Solution Of Optimization Problem Research Articles

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.

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

Optimal design of elastic plates

This paper is concerned with optimal design problems in the setting of the Kirchhoff–Love model for pure bending of a thin solid symmetric plate under a transverse load. For two isotropic elastic materials with a prescribed amount, the goal is to find their rearrangement within the domain that forms a least compliant structure. The homogenization method is used as a relaxation tool to overcome the lack of a classical solution of optimal design problem. Neccessary conditions of optimality were derived and an optimality criteria method for the single state compliance minimization problems is developed and tested on several examples.

Convex Combination Search Algorithm: A Novel Metaheuristic Optimization Algorithm for Solving Global Optimization and Engineering Design Problems

In this paper, a novel metaheuristic optimization algorithm (MHOA) called convex combination search (CCS) is proposed as a solution to global optimization problems and engineering design problems. CCS is based on a combination of rules that depend upon the concept of the linear convex combination. These rules are mathematically modeled to guarantee the variety of solutions at the initialization stage and achieve equilibrium between exploitation, exploration capabilities at the generation stage, the algorithm’s convergence, and robustness. A detailed mathematical model of the algorithm is offered. As an advantage for the CCS algorithm, it requires just two parameters which are the population size and the number of generations for determining the global optimal solution of any optimization problem. The effectiveness of the suggested algorithm is investigated on 17 unconstrained multimodal test functions, and 7 constrained benchmark problems having different characteristics. In addition, five engineering design challenges are resolved to confirm the robustness and dependability of CCS in resolving engineering applications. The efficiency and competitiveness of the proposed algorithm were illustrated in comparison with other methods. A statistical analysis of the results has been carried out to illustrate the competitiveness and power effectiveness of the proposed algorithm. Finally, the sensitivity of the CCS parameters is presented to show the sensitivities of these parameters to the performance of the proposed algorithm.

Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces

Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

Subdifferential calculus and ideal solutions for set optimization problems

Subdifferential calculus and ideal solutions for set optimization problems

Using Genetic Algorithms and Core Values of Cooperative Games to Solve Fuzzy Multiobjective Optimization Problems

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be transformed into a scalar optimization problem, which is a conventional optimization problem. Usually, the assignments of suitable coefficients to the corresponding scalar optimization problem are subjectively determined by the decision makers. However, these assignments may cause some biases by their subjectivity. Therefore, this paper proposes a mechanical procedure to avoid this subjective biases. We are going to formulate a cooperative game using the α-level functions of the multiple fuzzy objective functions. Under this setting, the suitable coefficients can be determined mechanically by involving the core values of the cooperative game, which is formulated using the multiple fuzzy objective functions. We shall prove that the optimal solutions of the transformed scalar optimization problem are indeed the nondominated solutions of fuzzy multiobjective optimization problem. Since the core-nondominated solutions will depend on the coefficients that are determined by the core values of cooperative game, there will be a lot of core-nondominated solutions that will also depend on the corresponding coefficients. In order to obtain the best core-nondominated solution, we shall invoke the genetic algorithms by evolving the coefficients.

Prediction of monkeypox infection from clinical symptoms with adaptive artificial bee colony-based artificial neural network

AbstractIn 2022, the World Health Organization declared an outbreak of monkeypox, a viral zoonotic disease. With time, the number of infections with this disease began to increase in most countries. A human can contract monkeypox by direct contact with an infected human, or even by contact with animals. In this paper, a diagnostic model for early detection of monkeypox infection based on artificial intelligence methods is proposed. The proposed method is based on training the artificial neural network (ANN) with the adaptive artificial bee colony algorithm for the classification problem. In the study, the ABC algorithm was preferred instead of classical training algorithms for ANN because of its effectiveness in numerical optimization problem solutions. The ABC algorithm consists of food and limit parameters and three procedures: employed, onlooker and scout bee. In the algorithm standard, artificial onlooker bees are produced as much as the number of artificially employed bees and an equal number of limit values are assigned for all food sources. In the advanced adaptive design, different numbers of artificial onlooker bees are used in each cycle, and the limit numbers are updated. For effective exploitation, onlooker bees tend toward more successful solutions than the average fitness value of the solutions, and limit numbers are updated according to the fitness values of the solutions for efficient exploration. The performance of the proposed method was investigated on CEC 2019 test suites as examples of numerical optimization problems. Then, the system was trained and tested on a dataset representing the clinical symptoms of monkeypox infection. The dataset consists of 240 suspected cases, 120 of which are infected and 120 typical cases. The proposed model's results were compared with those of ten other machine learning models trained on the same dataset. The deep learning model achieved the best result with an accuracy of 75%. It was followed by the random forest model with an accuracy of 71.1%, while the proposed model came third with an accuracy of 71%.

Multi-objective optimization for low hydrogen consumption and long useful life in fuel cell emergency power supply systems

The power system using hydrogen fuel cells (FCs) as the primary energy source holds significant potential for applications in emergency fields such as post-disaster relief and outdoor power supply. The operational environment of the FC emergency power supply system (FCEPSS) is challenging, with long continuous operation time, difficulties in hydrogen supply, high maintenance costs, and, accordingly, requirements for hydrogen consumption and useful life of FCs are heightened. Hence, this paper proposes a multi-objective energy management strategy (EMS) for FCEPSS. First, the structure of FCEPSS is designed based on the demand analysis in emergency scenarios. Then, the hydrogen consumption and life degradation models of FCEPSS are established. Aiming at the multi-objective optimization problem of minimizing hydrogen consumption and life degradation value in the FCEPSS, an improved multi-objective optimization algorithm is proposed. This paper converts complex constraints into the penalty term and incorporates it as one of the objectives, constructing a three-objective optimization model. To enhance the solution of multi-objective optimization problems, an improved strategy based on relaxation-tightening and three-objective sorting is proposed. Combining the fast non-dominated sorting genetic algorithm-II and the above improved strategy, an improved multi-objective optimization algorithm (IMOOA) is constructed. In the simulation, the advantages of the proposed IMOOA algorithm are verified. In the experimental part, compared with the logical threshold strategy, the proposed strategy saves 0.60% of hydrogen consumption and reduces 5.65% of life degradation within 24 h, respectively. Finally, the superiority of the multi-objective EMS utilizing the IMOOA is demonstrated.