Solution Of Optimization Problem Research Articles

Optimality analysis for $$\epsilon $$-quasi solutions of optimization problems via $$\epsilon $$-upper convexificators: a dual approach

Optimality analysis for $$\epsilon $$-quasi solutions of optimization problems via $$\epsilon $$-upper convexificators: a dual approach

Optimal Neumann control of the wave equation with L 1-control cost: the finite-time turnpike property

The finite-time turnpike property describes a situation where the optimal state reaches a steady state after finite time. The steady state is a solution of a static optimal control problem. We study an optimal control problem where the objective functional is the sum of an L 1 -norm control cost with a weight γ > 0 and a differentiable tracking term. We consider a vibrating string with homogeneous Dirichlet conditions at one end and Neumann control action at the other end. The tracking term is defined by the squared L 2 -norm of a non-collocated Neumann-observation. We show that the problem has a unique solution and that due to the non-smoothness of the L 1 -norm for sufficiently large T the optimal state reaches the desired state after a finite time that is equal to the minimal time where exact controllability holds. We also study the effect of smoothing of the control cost on the structure of the optimal control and show that the finite-time turnpike property also holds in the smoothing limit in a strong L 2 -sense.

Exponential stabilization of linear systems with feedback optimization and its application to microgrids control

This paper proposes a feedback-optimization-based control method for linear time-invariant systems, which is aimed to exponentially stabilize the system and, meanwhile, drive the system output to an approximate solution of an optimization problem with convex set constraints and affine inequality constraints. To ensure the exponential stability of the closed-loop system, the original optimization problem is first reformulated into a counterpart that has only convex set constraints. It is shown that the optimal solution of the new optimization problem is an approximate optimal solution of the original problem. Then, based on this new optimization problem, the projected primal–dual gradient dynamics algorithm is used to design the controller. By using the singular perturbation method, sufficient conditions are provided to ensure the exponential stability of the closed-loop system. The proposed method is also applied to microgrid control.

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

Co-Frequency Interference Suppression of Integrated Detection and Jamming System Based on 2D Sparse Recovery

The integrated detection and jamming system employs integrated signals devoid of typical radar signal characteristics for detection and jamming. This allows for the sharing of resources such as waveform, frequency, time, and aperture, significantly enhancing the overall utilization rate of system resources. However, to achieve effective interference, the integrated waveform must overlap with the adversary radar signal within the frequency band. Consequently, the detection echoes are susceptible to the strong co-frequency direct wave generated by the adversary signals. This paper proposes a co-frequency direct wave interference suppression algorithm based on 2D generalized smoothed-l0 norm sparse recovery. The algorithm exploits a joint dictionary comprising our integrated signals and adversary signals, along with the sparsity of 2D range-Doppler maps. The direct solution of the sparse decomposition optimization problem, formulated for the entire echo matrix, enhances the target detection performance for integrated signals even in the presence of robust co-frequency direct wave interference. Furthermore, the proposed method achieves robustness to interference of varying intensities through the adaptive updating and adjustment of relevant parameters. The effectiveness of the proposed method is validated through simulation and experimental results.

Neural network approach to portfolio optimization with leverage constraints: a case study on high inflation investment

Motivated by the current global high inflation scenario, we aim to discover a dynamic multi-period allocation strategy to optimally outperform a passive benchmark while adhering to a bounded leverage limit. We formulate an optimal control problem to outperform a benchmark portfolio throughout the investment horizon. To obtain strategies under the bounded leverage constraint among other realistic constraints, we propose a novel leverage-feasible neural network (LFNN) to represent the control, which converts the original constrained optimization problem into an unconstrained optimization problem that is computationally feasible with gradient descent, without dynamic programming. We establish mathematically that the LFNN approximation can yield a solution that is arbitrarily close to the solution of the original optimal control problem with bounded leverage. We further validate the performance of the LFNN empirically by deriving a closed-form solution under jump-diffusion asset price models and show that a shallow LFNN model achieves comparable results on synthetic data. In the case study, we apply the LFNN approach to a four-asset investment scenario with bootstrap-resampled asset returns from the filtered high inflation regimes. The LFNN strategy is shown to consistently outperform the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the end of the investment horizon.

