widely used to estimate ammonia emissions and their geographical distributions over China. However, high uncertainties are still associated with emission inventories due to inaccurate emission factors used. The Differential Evolution (DE) algorithm is a population-based stochastic optimization algorithm used to solve complicated optimization problems. We quantify NH3 emissions and lifetime from Infrared Atmospheric Sounding Interferometer (IASI) NH3 observations together with MERRA-2 wind fields based on the DE algorithm. Two inland cities, Urumchi and Golmud in China, are chosen to study of the NH3 emissions based on the distributions of NH3 total columns and wind fields. The NH3 emissions rate estimated is about 5.84 × 10−11 and 4.19 × 10−11 kg·m−2s−1 in Urumchi and in the Golmud area from May to September from 2008 to 2023, respectively. The lifetime of NH3 estimated in the two areas is 4.31 and 9.19 h, respectively. We compare the NH3 emissions and lifetime estimated in this study with the values in other studies, and the results show the reliability of the method used. This work is one of few quantitative studies of NH3 emissions from cities using satellite observations in China.

Enhancement of distribution system performance with reconfiguration, distributed generation and capacitor bank deployment

This paper presents a comparative study of optimal reconfiguration, distributed generation, and shunt capacitor bank deployment for power loss minimization and voltage profile improvement in distribution systems. A metaheuristic approach based on the grey wolf optimizer (GWO) algorithm has been proposed for solving this high-dimensional, nonlinear, constrained, combinatorial optimization problem. Two standard IEEE 33- and 69-bus radial distribution systems (RDSs), and a practical 83-bus RDS of Taiwan Power Company have been considered for this study. The solutions obtained are compared with one another and those in the recent literature which includes classical and non-classical, metaheuristic-based methods. Going further, the little-studied problem of simultaneous reconfiguration, distributed generation, and capacitor bank deployment has been solved. The results suggest that the GWO has excellent potential for solving complicated optimization problems in distribution systems and elsewhere.

Maximizing acoustic band gap in phononic crystals via topology optimization

Designing phononic crystals (PnCs) to exhibit the widest attainable band gap, or to encompass a designated frequency range, is imperative for the realization of PnCs tailored to specific functionalities. However, achieving a wide band gap of acoustic waves centered around a specified frequency remains a significant challenge. The challenge arises from the fact that the optimization objective function may be enhanced by disconnected air regions. Nonetheless, these disconnected regions obstruct the circulation of air, rendering PnCs devoid of practical engineering utility. In this study, we propose a topology optimization methodology aimed at crafting air/solid PnCs that maximize the band gap of acoustic waves at a specified central frequency. To ensure adequate air permeability within the PnCs, the optimization model incorporates the virtual temperature technique in conjunction with the minimum length scale technique. The topology of the PnC unit cell is represented with a low number of design variables through the material-field series expansion, and the Kriging-based optimization algorithm is used to solve the complicated optimization problem. Diverse optimized configurations are presented, and experimental findings compellingly underscore the efficacy of the proposed optimization approach in the design of phononic band gap crystals geared towards acoustic waves at the specified central frequency.

Novel hybrid kepler optimization algorithm for parameter estimation of photovoltaic modules

The parameter identification problem of photovoltaic (PV) models is classified as a complex nonlinear optimization problem that cannot be accurately solved by traditional techniques. Therefore, metaheuristic algorithms have been recently used to solve this problem due to their potential to approximate the optimal solution for several complicated optimization problems. Despite that, the existing metaheuristic algorithms still suffer from sluggish convergence rates and stagnation in local optima when applied to tackle this problem. Therefore, this study presents a new parameter estimation technique, namely HKOA, based on integrating the recently published Kepler optimization algorithm (KOA) with the ranking-based update and exploitation improvement mechanisms to accurately estimate the unknown parameters of the third-, single-, and double-diode models. The former mechanism aims at promoting the KOA’s exploration operator to diminish getting stuck in local optima, while the latter mechanism is used to strengthen its exploitation operator to faster converge to the approximate solution. Both KOA and HKOA are validated using the RTC France solar cell and five PV modules, including Photowatt-PWP201, Ultra 85-P, Ultra 85-P, STP6-120/36, and STM6-40/36, to show their efficiency and stability. In addition, they are extensively compared to several optimization techniques to show their effectiveness. According to the experimental findings, HKOA is a strong alternative method for estimating the unknown parameters of PV models because it can yield substantially different and superior findings for the third-, single-, and double-diode models.

