Solving Optimization Problems Research Articles

Parameter estimation in a whole-brain network model of epilepsy: Comparison of parallel global optimization solvers.

The Virtual Epileptic Patient (VEP) refers to a computer-based representation of a patient with epilepsy that combines personalized anatomical data with dynamical models of abnormal brain activities. It is capable of generating spatio-temporal seizure patterns that resemble those recorded with invasive methods such as stereoelectro EEG data, allowing for the evaluation of clinical hypotheses before planning surgery. This study highlights the effectiveness of calibrating VEP models using a global optimization approach. The approach utilizes SaCeSS, a cooperative metaheuristic algorithm capable of parallel computation, to yield high-quality solutions without requiring excessive computational time. Through extensive benchmarking on synthetic data, our proposal successfully solved a set of different configurations of VEP models, demonstrating better scalability and superior performance against other parallel solvers. These results were further enhanced using a Bayesian optimization framework for hyperparameter tuning, with significant gains in terms of both accuracy and computational cost. Additionally, we added a scalable uncertainty quantification phase after model calibration, and used it to assess the variability in estimated parameters across different problems. Overall, this study has the potential to improve the estimation of pathological brain areas in drug-resistant epilepsy, thereby to inform the clinical decision-making process.

Enhancing Reptile search algorithm with shifted distribution estimation strategy for coverage optimization in wireless sensor networks

The rapid development of the Internet of Things (IoT) has extensively promoted the development of Wireless Sensor Networks (WSNs), an essential technology for series displaying perception and data collected from the physical world. In densely distributed areas, sensor nodes are unevenly distributed, which leads to the network coverage build-up and the consequent efficiency and effectiveness of WSNs. To address this issue, this paper proposes a new method for WSN coverage optimization based on the Reptile Search Algorithm (RSA). In the past, the Reptile Search algorithm has been used to solve optimization problems, which means it can improve different processes. However, the RSA needs to track the trajectory of optimal individuals in each iteration, which will ignore non-optimal individuals' bioeconomic characteristics. Therefore, the paper introduces a distribution estimation strategy into the RSA framework, which can fully mine all the positional information hidden in the entire population. We selected several functions as optimization test benchmark functions to evaluate the feasibility of the proposed method. This paper compares the proposed improved RSA with the standard RSA and some traditional optimization algorithms. The result has been calculated through a series of experiments on network coverage optimization, and the change of parameters also determines the effect of the RSA in the optimization of network coverage. The simulated results of the three similar network coverage optimization experiments show that the improved RSA can be used efficiently within different scenarios.

Globally Optimal Relative Pose and Scale Estimation from Only Image Correspondences with Known Vertical Direction

Installing multi-camera systems and inertial measurement units (IMUs) in self-driving cars, micro aerial vehicles, and robots is becoming increasingly common. An IMU provides the vertical direction, allowing coordinate frames to be aligned in a common direction. The degrees of freedom (DOFs) of the rotation matrix are reduced from 3 to 1. In this paper, we propose a globally optimal solver to calculate the relative poses and scale of generalized cameras with a known vertical direction. First, the cost function is established to minimize algebraic error in the least-squares sense. Then, the cost function is transformed into two polynomials with only two unknowns. Finally, the eigenvalue method is used to solve the relative rotation angle. The performance of the proposed method is verified on both simulated and KITTI datasets. Experiments show that our method is more accurate than the existing state-of-the-art solver in estimating the relative pose and scale. Compared to the best method among the comparison methods, the method proposed in this paper reduces the rotation matrix error, translation vector error, and scale error by 53%, 67%, and 90%, respectively.

Exploring Markov Decision Processes: A Comprehensive Survey of Optimization Applications and Techniques

Markov decision process is a dynamic programming algorithm that can be used to solve an optimization problem. It was used in applications like robotics, radar tracking, medical treatments, and decision-making. In the existing literature, the researcher only targets a few applications area of MDP. However, this work surveyed the Markov decision process’s application in various regions for solving optimization problems. In a survey, we compared optimization techniques based on MDP. We performed a comparative analysis of past work of other researchers in the last few years based on a few parameters. These parameters are focused on the proposed problem, the proposed methodology for solving an optimization problem, and the results and outcomes of the optimization technique in solving a specific problem. Reinforcement learning is an emerging machine learning domain based on the Markov decision process. In this work, we conclude that the MDP-based approach is most widely used when deciding on the current state in some environments to move to the next state.

