Solution Of Optimization Problem Research Articles

Robust receive beamforming and reflection coefficients optimization in an IRS‐aided decode‐and‐forward relay system

AbstractConsider a decode‐and‐forward wireless relay system assisted by an intelligent reflection surface (IRS), where a robust design on receive beamforming at the relay and reflection coefficients at the IRS is studied. The worst‐case signal‐to‐noise ratio maximization problem is formulated, subject to the reflection coefficients (with either continuous or discrete phases) constraints, under the assumption of imperfect channel state information for all channels. To cope with the hard problem, an equivalent nonconvex quadratic optimization problem with a simpler form is derived, and then the Cauchy‐Schwarz inequality is applied to update the beamforming and a cyclic process is proposed to update the reflection coefficients, where a closed‐form optimal solution is computed in each step. It turns out that the proposed algorithm achieves a locally optimal solution for the robust design problem. Simulation results show that the proposed robust design outperforms an existing non‐robust design and two robust designs via semidefinite relaxation technique.

Displacement smoothness of entropic optimal transport

The function that maps a family of probability measures to the solution of the dual entropic optimal transport problem is known as the Schr¨odinger map. We prove that when the cost function is Ck+1 with k ∈ ℕ* then this map is Lipschitz continuous from the L2-Wasserstein space to the space of Ck functions. Our result holds on compact domains and covers the multi-marginal case. We also include regularity results under negative Sobolev metrics weaker than Wasserstein under stronger smoothness assumptions on the cost. As applications, we prove displacement smoothness of the entropic optimal transport cost and the well-posedness of certain Wasserstein gradient flows involving this functional, including the Sinkhorn divergence and a multi-species system.

Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making

<abstract><p>Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.</p></abstract>

A Fuzzy Bi-objective Mathematical Model for Perishable Medical Goods Supply Chain Network Considering Crisis Situations: An Empirical Study.

In case of crisis, the salvation of injuries depends on the timely provision of medical goods, relief supplies, and equipment. The aim of this study is to present a mathematical model for the supply chain network of perishable medical goods in crisis situation considering the uncertain environment. In this paper, a three-level supply chain including suppliers, intermediate warehouses, and final customers is developed for perishable medical items. The uncertainty of customer demand for service and the spent time in the intermediate warehouses are considered using the exponential distribution functions. Also, it is assumed that the life-cycle of perishable medical goods follow the Weibull distribution function. The model attempts to minimize the total costs of the supply chain and total presence time of perishable items in the whole chain. The LP-Metric method is employed for solving small-sized problems. Due to the NP-Hardness of the problem, the modified Multi-objective Particle Swarm Optimization (MOPSO) and Non-dominated Sorting Genetic Algorithm (NSGA-II) are utilized as 2 well-known and efficient meta-heuristic algorithms for solving large-sized problems. The findings indicate that the meta-heuristic algorithms are efficient in achieving close to the optimal solution for large-size problems in a reasonable time. Also, the results demonstrate that NSGA-II outperforms MOPSO in terms of the high quality solution. Finally, the applicability of the model to real-world problems is demonstrated using a real case study. This paper can assist the planners and decision-makers of perishable drugs supply chain networks in crisis conditions with on-time supplying and distributing the required emergency items.

Optimizing Path-Planning Solutions Obtained by Using Petri Nets Models

This paper addresses the multirobot path planning problem using Petri net (PN) models, integrating insights from linear integer programming with a focus on totally unimodular matrices. Initially, we establish theoretical foundations linking optimal solutions of linear integer problems to their relaxed counterparts. Subsequently, we adapt these findings to robot path planning. The core contribution lies in the introduction of an innovative algorithm designed to iteratively converge on the optimal solution by solving successive continuous linear problems. A key feature of this algorithm is its proven efficiency, which converges to the optimal solution of the integer problem within a theoretically established finite number of iterations. Empirical validation is achieved through the resolution of 300 different path planning scenarios, which include varying numbers of robots, maps, and missions. These cases, solved using both the proposed method and existing techniques, demonstrate the superiority of the proposed method in performance.