Merging preferences into the best solution seeking for many-objective optimization problems

Finding out a best solution of the multi-objective optimization problem (MOP) or many-objective optimization problem (MaOP) in the user’s view, is a significant and practical problem. The multi-objective evolutionary algorithms (MOEAs) are applied to solve the MaOPs. Considering many conflicting objectives, they would generate numerous nondominated solutions. Merging the preferences from the user to objectives is an effective way to measure the nondominated solutions and find out the best one (a posterior approach). But the preference relations may be contradictory and highly sparse. In this paper, we propose a process of finding out a best solution with preference relations among attributes (BSPA). In which, we emphasize to test the contradiction and ease the high sparsity of preference relations, then an available preference degree matrix is obtained and merged into the selection of best solution. Based on the proposed process, three methods of NSGA-II-BSPA, P-NSGA-II and P-GA are proposed to solve the best solution of an MOP or MaOP. The experiments are conducted, and the metrics of contradiction probability, feasibility and availability are proposed to measure the BSPA and the vigorous results are obtained. At last, three case studies are adopted to verify the proposed methods’ effectiveness and efficiency. Meanwhile, the hypothesis tests are conducted and the results indicate that the obtained best solutions of proposed methods are satisfiable.

Distributed power system coordination via parametric optimization and ADMM

In this paper we present an efficient model predictive control algorithm for distributed coordination of an electrical power system comprising many spatially distributed controllable units. The coordination problem is formulated using parametric solutions of local optimization problems corresponding to individual subsystems leading to favorable problem structure which can be split across all subsystems and nodes in the network. The structure of the obtained coordination problem is exploited to develop a very efficient solution algorithm based on an ADMM technique. The key features of the overall approach are: (i) private data of individual subsystems are protected, (ii) simple and efficient on-line computations, (iii) parallelization of computation across all subsystems and all nodes in the network. Efficiency of the proposed control strategy is demonstrated on a number of numerical case studies of varying size.

Hybridization of Social Group Optimization and Differential Evolution Algorithm for Solving Speed Reducer Design Problem

Objectives: The objective of this study is to present a hybrid approach named SGO-DE, which combines the Social Group Optimization (SGO) algorithm and differential evolution (DE), aiming to balance exploration and exploitation capacities to improve the accuracy of the optimization algorithm in finding optimal solution for speed reducer design problem. This hybrid approach is simulated for a speed reducer mechanical engineering design problem and the results are compared to several other state-of-the-art optimization algorithms. Method: To improve the exploration and exploitation of SGO, in its acquiring phase Differential Evolution (DE) is introduced. The individual candidate solutions derived from the Improving phase of SGO tries to acquire better values using DE. This helps in striking a better balance between exploration and exploitation, there by achieving improved optimal values and not getting trapped in local optima. The performance of the SGO-DE method is then evaluated and compared to other optimization algorithms through experimentation on the speed reducer design challenge. Findings: The findings of this study indicate that the SGO-DE hybrid approach outperforms other state-of-the-art algorithms by a significant margin in terms of optimization results. The numbers of function evaluations (FEs) significantly go low as less as 6000 compared to other state-of-the algorithms. The comparison demonstrates the efficacy of the SGO-DE method in enhancing solution quality and speeding up execution. Novelty: The novelty of this study lies in the development a hybrid approach of SGO and DE which is efficient in achieving competitive performance in less numbers of function evaluation in speed reducer design problem. This hybridization can strike a better balance between exploration and exploitations. Keywords: SGO, DE, Hybridization, Nature-inspired, Optimization algorithm

Multi-objective topology optimization method for multi-axis random vibration based on hybrid cellular automata

Considering the lack of effective solutions for multi-axis random vibration topology optimization problems, and recognizing that multi-axis random vibration excitation is the most common loading conditions experienced by structures during their operational life, this paper proposes a multi-objective topology optimization method for multi-axis random vibration. By combining Hybrid Cellular Automata (HCA) and Analytic Hierarchy Process (AHP), this method aims to enhance the vibration resistance of structures and extend their fatigue life during the topology optimization phase. To validate the effectiveness and engineering practicality of this method, two engineering cases were designed: a cantilever beam case and an automotive steering knuckle case. Multi-objective topology optimization were conducted with objectives including mass, stiffness, and vibration intensity metric (root-mean-square stress). The two cases demonstrate that the control group's topology model exhibits weaker resistance to random vibrations and shorter fatigue life. In contrast, the validation group's topology model introduces an additional load path near the excitation point, effectively dissipating the impact of vibration excitation. This enhances the structure's vibration resistance and significantly extends its fatigue life.