Hybrid Approaches: Combining Computational Mathematics and Artificial Intelligence for Enhanced Performance

The combination of computer mathematics and artificial intelligence (AI) looks like a good way to solve hard problems in many areas. In this outline, the possibility for these two fields to work together to improve problem-solving skills is looked at. Computational mathematics is a thorough way to understand and solve difficult mathematical problems. It is based on numerical analysis, optimization, and mathematical models. Artificial intelligence methods, on the other hand, like machine learning, deep learning, and neural networks, are very useful for making decisions and learning from data. Hybrid techniques can use the best parts of both computational mathematics and artificial intelligence to solve problems that standard approaches might not be able to solve. These methods make it possible to create complex algorithms that can quickly solve optimization problems, model complicated systems, and draw useful conclusions from big datasets. For example, hybrid methods can improve the accuracy and speed of computing in engineering and science exercises by mixing numerical methods with machine learning models for mistake correction and flexible improvement. Hybrid methods make it easier for people from different fields to work together, connecting academic theory to real-world uses. Researchers and professionals from different fields can come together to come up with new solutions that use the skills of both computational mathematics and artificial intelligence. This cross-disciplinary synergy can be seen in areas like banking, healthcare, and defense, where using both mathematical rigor and AI-driven predictive analytics can help with making difficult decisions. When you put together computer mathematics and AI, you can do new kinds of core study. AI can be used to study huge sets of solutions and find trends in data. This helps researchers learn more about mathematical events and make programs that work better. This looping process of learning and optimizing allows for constant improvement and revision, which finds new answers to math problems that have been around for a long time. Combining computational mathematics and artificial intelligence into hybrid methods has a huge amount of promise to speed up study and new ideas in many areas.

Conceptions of The Instruction of Maxima And Minima Problem-Solving to Calculus Students: A Study on University Education

Theoretical Framework: The teaching of calculus is indispensable in many scientific careers, and maxima and minima problems hold a prominent place among its contents. However, students often encounter difficulties solving optimization problems. Objective: Considering this, our study aims to determine the perception of calculus teachers regarding the importance of contextualization and the use of diverse resources when they teach these problems. Method: Our study has a descriptive nature and to achieve our goal, a sample of university calculus professors from the Dominican Republic was analyzed using a Likert-type test. Results and Discussion: The results demonstrate a favorable trend towards contextualization and the integration of resources in teaching maxima and minima problems, although some professors still prefer traditional methods based on textbooks. Research Implications: The findings highlight the importance of exploring contextual teaching strategies, promoting resource diversity, and adopting innovative pedagogical approaches to enhance learning, comprehension, and student motivation.

Ant Colony Optimization for solving Directed Chinese Postman Problem

The Chinese Postman Problem (CPP) is a well-known optimization problem involving determining the shortest route, modeling the system as an undirected graph, for delivering mail, ensuring all roads are traversed while returning to the post office. The Directed Chinese Postman Problem (DCPP) extends the Chinese Postman Problem (CPP), where the underlying graph representing the system incorporates exclusively directed edges. Similarly to CPP, this problem has plenty of applications in route optimization, interactive system analysis, and circuit design problems. However, due to the added constraint (directionality of edges), DCPP results are more challenging to solve. Although methods to solve it in literature are proposed, typically by using minimum-cost-flow algorithms, the meta-heuristics approaches proposed to deal with it are very limited. In this paper, we propose an innovative meta-heuristic approach to solve DCPP by using an ant colony optimization (ACO) algorithm, i.e., an algorithm that simulates in a simplified way the behavior of some species of ants to solve optimization problems. The efficiency of our ant colony optimization for solving the Directed Chinese Postman Problem (ACO-DCPP) is measured by comparing the ACO outcomes with the results obtained by a recursive algorithm that explores all the possible solutions. Results show that ACO-DCPP is stable and gets the global optimum frequently by using an extremely limited number of solutions explored.

