Solving Optimization Problems Research Articles

White-faced capuchin optimizer: a new bionic metaheuristic algorithm for solving optimization problems

White-faced capuchin optimizer: a new bionic metaheuristic algorithm for solving optimization problems

Resilient and Adaptive Secure Routing Protocol for Wireless Sensor Networks Using a Grey Wolf Optimizer and Lightning Search Algorithm

The ability of Wireless Sensor Networks (WSNs) to efficiently monitor and collect data from difficult and distant places has made them a notable technical solution for a variety of applications. It is crucial to optimize energy usage and secure data integrity in order to put these technologies to reality with the Internet of Things (IoT). Maintaining a balance between energy economy, flexibility to changing network circumstances, and security is a common difficulty for contemporary routing systems. Because of this, the performance of these protocols drops and they become vulnerable. Specifically, for WSNs, this research presents HGL-ASRP, a state-of-the-art Resilient and Adaptive Secure Routing Protocol. By integrating the Quantum Assisted Grey Wolf Optimizer (GWO) with the Lightning Search Algorithm (LSA), this protocol overcomes the challenges faced by previous routing protocols in the Internet of Things (IoT) setting. Hybrid GWO takes cues from the social behavior of grey wolves and uses them to solve optimization problems very well. As a result of this hybrid GWO and hypercube sampling, grey wolves can only go to a better area to live. With hypercube sampling, the HGL-ASRP method performs better in a number of areas, including speed (90.9 kbps), end-to-end delay (88.8 ms), packet delivery ratio (91.2%), energy efficiency (92.09%), network lifetime (163.63 hours), and security (87.59%). The HGL-ASRP system ensures continuous data transmission even in demanding environments by successfully managing node failures and changing topologies

Efficient FPGA Implementation of Sine Cosine Algorithm using High Level Synthesis

Sine Cosine Algorithm (SCA) finds the best solution to the optimization problem by the periodicity of sine and cosine trigonometric functions. However, it is computationally intensive and contains many parameters to be determined. Fortunately, there are FPGA platforms that can be used to overcome these limitations by improving latency. Sine and cosine calculation in library functions is very complex and time-consuming. Therefore, this paper proposes a hardware-accelerated CORDIC algorithm to improve the sine cosine trigonometric function that needs to be computed in the SCA algorithm. The proposed algorithm (HSCA) combines the accelerated SCA algorithm and the CORDIC algorithm. HSCA performance is tested by using six test functions run on the FPGA. The experimental results show that HSCA is 3.25 times faster and 33% fewer resource utilizations for solving optimization problems, and runs significantly faster on FPGAs with IP cores than on Soc chips in FPGAs. The performance of the HSCA algorithm is demonstrated by applying it to the TDOA localization problem.

Multiple strategies improved spider wasp optimization for engineering optimization problem solving

The Spider Wasp Optimization (SWO) algorithm is a swarm intelligence optimization technique inspired by the collective behaviors of social animals. This algorithm, designed to address optimization challenges, emulates the unique hunting, nesting, and mating behaviors of female spider wasps. It offers several advantages, including rapid search speed and high solution accuracy. However, when tackling complex optimization problems, it can encounter issues such as getting trapped in local optima, slow early convergence, and the need for manual adjustment of the “Trade-off Rate” (TR) parameter for different problems.To improve the performance and versatility of the SWO algorithm, a Multi-strategy Improved Spider Wasp Optimizer (MISWO) is proposed. Firstly, the Grey Wolf Algorithm is integrated into the initialization phase to enhance early convergence and improve the fitness of the initial population, thereby boosting the algorithm’s global optimization capabilities.Secondly, an adaptive step size operator and Gaussian mutation are introduced during the search phase to automatically adjust the search range at different optimization stages. This enhancement increases both the optimization accuracy and the algorithm’s ability to avoid local optima. The Trade-off Rate (TR) is dynamically selected to better accommodate a variety of problems. Finally, a dynamic lens imaging reverse learning strategy is employed to update optimal individuals, further improving the algorithm’s capacity to escape local optima. To validate the effectiveness of MISWO, it was tested on 23 benchmark functions and 7 engineering optimization problems, and compared with several state-of-the-art algorithms. Experimental results show that MISWO outperforms other algorithms in terms of optimization capability, stability, and adaptability across diverse problems.

