Solving Optimization Problems Research Articles

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.

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.

A Survey on Quantum Computing Architectures: Implications for Electrical Circuit Design and Optimization

Quantum computing, a paradigm shift with the potential to revolutionize fields ranging from cryptography to optimization, is rapidly evolving. This survey delves into the key quantum computing architectures—gate-based and quantum annealing—and their profound impact on circuit design and optimization. Gate-based systems, such as those utilizing superconducting qubits and trapped ions, offer versatile platforms capable of executing a broad array of quantum algorithms. However, they present unique challenges for circuit designers, including noise sensitivity, scalability, and the need for complex error correction circuits. Quantum annealing, exemplified by D-Wave systems, offers a more specialized approach to solving optimization problems, requiring distinct circuit design considerations focused on energy efficiency and coherence preservation.This paper reviews the foundational research on these architectures, compares their respective design challenges, and examines the optimization techniques that have emerged in response to these challenges. Gate count reduction, error correction, and hybrid quantum-classical methods are highlighted as key approaches for improving circuit efficiency and scalability in quantum systems. Furthermore, this survey emphasizes the importance of interdisciplinary collaboration between quantum physicists, electrical engineers, and computer scientists to address the complex challenges associated with quantum circuit design. By combining expertise from these fields, researchers can develop innovative solutions that bridge the gap between theoretical concepts and practical hardware implementations. Ultimately, this survey underscores the need for continued innovation at the intersection of quantum computing and electrical engineering, as researchers strive to overcome current limitations and develop practical, large-scale quantum systems that can harness the full potential of this revolutionary technology.

Application of spiral enhanced whale optimization algorithm in solving optimization problems

The Whale Optimization Algorithm (WOA) is regarded as a classic metaheuristic algorithm, yet it suffers from limited population diversity, imbalance between exploitation and exploration, and low solution accuracy. In this paper, we propose the Spiral-Enhanced Whale Optimization Algorithm (SEWOA), which incorporates a nonlinear time-varying self-adaptive perturbation strategy and an Archimedean spiral structure into the original WOA. The Archimedean spiral structure enhances the diversity of the solution space, aiding the algorithm in escaping local optima. The nonlinear time-varying self-adaptive optimization dynamic perturbation strategy improves the algorithm’s local search capability and enhances solution accuracy. The effectiveness of the proposed algorithm is validated from multiple perspectives using CEC2014 test functions, CEC2017 test functions, and 23 benchmark test functions. The experimental results demonstrate that the enhanced Whale Optimization Algorithm significantly improves population diversity, balances global and local search, and enhances solution accuracy. Additionally, SEWOA exhibits excellent performance in solving three engineering design problems, showcasing its value and wide range of potential applications.

Algorithm XXX: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

Algorithm XXX: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

The Model of the Armament And Military Equipment Repair System

The purpose of the study, the results of which are presented in the article, is to develop a mathematical model of the process of restoring weapons and military equipment (IWT), taking into account their losses due to combat and operational and technical reasons, as well as the production capabilities of repair and restoration bodies (RVOS) of the first and second levels. For the operational solution of the recovery system planning and managing tasks, it is necessary to have models that allow approximate assessment of the system effectiveness at various levels of management. The hypothesis of the study is to increase the efficiency of restoring weapons and military equipment using the forces and means of military repair bodies, field repair brigades (VRB) in the conditions of the operation, as well as the production capacities of enterprises of the local industrial economic base. As criteria for effectiveness evaluation, the indicators characterizing the combat capabilities of military formations for a certain period of military planning in peacetime and wartime are considered. Research methods are mathematical apparatus of the theory of queuing systems and differential equations of 'dynamics of averages', system analysis, comparative analysis, generalization, forecasting, and document analysis. The resulting model establishes a relationship between the input parameters and the output indicators of the recovery system, characterizing the serviceability of the IWT. In this case, the control parameter is a parameter that characterizes the ratio of the number of samples of military equipment repaired in the 1st-level RVR. Results: the developed model can be used for: analyzing the technical support system of troops; solving optimization problems of managing the technical support of troops: finding the optimal ratio of the number of samples of military equipment repaired by the first and second level RVOS; determining the optimal number of field crews for repairing military equipment while ensuring a given level of serviceability of military equipment and minimizing the cost of repairing military equipment.