Convex Approach to Real-Time Multiphase Trajectory Optimization for Urban Air Mobility

Electric vertical takeoff and landing technology has emerged as a promising solution to alleviate ground transportation congestion. However, the limited capacity of onboard batteries enforces hard time constraints for vehicle operations in a complex urban environment. Therefore, a constrained, real-time trajectory optimization method is necessary to enable safe and energy-efficient vehicle flight. Unfortunately, most existing trajectory optimization methods suffer from low computational efficiency, unpredictable convergence processes, and strong dependence on a good initial trajectory. In this paper, we employ a successive convex programming approach to solve the multiphase minimum-energy-cost electric vertical takeoff and landing vehicle trajectory optimization problem for urban air mobility applications. The main contribution is the development and validation of two novel convexification methods that find approximate optimal solutions to the multiphase nonlinear trajectory optimization problem in real time by solving a sequence of convex subproblems. Specifically, the first method transforms the original nonlinear problem into a sequence of second-order cone programming problems through a convenient change of variables and lossless convexification, while the second approach achieves a similar goal without the need for control convexification. The resulting convex subproblems can be solved reliably in real time by advanced interior point methods. The proposed methods are demonstrated through numerical simulations of two different urban air mobility scenarios and compared with the solution obtained from GPOPS-II, a state-of-the-art general-purpose optimal control solver. Our proposed sequential convex programming methods can obtain near-optimal solutions with faster computational speed than GPOPS-II.

Chaotic RIME optimization algorithm with adaptive mutualism for feature selection problems

The RIME optimization algorithm is a newly developed physics-based optimization algorithm used for solving optimization problems. The RIME algorithm proved high-performing in various fields and domains, providing a high-performance solution. Nevertheless, like many swarm-based optimization algorithms, RIME suffers from many limitations, including the exploration-exploitation balance not being well balanced. In addition, the likelihood of falling into local optimal solutions is high, and the convergence speed still needs some work. Hence, there is room for enhancement in the search mechanism so that various search agents can discover new solutions. The authors suggest an adaptive chaotic version of the RIME algorithm named ACRIME, which incorporates four main improvements, including an intelligent population initialization using chaotic maps, a novel adaptive modified Symbiotic Organism Search (SOS) mutualism phase, a novel mixed mutation strategy, and the utilization of restart strategy. The main goal of these improvements is to improve the variety of the population, achieve a better balance between exploration and exploitation, and improve RIME's local and global search abilities. The study assesses the effectiveness of ACRIME by using the standard benchmark functions of the CEC2005 and CEC2019 benchmarks. The proposed ACRIME is also applied as a feature selection to fourteen various datasets to test its applicability to real-world problems. Besides, the ACRIME algorithm is applied to the COVID-19 classification real problem to test its applicability and performance further. The suggested algorithm is compared to other sophisticated classical and advanced metaheuristics, and its performance is assessed using statistical tests such as Wilcoxon rank-sum and Friedman rank tests. The study demonstrates that ACRIME exhibits a high level of competitiveness and often outperforms competing algorithms. It discovers the optimal subset of features, enhancing the accuracy of classification and minimizing the number of features employed. This study primarily focuses on enhancing the equilibrium between exploration and exploitation, extending the scope of local search.

Zeroth-order gradient tracking for decentralized learning with privacy guarantees

This paper proposes a differential privacy decentralized zeroth-order gradient tracking optimization (DP-DZOGT) algorithm for solving optimization problems of decentralized systems, where the gradient information of the function is unknown. To address the challenge of unknown gradient information, a one-point zeroth-order gradient estimator (OPZOGE) is constructed, which can estimate the gradient based on the function value and guide the update of decision variables. Additionally, to prevent privacy leakage of agents, random noise is introduced into both the state and the gradient of the agents, which effectively enhances the level of privacy protection. The linear convergence of the proposed DP-DZOGT under a fixed step size can be guaranteed. Moreover, it has been applied to the fields of smart grid (SG) and decentralized federated learning (DFL). Finally, the effectiveness of the algorithm is validated through three numerical simulations.

Quantum optimization algorithm based on multistep quantum computation

We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation, and apply the algorithm for solving optimization problems with continuous variables. We construct the state space of the problem by discretizing the variables of the problem, and divide the state space according to the function values of the vectors of the state space. By comparing the function values of the vectors with a series of threshold values in decreasing order, we construct a sequence of Hamiltonians where the search space of a Hamiltonian is nested in that of the previous one. By applying a multistep quantum computation process for finding the ground state of the last Hamiltonian, the optimal vector of the state space of the problem is located in a small search space and can be determined efficiently. One of the most difficult problems in optimization algorithms is that a trial vector is trapped in a deep local minimum while the global minimum is missed, this problem can be alleviated in our algorithm and the run time is proportional to the number of the steps of the algorithm, provided that the reduction rate of the search spaces is polynomial large. We discuss the implementation of the algorithm and test the algorithm for some test functions.