Using continuation methods to analyse the difficulty of problems solved by Ising machines

Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation methods, we show that this is closely linked to how the ground state emerges from other states when a system parameter is changed, i.e. its bifurcation sequence. From this analysis, we can determine the effectiveness of solution schemes. Moreover, we find that the proper choice of implementation of the Ising machine can drastically change this bifurcation sequence and therefore vastly increase the probability of finding the optimal solution. Lastly, we also show that continuation methods themselves can be used directly to solve optimization problems.

Cooperative metaheuristic algorithm for global optimization and engineering problems inspired by heterosis theory

Swarm Intelligence-based metaheuristic algorithms are widely applied to global optimization and engineering design problems. However, these algorithms often suffer from two main drawbacks: susceptibility to the local optima in large search space and slow convergence rate. To address these issues, this paper develops a novel cooperative metaheuristic algorithm (CMA), which is inspired by heterosis theory. Firstly, simulating hybrid rice optimization algorithm (HRO) constucted based on heterosis theory, the population is sorted by fitness and divided into three subpopulations, corresponding to the maintainer, restorer, and sterile line in HRO, respectively, which engage in cooperative evolution. Subsequently, in each subpopulation, a novel three-phase local optima avoidance technique-Search-Escape-Synchronize (SES) is introduced. In the search phase, the well-established Particle Swarm Optimization algorithm (PSO) is used for global exploration. During the escape phase, escape energy is dynamically calculated for each agent. If it exceeds a threshold, a large-scale Lévy flight jump is performed; otherwise, PSO continues to conduct the local search. In the synchronize phase, the best solutions from subpopulations are shared through an elite-based strategy, while the classical Ant Colony Optimization algorithm is employed to perform fine-tuned local optimization near the shared optimal solutions. This process accelerates convergence, maintains population diversity, and ensures a balanced transition between global exploration and local exploitation. To validate the effectiveness of CMA, this study evaluates the algorithm using 26 well-known benchmark functions and 5 real-world engineering problems. Experimental results demonstrate that CMA outperforms the 10 state-of-the-art algorithms evaluated in the study, which is a very promising for engineering optimization problem solving.

Model-Driven Cooperative Path Planning for Dynamic Target Searching of Unmanned Unterwater Vehicle Formation

With the increasing complexity of ocean missions, using multiple unmanned underwater vehicles to collaborate in executing tasks has become an effective way to improve the overall efficiency of ocean operations. Current research on path planning for multiple unmanned underwater vehicles mainly focuses on the basis of particle models or fully known environmental information, while research directions mainly focus on single indicators such as completion time and energy consumption. This paper first constructs a UUV model and a task scenario with detection success rate as the objective function. Then, a parameterization method based on a spiral search path was proposed for designing variables. A hierarchical control strategy is designed to ensure handle formation constraints. A general optimization framework for task scenarios has been constructed and combined with algorithms to solve optimization problems. Finally, this study compared and analyzed the performance of different optimization algorithms under the optimization framework, evaluated the optimization results of different search strategies, and explored the impact of dynamic objectives on the detection success rate. The results showed that the optimized path had a search success rate that increased by more than 50% compared to the direct path and the cover search path, which verified the effectiveness of the proposed method and strategy.

Stochastic Normal Orientation for Point Clouds

We propose a simple yet effective method to orient normals for point clouds. Central to our approach is a novel optimization objective function defined from global and local perspectives. Globally, we introduce a signed uncertainty function that distinguishes the inside and outside of the underlying surface. Moreover, benefiting from the statistics of our global term, we present a local orientation term instead of a global one. The optimization problem can be solved by the commonly used numerical optimization solver, such as L-BFGS. The capability and feasibility of our approach are demonstrated over various complex point clouds. We achieve higher practical robustness and normal quality than the state-of-the-art methods.

Artificial meerkat algorithm: a new metaheuristic algorithm for solving optimization problems

Abstract In this study, a novel artificial meerkat optimization algorithm (AMA) is proposed to simulate the cooperative behaviors of meerkat populations. The AMA algorithm is designed with two sub-populations, multiple search strategies, a multi-stage elimination mechanism, and a combination of information sharing and greedy selection strategies. Drawing inspiration from the intra-population learning behavior, the algorithm introduces two search mechanisms: single-source learning and multi-source learning. Additionally, inspired by the sentinel behavior of meerkat populations, a search strategy is proposed that combines Gaussian and Lévy variations. Furthermore, inspired by the inter-population aggression behavior of meerkat populations, the AMA algorithm iteratively applies these four search strategies, retaining the most suitable strategy while eliminating others to enhance its applicability across complex optimization problems. Experimental results comparing the AMA algorithm with seven state-of-the-art algorithms on 53 test functions demonstrate that the AMA algorithm outperforms others on 71.7% of the test functions. Moreover, experiments on challenging engineering optimization problems confirm the superior performance of the AMA algorithm over alternative algorithms.