Recurrent dynamic message passing with loops for epidemics on networks

Several theoretical methods have been developed to approximate the prevalence and threshold of epidemics in networks. Among them, the recurrent dynamic message-passing (rDMP) theory offers state-of-the-art performance by preventing the echo chamber effect at network edges. However, the rDMP theory was derived intuitively in an ad-hoc manner, lacking a solid theoretical foundation, resulting in a probabilistic inconsistency flaw. Furthermore, real-world networks are clustered and full of local loops, such as triangles, while rDMP is based on the assumption of a locally tree-like network structure, potentially making rDMP inefficient in real-world applications. In this work, we first show for recurrent state epidemics that the echo chamber effect exists not only at edges but also in local loops, which rDMP-like methods cannot avoid. We then correct the rDMP deficiency in a principled way, naturally introducing new higher-order dynamic messages, thereby extending rDMP to handle local loops. By linearizing the extended message-passing equations, a new epidemic threshold estimation is provided by the inverse of the leading eigenvalue of a matrix called the triangular non-backtracking matrix. Numerical experiments have been conducted on synthetic and real networks to evaluate our method, whose effectiveness is validated in epidemic prevalence and threshold prediction tasks. In addition, our method has the potential to speed up the solution of immunization, influence maximization, and robustness optimization problems in networks.

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

Positive Competitive Networks for Sparse Reconstruction.

We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (PFCN), to tackle sparse reconstruction problems with nonnegativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including, for example, neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then we prove that the PFCN is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence depends only on a property of the dictionary and is linear-exponential in the sense that initially, the convergence rate is at worst linear and then, after a transient, becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without nonnegativity constraints. Finally, we validate the effectiveness of our approach using a numerical example.

Intelligent optimization algorithm-driven informational teaching model for English reading and writing in universities

English reading and writing are important parts of language teaching. In order to improve the English reading and writing ability of college students, the TLBO (teaching learning-based optimization) algorithm is used in this research to improve the way that English reading and writing are taught in colleges and universities. It is chosen as the primary model for this study. The TLBO algorithm is further optimized in this paper, and a convergence analysis is performed between the optimized model M-TLBO (multi-learning teaching learning-based optimization) algorithm and other TLBO algorithms in order to address the issues that the TLBO algorithm has an excessively single teaching ability and readily settles into local optimal solutions for some large-scale complex problems. In terms of stability and convergence accuracy, M-TLBO outperforms other algorithms. In order to investigate the impact of the M-TLBO algorithm on students’ writing performance, this paper uses the teaching-learning optimization algorithm to conduct a pre-and post-test on students’ English reading and writing performance in five dimensions. The study’s findings revealed that students’ pre-test writing scores had a mean value of 8.4770 and a standard deviation of 1.72449, and that their post-study writing scores had increased by 5.05 points. The English reading and writing information-based teaching model can improve students’ English writing performance. It is hoped to promote the development of English teaching and improve the efficiency of students’ English learning.

Minimum Congestion and Wirelength of Embedding the nth Cartesian Product of K4 into Various Kinds of Grid Networks

Embedding an interconnection network into another network is one of the main problems in parallel processing and computing systems. Interconnection networks in multiprocessing systems facilitate effective communication among various system components. Obtaining the minimum cutwidth, congestion, and wirelength in graph embedding problems is of great significance for network design and architecture, where the minimum is taken over all embedding of guest graphs into host graphs, and addressing these issues can reduce time and cost in embedded design. This work aims to accurately calculate the minimum congestion and wirelength for the [Formula: see text] (the [Formula: see text]th Cartesian product of [Formula: see text]) layout into [Formula: see text]-dimensional, [Formula: see text]-dimensional, and [Formula: see text]-dimensional grids by the optimal solution of edge isoperimetric problem on [Formula: see text].