OPTIMIZATION OF THE PROCESS OF SELECTION OF TECHNOLOGIES AND EQUIPMENT FOR PURIFICATION OF WASTEWATER OF ELECTROPLATE PRODUCTION

More and more attention is being paid to energy and resource efficiency issues, which is why for existing technological processes the solution of optimization problems comes to the fore in order to optimize material costs. No less important is the assessment of the human resource, as well a minimizing the possibility of errors at the stage of making a decision on the implementation / design of new processes. It is the environmental sphere that is associated with a high degree of investment risks and requires a careful approach to justifying the introduction of environmental technologies. As part of the work done, the concept of automated decision making was proposed and an economic and mathematical model was developed for solving the optimization problem for choosing a technology or equipment for wastewater treatment systems of an enterprise using the example of electrochemical enterprises (electroplating production) at the stage of justifying investments. As the main tool for processing input data, it is proposed to use software systems based on the use of partial-integer linear programming methods. As input parameters of the system, the initial concentrations of pollutants, volume flow and the required cleaning efficiency are selected. The main technologies for the treatment and neutralization of wastewater from galvanic production, which are currently used or included in the list of the best available technologies, are presented, and a model is proposed that allows the choice of methods and instrumentation for multi-stage treatment processes to achieve the required quality of discharged water with minimal integral costs for the creation and operation of the designed system. The proposed mathematical model can be used both as a training tool for training specialists in water treatment, and for management personnel in the process of selecting and justifying environmental protection measures or at the stage of supervision of equipment suppliers.

Analytical and Comparative Study for Optimization Problems

Finding an optimal solution to some problem, like minimizing and maximizing the objective function, is the goal of Single-Objective Optimization (SOP). Real-world problems, on the other hand, are more complicated and involve a wider range of objectives, several objectives should be maximized in such problems. No single solution could be enhanced in all objectives without deteriorating at least one other goal, which is the definition of Pareto-optimality. Understanding the idea of Multi-Objective Optimization (MOP) is thus necessary to find the optimum solution. Multi-objective evolutionary algorithm (MOEA) are made to simultaneously assess many objectives and find Pareto-optimal solutions, MOEA can resolve multi-objective and single-objective optimization problems. This paper aims to introduce a survey study for optimization problem solutions by comparing techniques, advantages, and disadvantages of SOP and MOP with metaheuristics and evolutionary algorithms. From this study, we conduct that the efficiency of MOP lies in the present more than one SOP, but it takes a longer time to process and train and is not suitable for all applications, While SOP is faster and more useful in stock and profit maximization applications. And the posterior techniques are considered the dominant approach to solving multi-objective problems by the use of the field of metaheuristics. Index Terms— Multi-Objective Evolutionary Algorithm, Multi-Objective Optimization, Optimization problem, Objective Function, Single-Objective Optimization.

Accurate solutions of interval linear quadratic regulator optimal control problems with fractional-order derivative

Accurate solutions of interval linear quadratic regulator optimal control problems with fractional-order derivative

Solving Fuzzy Convex Programming Problems via a Projection Neural Network Framework

In this paper, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is given using a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOP by RNNs, we describe a new framework to solve the problem. By reformulating the original program to an interval problem and then weighting problem, the Karush–Kuhn–Tucker (KKT) conditions are obtained. Moreover, we utilize the KKT conditions into a RNN as a capable tool to solve the problem. Besides, the global convergence and the Lyapunov stability of the neuro-dynamic model are established. In the final step, some simulation examples are stated to validate the obtained results. Reported results are compared with some other previous neural networks.

Quafu-Qcover: Explore combinatorial optimization problems on cloud-based quantum computers

We introduce Quafu-Qcover, an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends. Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm (QAOA). It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization (QUBO) model and its corresponding Ising model, which can be subsequently transformed into a weight graph. The core of Qcover relies on a graph decomposition-based classical algorithm, which efficiently derives the optimal parameters for the shallow QAOA circuit. Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers. Compared to a general-purpose compiler, our compiler demonstrates the ability to generate shorter circuit depths, while also exhibiting superior speed performance. Additionally, the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time, utilizing the most recent calibration data from the superconducting quantum devices. This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity. The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time, enabling asynchronous processing. Moreover, it incorporates modules for results preprocessing and visualization, facilitating an intuitive display of solutions for combinatorial optimization problems. We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.

Distributed dynamic task allocation for unmanned aerial vehicle swarm systems: A networked evolutionary game-theoretic approach

Task allocation is a key aspect of Unmanned Aerial Vehicle (UAV) swarm collaborative operations. With an continuous increase of UAVs’ scale and the complexity and uncertainty of tasks, existing methods have poor performance in computing efficiency, robustness, and real-time allocation, and there is a lack of theoretical analysis on the convergence and optimality of the solution. This paper presents a novel intelligent framework for distributed decision-making based on the evolutionary game theory to address task allocation for a UAV swarm system in uncertain scenarios. A task allocation model is designed with the local utility of an individual and the global utility of the system. Then, the paper analytically derives a potential function in the networked evolutionary potential game and proves that the optimal solution of the task allocation problem is a pure strategy Nash equilibrium of a finite strategy game. Additionally, a PayOff-based Time-Variant Log-linear Learning Algorithm (POTVLLA) is proposed, which includes a novel learning strategy based on payoffs for an individual and a time-dependent Boltzmann parameter. The former aims to reduce the system’s computational burden and enhance the individual’s effectiveness, while the latter can ensure that the POTVLLA converges to the optimal Nash equilibrium with a probability of one. Numerical simulation results show that the approach is optimal, robust, scalable, and fast adaptable to environmental changes, even in some realistic situations where some UAVs or tasks are likely to be lost and increased, further validating the effectiveness and superiority of the proposed framework and algorithm.