Dollmaker Optimization Algorithm: A Novel Human-Inspired Optimizer for Solving Optimization Problems

Dollmaker Optimization Algorithm: A Novel Human-Inspired Optimizer for Solving Optimization Problems

DEVELOPMENT AND APPLICATION OF AN INTEGRATED INFORMATION MODEL FOR OPTIMIZING LAND USE AND FORECASTING YIELDS IN AGRICULTURAL PRODUCTION

The paper presents the development of a conceptual information model for optimizing land use and crop forecasting in agriculture, implemented using the PHP programming language, Javascript and the MYSQL database management system. The model is designed to solve optimization problems in various fields such as logistics, manufacturing, finance, etc. As part of the work, an information model was developed, which is a set of data, algorithms and software modules designed to solve optimization problems. The model is implemented based on PHP, Javascript, and MYSQL technologies. The model allows you to solve optimization problems of varying complexity using various optimization methods such as linear programming, nonlinear programming, artificial intelligence methods, etc. The model can be applied to solve optimization problems in various fields. In addition, the model allows you to solve optimization problems with a high degree of accuracy and in a short time, and also has a user-friendly interface that allows users to easily and quickly set optimization tasks. An information model has been developed that will make it possible to predict the harvest taking into account data on weather, soil, crops and historical yield data, as well as optimize land use taking into account data on soil type, climate, crop rotation and financial indicators. The developed information model can improve the efficiency and sustainability of agricultural production. The model can be used by agronomists and farmers to make more informed decisions. The model takes into account data on soil type, climate, crop rotation and financial indicators to optimize land use.

Hybridize the Dwarf Mongoose Optimization (DMO) Algorithm to Obtain the Optimal Solution for Solve Optimization Problems

Hybridize the Dwarf Mongoose Optimization (DMO) Algorithm to Obtain the Optimal Solution for Solve Optimization Problems

Refinement of Jensen Mercer and Hermite–Hadamard-Mercer type inequalities for generalized convex functions on co-ordinates with their computational analysis

In the current study, the Jensen-Mercer inequality is extended to co-ordinated h-convex functions. Additionally, a novel inequality is employed to derive Hermite–Hadamard-Mercer type inequalities for h-convex functions defined on the co-ordinates of a rectangle in the plane. These developments not only reinforce the core tenets of convex analysis but also expand the applicability of Hermite-Hadamard-Mercer type inequalities to generalized convex functions on co-ordinates. This provides valuable tools for data analysis and optimization problem-solving. The practical utility and efficacy of this generalized inequality in real-world scenarios involving co-ordinates are demonstrated through a computational study. Mathematics Subject Classification: 26D10, 26D15, 26A51, 34A08.

Development of a method for managing technical systems using a bio-inspired algorithm

Today’s management solutions depend precisely on the successful solution of optimization problems, which are discontinuous, undifferentiated and multimodal. One of the approaches to increase the efficiency of solving optimization problems is bio-inspired algorithms. The object of the study is complex dynamic objects. The subject of the study is the decision-making process in the problems of managing complex dynamic objects. A management method using a bio-inspired algorithm is proposed. The research is based on the goose algorithm – for finding a solution to the state of dynamic objects with a hierarchical structure. Evolving artificial neural networks are used to train goose agents (GA) and an advanced genetic algorithm is used to select the best ones in the combined swarm algorithm. The originality of the proposed method lies in setting GA taking into account the uncertainty of the initial data, improved global and local search procedures. Also, the originality of the study lies in determining GA food locations, which allows choosing the priority of search in a given direction. The next element in the originality of the study is the ability to determine the indicators of guard GA, which allows adjusting the amount of time during which the GA flock will be located. Another original element of the study is the determination of the initial velocity of each GA. This makes it possible to optimize the speed of conducting exploration by each GA in a certain research direction. The method allows increasing the efficiency of data processing at the level of 10–12 % by using additional improved procedures. The proposed method should be used to solve problems of evaluating complex dynamic objects

Non‐fragile reliable guaranteed cost control and L2‐gain analysis for saturated switched nonlinear systems