Dynamic Supplier Selection and Its Optimal Strategy Considering Full Truck Load and Fuzzy Demand using Fuzzy Expected Value-Based Programming

This article proposes a linear integer optimization model incorporating fuzzy parameters to find the optimal solution for a dynamic supplier selection problem with uncertain demand. The uncertain demand value is represented using a fuzzy variable. A fuzzy expected value-based linear optimization solver is used to address the optimization problem, to minimize the total cost under fuzzy demand values. Several computational experiments were conducted to evaluate and analyze the model. The results show that the proposed model effectively identifies the optimal suppliers for each product. Additionally, the model determines the optimal purchase volumes for each product type from the selected suppliers, leading to the minimal total expected cost.

Optimization of High-Speed Rail Express Transportation Scheduling Based on Spatio-Temporal-State Network Modeling

High-speed rail express is gradually gaining attention due to its low cost and high on-time performance. This paper studied the optimization of high-speed rail express transportation modes considering passenger capacity loss. A spatio-temporal network was constructed that includes the fixed passenger train schedule and the high-speed rail express transportation status. Based on this network, an optimization model for transportation schemes considering passenger capacity loss with non-splittable freight flows was developed. The model aims to minimize passenger loss and maximize net revenue from express transportation while comprehensively considering practical constraints such as transfer, loading and unloading, and carrying capacity. The Gurobi optimization solver was used to solve numerical cases, and the optimization results and solution effectiveness were comparatively analyzed under scenarios of sufficient and insufficient capacity.

16-channel photonic solver for optimization problems on a silicon chip

A programmable photonic solver for quadratic unconstrained binary optimization (QUBO) problems is demonstrated with a hybrid optoelectronic scheme, which consists of a photonic chip and an electronic driving board. The photonic chip is employed to perform the optical vector-matrix multiplication (OVMM) to calculate the cost function of the QUBO problem, while the electronic processor runs the heuristic algorithm to search for the optimal solution. Due to the parallel and low-latency propagation of lightwave, the calculation of the cost function can be accelerated. The photonic chip is fabricated on the silicon on insulator (SOI) substrate and integrates 16 high-speed electro-optic modulators, 88 thermo-optic phase shifters, and 16 balanced photodetectors. The computing speed of the photonic chip is 1.66 TFLOP/s. As a proof of principle, two randomly generated 16-dimensional QUBO problems are solved with high successful probabilities. These results present the potential of fast solving optimization problems with integrated photonic systems.

К МЕТОДИКЕ ФОРМИРОВАНИЯ ЦИФРОВОГО ДВОЙНИКА ТЕХНОЛОГИЧЕСКОГО ПРОЦЕССА СУШКИ ОРГАНИЧЕСКИХ СЕМЯН ТИМОФЕЕВКИ

An important specific feature of the functioning of machines and equipment in the technologies of post-harvest processing of grain and seeds is the probabilistic variability of external conditions that negatively affect the efficiency of their work. The drying process is also characterized by non-stationarity in its probabilistic and statistical characteristics. The methods of forming digital twins of stationary processes are quite well mastered, but the construction of digital twins of non-stationary processes is a much more complex task, the solution of which requires taking into account the nature of non-stationarity, as well as the features and internal structure of the processes being modeled. The purpose of the research is to build a digital twin of the non-stationary process of drying timothy seeds and assess the reliability of the resulting model. The experimental data were obtained by drying Leningradskaya 204 timothy grass seeds from the field organic crop rotation using a universal drying unit with a Fauna PMDR4 digital seed moisture meter equipped with submersible flow sensors. As a result of the experimental studies, realizations of random processes of change in seed moisture content at the final stage of drying were obtained for constructing mathematical models using statistical identification methods. Discrete analogs of the processes under study were constructed using experimental correlation functions approximated by the corresponding functions to obtain the parameters of the modeling recurrent equations. The considered algorithm for modeling the dryer operation allows reproducing processes of unlimited length and modeling various conditions and operating modes to find the specified optima for quality, energy consumption and environmental friendliness. The accuracy of the simulation results was determined based on the convergence of the moment functions of the experimental and modeled technological processes. Estimates of statistical characteristics of the simulated process of drying timothy grass seeds with 95% probability correspond to statistical estimates of the drying process obtained in the course of experimental studies, and the graphs of their normalized correlation functions clearly confirm the identity of the processes. The obtained mathematical dependencies of the technological process of drying organic timothy grass seeds are its digital twin, allowing the methods of simulation modeling to solve optimization problems.