This is SpArta: Rigorous Optimization of Regionally Resolved Energy Systems by Spatial Aggregation and Decomposition

Energy systems with high shares of renewable energy are characterized by local variability and grid limitations. The synthesis of such energy systems, therefore, requires models with high spatial resolution. However, high spatial resolution increases the computational effort. Here, we present the SpArta method for rigorous optimization of regionally resolved energy systems by Spatial Aggregation and decomposition. SpArta significantly reduces computational effort while providing a near-optimal solution at the full spatial resolution of sector-coupled energy systems.SpArta first reduces problem size by spatially aggregating the energy system using clustering. The aggregated problem is then relaxed and restricted to obtain a lower and an upper bound. The spatial resolution is iteratively increased until the difference between upper and lower bound satisfies a predefined optimality gap.Finally, each cluster of the aggregated problem is redesigned at full resolution. For this purpose, SpArta decomposes the original synthesis problem into subproblems for each cluster. Combining the redesigned cluster solutions yields an optimal feasible solution of the full-scale problem within a predefined optimality gap. SpArta thus optimizes large-scale energy systems rigorously with significant reductions in computational effort. We apply SpArta to a case study of the sector-coupled German energy system, reducing the computational time by a factor of 7.5, compared to the optimization of the same problem at full spatial resolution. As SpArta shows a linear increase in computational time with problem size, SpArta enables computing larger problems allowing to resolve energy system designs with improved accuracy.

Solving Convex Multi-Objective Optimization Problems via a Capable Neural Network Scheme

A neural network architecture is constructed to solve Convex Multi-objective Programming Problem (CMPP). By using the weighted sum method, a single-objective optimization problem related to the CMPP is formulated, in which the scalar objective is summation of weighted original objective functions. The Pareto Optimal Solution (POS) is given by using different values of weights. A neural network framework is then designed for solving the obtained convex problem. Based on employing Lyapunov theory, the proposed model is established to be stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the convex programming problem with different values of weights. The computer simulations shows the feasibility and the efficiency of the suggested model.

A mid-range approximation method assisted by trust region strategy for aerodynamic shape optimization

This paper presents an efficient solution for high-fidelity large-scale aerodynamic shape optimization problems based on several developments in the mid-range approximation method within a trust region optimization framework. The mid-range approximation method is an iterative optimization technique that utilizes mid-range approximations to replace the physical experiments or simulations during the optimization based on the selected trust region strategy. It could transform the original optimization problem into a sequence of approximate sub-optimization problems. In this work, an improved trust region strategy is proposed to contain more optimization states with a flexible and controllable performance to suit different types of problems. A metamodel assembly technique and its gradient-enhanced version are developed to further relax the requirements of computational costs in the mid-range approximation method. Its performance is discussed through a detailed comparison of metamodel performance using a mathematical benchmark case named Vanderplaats scalable beam. The wing only of the Common Research Model is offered to the proposed method for aerodynamic shape optimization. The optimization has 1 design objective, 232 design variables, and 135 design constraints. With all constraints satisfied, the optimized configuration has a 4.85 % improvement in wing drag performance. The shock region is greatly reduced and the wing pressure distribution is smooth and nearly parallel. These results show that the proposed method could achieve the design goal successfully within a reasonable computational cost for large-scale problems.

Time-reliability optimization for the stochastic traveling salesman problem

This paper presents a novel approach to addressing the Stochastic Traveling Salesman Problem (STSP), a classical problem in combinatorial optimization, by integrating travel time and reliability factors into the decision-making process. Traditional TSP models primarily focus on minimizing the total travel distance or cost without considering the reliability of each route. In real-world situations, especially in logistics and network design, it's just as important to have reliable routes. A reliable route means there's a good chance it will be completed successfully and on time. Our research extends the conventional STSP framework by incorporating a reliability metric for each route, alongside the standard travel time metric. A tri-objective optimization model is proposed to minimize the mean and standard deviation of travel time and maximize route reliability simultaneously. A new algorithm called Permutation Binary-Addition-Tree (BAT) is proposed to solve the problem more efficiently when there is uncertainty. Our approach marks a significant step towards more realistic and practical solutions for route optimization problems in dynamic and uncertain environments. We also present a complexity analysis of our model against traditional cost-only TSP solutions, demonstrating the efficacy of considering reliability in route planning.

An Ensemble Approach To Face Recognition In Access Control Systems

An Ensemble Approach To Face Recognition In Access Control Systems