AbstractFor the nonlinear continuous‐time saturated switched system, this article investigates the problem of non‐fragile reliable guaranteed cost control of the system. Due to the simultaneous occurrence of controller perturbation, actuator saturation and actuator failure, when designing the cost function, this article considers three scenarios affecting the system performance, controller perturbation, actuator saturation and actuator failure, simultaneously in the cost function, which has not been investigated in the existing literature. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization of non‐fragile reliable guaranteed cost control and the performance index. In order to ensure the exponential stabilization of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and the non‐fragile reliable guaranteed cost state feedback controllers are designed by using the minimum dwell‐time method. Furthermore, by solving optimization problems with linear matrix inequality constraints, the minimum upper bound of the cost function and the performance of the system are determined. At the end of the article, we give a numerical example to verify the effectiveness of the proposed approach.

Parameterless Gene-pool Optimal Mixing Evolutionary Algorithms.

When it comes to solving optimization problems with evolutionary algorithms (EAs) in a reliable and scalable manner, detecting and exploiting linkage information, i.e., dependencies between variables, can be key. In this article, we present the latest version of, and propose substantial enhancements to, the Gene-pool Optimal Mixing Evoutionary Algorithm (GOMEA): an EA explicitly designed to estimate and exploit linkage information. We begin by performing a largescale search over several GOMEA design choices to understand what matters most and obtain a generally best-performing version of the algorithm. Next, we introduce a novel version of GOMEA, called CGOMEA, where linkage-based variation is further improved by filtering solution mating based on conditional dependencies. We compare our latest version of GOMEA, the newly introduced CGOMEA, and another contending linkage-aware EA, DSMGA-II, in an extensive experimental evaluation, involving a benchmark set of 9 black-box problems that can only be solved efficiently if their inherent dependency structure is unveiled and exploited. Finally, in an attempt to make EAs more usable and resilient to parameter choices, we investigate the performance of different automatic population management schemes for GOMEA and CGOMEA, de facto making the EAs parameterless. Our results show that GOMEA and CGOMEA significantly outperform the original GOMEA and DSMGA-II on most problems, setting a new state of the art for the field.

Fleet Repositioning, Flag Switching, Transportation Scheduling, and Speed Optimization for Tanker Shipping Firms

In response to the European Union (EU)’s sanctions on Russian oil products, tanker shipping firms may adopt two strategies to reoptimize their shipping networks. The first strategy is to switch the flag states of tankers that are not eligible to operate on certain routes. The second strategy is to reposition tankers based on their flag states, i.e., moving those tankers that are eligible from other groups to specified routes. To help tanker shipping firms minimize the total operating cost during the planning horizon in the context of EU oil sanctions, including costs of fleet repositioning, flag switching, and fuel, this study investigates an integrated problem of fleet repositioning, flag switching, transportation scheduling, and speed optimization considering the dynamic relationships among fuel consumption, speed, and load. By formulating the problem as a nonlinear integer programming model and applying various linearization techniques to convert the nonlinear model into a linear optimization model solvable by off-the-shelf linear optimization solvers, this study demonstrates the practical application potential of the proposed model, with the longest solution time of less than two hours for a numerical instance with seven routes. Furthermore, through sensitivity analyses on important factors including unit fuel prices, crude oil transportation demand, and the tanker repositioning cost, this study provides managerial insights into the operations management of tanker shipping firms.

Mass‐lumping discretization and solvers for distributed elliptic optimal control problems

AbstractThe purpose of this article is to investigate the effects of the use of mass‐lumping in the finite element discretization with mesh size of the reduced first‐order optimality system arising from a standard tracking‐type, distributed elliptic optimal control problem with regularization, involving a regularization (cost) parameter on which the solution depends. We show that mass‐lumping will not affect the error between the desired state and the computed finite element state , but will lead to a Schur‐complement system that allows for a fast matrix‐by‐vector multiplication. We show that the use of the Schur‐complement preconditioned conjugate gradient method in a nested iteration setting leads to an asymptotically optimal solver with respect to the complexity. While the proposed approach is applicable independently of the regularity of the given target, our particular interest is in discontinuous desired states that do not belong to the state space. However, the corresponding control belongs to whereas the cost as . This motivates to use in order to balance the error and the maximal costs we are willing to accept. This can be embedded into a nested iteration process on a sequence of refined finite element meshes in order to control the error and the cost simultaneously.