Dynamic output feedback model predictive control for polytopic uncertain systems under decode and forward cooperative relay protocol

This paper addresses the robust model predictive control (RMPC) problem for a class of polytopic uncertain systems under the decode and forward cooperative relay protocol (DFCP). In order to combat signal fading from sensors to controllers and improve communication reliability, spatial diversity is achieved through cooperative terminal relay signals. At each transmission instant, the terminal only selects a better signal for transmission and a switched system is constructed. The aim of this paper is to design a set of desired dynamic output feedback controllers in the framework of RMPC such that the switched system with the underlying DFCP is exponentially stable. By taking the influence of the randomness of DFCP derived from a three nodes model composed of DF relay, a new objective function based on the mathematical expectation of the traditional quadratic function of MPC is established. Then, the orthogonal complement technique is applied to handle the inherent couplings of variables to formulate a solvable optimisation problem. Moreover, the sufficient conditions are provided to guarantee the recursive feasibility of the MPC strategy and the stability of the established closed-loop system in terms of the average dwell time (ADT) method. Finally, three experiments are given to illustrate the effectiveness of the proposed method.

Optimal quantum controls robust against detuning error

Abstract Precise control of quantum systems is one of the most important milestones for achieving practical quantum technologies, such as computation, sensing, and communication. Several factors deteriorate the control precision and thus their suppression is strongly demanded. One of the dominant factors is systematic errors, which are caused by discord between an expected parameter in control and its actual value. Error-robust control sequences, known as composite pulses, have been invented in the field of nuclear magnetic resonance (NMR). These sequences mainly focus on the suppression of errors in one-qubit control. The one-qubit control, which is the most fundamental in a wide range of quantum technologies, often suffers from detuning error. As there are many possible control sequences robust against the detuning error, it will practically be important to find ‘optimal’ robust controls with respect to several cost functions such as time required for operation, and pulse-area during the operation, which corresponds to the energy necessary for control. In this paper, we utilize the Pontryagin’s maximum principle (PMP), a tool for solving optimization problems under inequality constraints, to solve the time and pulse-area optimization problems. We analytically obtain pulse-area optimal controls robust against the detuning error. Moreover, we found that short-CORPSE, which is the shortest known composite pulse so far, is a probable candidate of the time optimal solution according to the PMP. We evaluate the performance of the pulse-area optimal robust control and the short-CORPSE, comparing with that of the direct operation.

Causal Structure Learning for Recommender System

A fundamental challenge of recommender systems (RS) is understanding the causal dynamics underlying users’ decision making. Most existing literature addresses this problem by using causal structures inferred from domain knowledge. However, there are numerous phenomenons where domain knowledge is insufficient, and the causal mechanisms must be learned from the feedback data. Discovering the causal mechanism from RS feedback data is both novel and challenging, since RS itself is a source of intervention that can influence both the users’ exposure and their willingness to interact. Also for this reason, most existing solutions become inappropriate since they require data collected free from any RS. In this article, we first formulate the underlying causal mechanism as a causal structural model and describe CSL4RS , a general causal structure learning framework for RS grounded in the real-world working mechanism. The essence of our approach is to acknowledge the unknown nature of RS intervention. We then derive the learning objective from our framework and utilize an augmented Lagrangian solver for efficient optimization. We conduct both simulation and real-world experiments to demonstrate how our approach compares favorably to existing solutions, together with the empirical analysis from sensitivity and ablation studies.