Multiobjective trajectory optimization algorithms for solving multi-UAV-assisted mobile edge computing problem

The Internet of Things (IoT) devices are not able to execute resource-intensive tasks due to their limited storage and computing power. Therefore, Mobile edge computing (MEC) technology has recently been utilized to provide computing and storage capabilities to those devices, enabling them to execute these tasks with less energy consumption and low latency. However, the edge servers in the MEC network are located at fixed positions, which makes them unable to be adjusted according to the requirements of end users. As a result, unmanned aerial vehicles (UAVs) have recently been used to carry the load of these edge servers, making them mobile and capable of meeting the desired requirements for IoT devices. However, the trajectories of the UAVs need to be accurately planned in order to minimize energy consumption for both the IoT devices during data transmission and the UAVs during hovering time and mobility between halting points (HPs). The trajectory planning problem is a complicated optimization problem because it involves several factors that need to be taken into consideration. This problem is considered a multiobjective optimization problem since it requires simultaneous optimization of both the energy consumption of UAVs and that of IoT devices. However, existing algorithms in the literature for this problem have been based on converting it into a single objective, which may give preference to some objectives over others. Therefore, in this study, several multiobjective trajectory planning algorithms (MTPAs) based on various metaheuristic algorithms with variable population size and the Pareto optimality theory are presented. These algorithms aim to optimize both objectives simultaneously. Additionally, a novel mechanism called the cyclic selection mechanism (CSM) is proposed to manage the population size accurately, optimizing the number of HPs and the maximum function evaluations. Furthermore, the HPs estimated by each MTPA are associated with multiple UAVs using the k-means clustering algorithm. Then, a low-complexity greedy mechanism is used to generate the order of HPs assigned to each UAV, determining its trajectory. Several experiments are conducted to assess the effectiveness of the MTPAs with variable population size and cyclic selection mechanisms. The experimental findings demonstrate that the MTPAs with the cyclic selection mechanism outperform all competing algorithms, achieving better outcomes.

Evolutionary feature selection based on hybrid bald eagle search and particle swarm optimization

Feature selection is a complicated multi-objective optimization problem with aims at reaching to the best subset of features while remaining a high accuracy in the field of machine learning, which is considered to be a difficult task. In this paper, we design a fitness function to jointly optimize the classification accuracy and the selected features in the linear weighting manner. Then, we propose two hybrid meta-heuristic methods which are the hybrid basic bald eagle search-particle swarm optimization (HBBP) and hybrid chaos-based bald eagle search-particle swarm optimization (HCBP) that alleviate the drawbacks of bald eagle search (BES) by utilizing the advantages of particle swarm optimization (PSO) to efficiently optimize the designed fitness function. Specifically, HBBP is proposed to overcome the disadvantages of the originals (i.e., BES and PSO) and HCBP is proposed to further improve the performance of HBBP. Moreover, a binary optimization is utilized to effectively transfer the solution space from continuous to binary. To evaluate the effectiveness, 17 well-known data sets from the UCI repository are employed as well as a set of well-established algorithms from the literature are adopted to jointly confirm the effectiveness of the proposed methods in terms of fitness value, classification accuracy, computational time and selected features. The results support the superiority of the proposed hybrid methods against the basic optimizers and the comparative algorithms on the most tested data sets.

Robust fuzzy adaptive yaw moment control of humanoid robot with unknown backlash nonlinearity

To achieve an excellent dynamic balance during humanoid robot walks, it is essential to counteract the undesired yaw moment and deal with the nonlinearities existing in the system dynamics. In this paper, the problems of the dynamic balance optimization and yaw moment control for humanoid robot are investigated. First we formulate a constrained dynamic model of compliant joints for robots. Then, a yaw moment control approach based on quadratic objective function is proposed for computing optimal ankle torque to equilibrate the undesired yaw moment. In order to deal with the complicated optimization problem with inequality and equality constraints, a Quadratic Programming (QP) solver based on Linear Variational Inequality (LVI) is adopted. In comparison with the yaw moment control approaches studied previously, the main contributions of this paper are summarized as follows. 1) our newly proposed control scheme is more effective in counteracting the undesired yaw moment for the case of handling object-carrying tasks during walking. 2) a novel adaptive backlash inverse is included in the proposed scheme to cancel the unknown actuator backlash nonlinearity without a prior knowledge of the backlash nonlinearity. By the strict Lyapunov argument, the asymptotic convergence of the system tracking error to arbitrarily small neighborhood of the origin is proved. The simulation examples involving humanoid robot walking are constructed to validate the proposed algorithm.

Federated Learning-Based Service Caching in Multi-Access Edge Computing System

Multi-access edge computing (MEC) brings computations closer to mobile users, thereby decreasing service latency and providing location-aware services. Nevertheless, given the constrained resources of the MEC server, it is crucial to provide a limited number of services that properly fulfill the demands of users. Several static service caching approaches have been proposed. However, the effectiveness of these strategies is constrained by the dynamic nature of the system states and user demand patterns. To mitigate this problem, several investigations have been conducted on dynamic service caching techniques that can be categorized as centralized and distributed. However, centralized approaches typically require gathering comprehensive data from the entire system. This increases the burden on resources and raises concerns regarding data security and privacy. By contrast, distributed strategies require the formulation of complicated optimization problems without leveraging the inherent characteristics of the data. This paper proposes a distributed service caching strategy based on federated learning (SCFL) that works efficiently in a distributed system with user mobility. An autoencoder model is utilized to extract features regarding the service request distribution of individual MEC servers. The global model is then generated using federated learning, which is utilized to make service-caching decisions. Extensive experiments are conducted to demonstrate that the performance of the proposed method is superior to that of other methods.