Pavement Distress Detection Based on the Staged Deep Learning Classifier Approach

Pavement crack detection is a critical task that is essential to ensure the safety of roads and highways. Accurate detection and classification of pavement cracks can help transportation agencies to identify potential maintenance needs and plan appropriate interventions. In this project, we propose a staged deep learning classifier approach for pavement crack detection to provide accurate and comprehensive information about the pavement condition. In this proposed pavement crack detection model, there are four main phases: pre-processing, feature extraction, feature selection, and crack detection. Firstly, raw images are pre-processed through median filtering and histogram equalization for noise removal and contrast enhancement. Next, features such as the improved local binary pattern, gray-level co-occurrence matrix, and gray-level run length matrix are extracted from the pre-processed images. The optimal features are selected using a hybrid optimization model, the tuna customized honey badger optimization algorithm, which combines the honey badger algorithm and tuna swarm optimization. This new hybrid optimization model will enhance the search strategy for solving optimization problems. The loss function of an augmented convolutional neural network (A-CNN) is modified to compute the root mean square error instead of the entropy-based loss function. The final detected outcomes (presence or absence of cracks) are acquired from the A-CNN.

Assessing the behavior of highly damped multilayered structures with controllable patches using condensation models

This study presents the finite element modeling of an adaptive sandwich structure that can be configured to exhibit various behaviors depending on the arrangement of the temperature fields in its core, which is made of a shape memory polymer with outstanding damping capacity. The sandwich structure is divided into patches corresponding to homogeneous temperature fields. Each patch is modeled as an equivalent thin plate using a condensation model and the effective properties are determined by preserving the real part of bending, shear (transverse) and extension (quasi-longitudinal) wavenumbers. The damping loss factor is estimated independently using the forced response from an analytical discrete model of the sandwich structure and the Power Input Method. Two different configurations of the sandwich structure are presented: in the first, the modal behavior of the sandwich structure is slightly affected; In the second, vibrations are reduced throughout the frequency range. The use of a suitable condensation model can be particularly interesting for solving optimization problems and determining optimal configurations. The behavior of the sandwich structure can be evaluated with reduced computational cost whenever an update of the temperature fields is required.

Optimizing acoustic black hole structures for vibration control in beams: a comprehensive analysis

Acoustic black holes (ABH) have caught the attention of researchers because of their potential to absorb sound and control vibrations. This study presents an analytical framework that determines reflection coefficients in ABH structures. It focuses on implementing an acoustic black hole with a power-law tapered profile on beams. Moreover, this research investigates how various geometric shapes affect Damping Loss Factor (DLF) coefficients. This helps identify optimal approaches to optimize ABH structures based on specific requirements. The finite element method and a topology optimization solver were used to optimize various parameters systematically. The aim is to reduce weight and response, thereby improving the efficiency of ABH designs, especially in low-frequency insulation applications. The results demonstrate that ABH exhibits excellent performance in suppressing vibrations.

Solving optimization problems in steady operation of regulated asynchronous motor

Solving optimization problems in steady operation of regulated asynchronous motor

Computing Euclidean distance and maximum likelihood retraction maps for constrained optimization

Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to approximate the exponential map and return to the manifold. For many common matrix manifolds, retraction maps are available, with more or less explicit formulas. For implicitly-defined manifolds, suitable retraction maps are difficult to compute. We therefore develop an algorithm which uses homotopy continuation to compute the Euclidean distance retraction for any implicitly-defined submanifold of Rn, and prove convergence results.We also consider statistical models as Riemannian submanifolds of the probability simplex with the Fisher metric. Replacing Euclidean distance with maximum likelihood results in a map which we prove is a retraction. In fact, we prove the retraction is second-order; with the Levi-Civita connection associated to the Fisher metric, it approximates geodesics to second-order accuracy.

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.