Nonlinear Optimization and Adaptive Heuristics for Solving Irregular Object Packing Problems

We review and present several challenging model classes arising in the context of finding optimized object packings (OP). Except for the smallest and/or simplest general OP model instances, it is not possible to find their exact (closed-form) solution. Most OP problem instances become increasingly difficult to handle even numerically, as the number of packed objects increases. Specifically, here we consider classes of general OP problems that can be formulated in the framework of nonlinear optimization. Research experience demonstrates that—in addition to utilizing general-purpose nonlinear optimization solver engines—the insightful exploitation of problem-specific heuristics can improve the quality of numerical solutions. We discuss scalable OP problem classes aimed at packing general circles, spheres, ellipses, and ovals, with numerical (conjectured) solutions of non-trivial model instances. In addition to their practical relevance, these models and their various extensions can also serve as constrained global optimization test challenges.

Selection of aerodynamic characteristics and engine parameters of a maneuverable aircraft under epistemic uncertainty

At the preliminary stage of aircraft design, it is usually required to solve the problem of insufficient initial data for applying traditional algoristic-type mathematical programming models. In many cases, numerous input parameters cannot be accurately specified at the time of making design decisions. If the inaccuracy of parameters is not taken into account, the actual values of target functions may differ significantly from the calculated ones when solving optimization problems. In this regard, the issue of current interest is the development of algorithms to improve the reliability of design decisions under conditions of epistemological uncertainty when experts engage in the formation of initial data. The paper considers the problem of selecting aerodynamic characteristics and engine parameters of maneuverable aircraft under conditions of uncertainty associated with inaccuracy of expert data. The applied problem under consideration is further complicated by the necessity to include “black box” models in the algorithms being developed. The paper proposes algorithms that apply the uncertainty theory together with “black box” models that implement optimization calculation techniques derived from previous engineering practice of aircraft design. Using these algorithms, experts are able to set uncertain parameters whereby the lack of data is factored in using uncertainty distribution functions. In cases of monotonicity of uncertain parameters in target functions, application of the uncertainty theory provides a significant reduction in computational costs compared to the method of statistical modeling in optimization calculations. The paper presents the results of computational studies of the developed algorithms. A genetic algorithm (mathematical optimization solver) is used to optimize the search for design solutions. Pareto frontiers are obtained for different confidence levels enabling to make design decisions including values of aerodynamic characteristics and engine parameters of maneuverable aircraft.

Differential evolution-based topology optimization using Karhunen-Loève expansion

Topology optimization is a widely adopted structural optimization approach that aims to maximize desired performance based on mathematical and physical principles. Gradient-based methods are common for obtaining optimal configurations; however, they struggle with problems involving numerous local optima and non-differentiable problems, which prevent the derivation of design sensitivity. To address these issues, this study explores the application of the Success History-Based Differential Evolution with Linear Population Size Reduction and Semi-Parameter Adaptation, which is regarded as LSHADE-SPA algorithm, known for its strong search capabilities. Nevertheless, its computational cost makes it impractical for topology optimization, especially as the number of design variables increases. To overcome this challenge, a novel structure representation method utilizing the Karhunen-Loève (KL) expansion is constructed. Applying truncated KL expansion instead of conventional density methods to represent structural configurations reduces the number of design variables. This article introduces a differential evolution-based topology optimization method utilizing truncated KL expansion and validates its effectiveness through applications in various structural and fluid problems. The method is particularly suited to highly nonlinear problems, such as negative Poisson's ratio structures and micro-mixer designs. The findings here indicate that differential evolution with truncated KL expansion can serve as an efficient and robust topology optimization method, proving particularly effective for solving optimization problems that are challenging for conventional gradient-based approaches. Notably, the proposed methodology not only delivers superior results but also alleviates computational burdens, thereby advancing the prospects of topology optimization in various engineering applications.

Combining Genetic Algorithm with Local Search Method in Solving Optimization Problems

This research is focused on evolutionary algorithms, with genetic and memetic algorithms discussed in more detail. A graph theory problem related to finding a minimal Hamiltonian cycle in a complete undirected graph (Travelling Salesman Problem—TSP) is considered. The implementations of two approximate algorithms for solving this problem, genetic and memetic, are presented. The main objective of this study is to determine the influence of the local search method versus the influence of the genetic crossover operator on the quality of the solutions generated by the memetic algorithm for the same input data. The results show that when the number of possible Hamiltonian cycles in a graph is increased, the memetic algorithm finds better solutions. The execution time of both algorithms is comparable. Also, the number of solutions that mutated during the execution of the genetic algorithm exceeds 50% of the total number of all solutions generated by the crossover operator. In the memetic algorithm, the number of solutions that mutate does not exceed 10% of the total number of all solutions generated by the crossover operator, summed with those of the local search method.