Modified African Buffalo for Optimal Accommodation of Distributed Energy Resources (DERs) for Annual Energy Loss Minimization in Active Distribution Systems

Abstract. The paper is acquainted with a new optimization technique. Modified African Buffalo optimization (MABO), to solve optimal Distributed Energy Resources (DERs) accommodation problem formulated for annual energy loss minimization esteeming multiple distributed generations and shunt capacitors contemporaneously. To demonstrate the proposed MABO, primitively, the optimal endowment of DERs is obtained for power loss minimization of benchmark 33 – bus test active distribution system (ADN) and simulation resultants are compared with well - established optimization techniques. The optimal DER allocation is also predetermined for depreciation of annual energy loss in conjuration with node voltage deviation over three different load levels. The simulation results obtained are further compared with some of the existing optimization methods. The two-level comparability of optimization methods shows that the Modified African Buffalo method has better searching potency to determine optimal solutions for optimal DERs allocation problems of ADN.

Energy, exergy and exergo-economic analysis of a novel SOFC based CHP system integrated with organic Rankine cycle and biomass co-gasification

This paper proposes a novel SOFC based cogeneration system, consisting of biomass co-gasification, SOFC power generation and ORC waste heat recovery, to achieve the efficient and clean utilization of poultry litter. Based on the conceptual design, the energy, exergy and exergo-economic analysis are conducted, including sensitivity analysis, uncertainty analysis and multi-objective optimization. Results show that when using straw as the co-gasification biomass with poultry litter, the highest energy utilization efficiency of 44.70 % is obtained with the electricity and heat production of 162.02 kW and 52.41 kW, respectively. The biomass gasifier and the SOFC stack have the highest exergy destruction, accounting for 24.43 % and 19.99 % of the total. Sensitivity analysis presents complex results concerning mass fraction of poultry litter, water content, equivalent air ratio and water-carbon ratio, etc. The optimal solution for the current optimization problem is obtained. When poultry litter mass fraction is fixed at 25 %, TSOFC = 852 °C and uf = 0.73, the exergy efficiency is obtained as 41.95 % and the overall exergy cost per unit is obtained as 42.35 $/GJ. This paper investigates a novel cogeneration system relying on the biomass co-gasification of poultry litter, providing a new solution for poultry litter treatment and sustainable development of agriculture, forestry and husbandry.

A proximal forward-backward splitting based algorithmic framework for Wasserstein logistic regression using heavy ball strategy

ABSTRACT In this paper, a forward-backward splitting based algorithmic framework incorporating the heavy ball strategy is proposed so as to efficiently solve the Wasserstein logistic regression problem. The proposed algorithmic framework consists two phases: the first phase involves a gradient descent step extension method, whilst the second phase involves a problem of instantaneous optimisation which balances the minimisation of a regularisation term while maintaining close proximity to the interim state given in the first phase. Then, it proves that the proposed algorithmic framework converges to the optimal solution of the Wasserstein logistic regression problem. Finally, numerical experiments are conducted, which illustrate the efficient implementation for high-dimensional sparsity data. The numerical results demonstrate that the proposed algorithmic framework outperforms not only the off-the-shelf solvers, but also some existing first-order algorithms.

A DIGITAL-AGE APPROACH OF MANUFACTURING OPTIMIZATION

The problem of manufacturing process optimization is one of the most addressed issues across literature concerning the manufacturing field. Until now, this optimization has been based on indirect description of manufacturing, through prefabricated algorithmic models (be they analytical or numerical), as well as on information processing, by composing this kind of models. This is why the optimization is difficult and complicated, even in the case of the simplest processes. This paper presents a new approach of the manufacturing optimization concept, having as main defining aspects: i) The manufacturing process is regarded as decisional instead of physical process, ii) The optimization object is the manufacturing task, defined as product transition from current state up to final state, iii) The manufacturing model consists in a dataset, and, iv) The optimization problem solution consists in task configuring, task accomplishment, and task modeling. According to the new approach, the optimization result consists in the ensemble formed by an optimal structure (optimal configuration of the given task), an optimal process (optimal values of the process variables), and an optimal model (obtained by iterative rebuilding of the manufacturing model). The application of the proposed approach is sampled through a comparative illustration.

A hybrid approach for unit commitment with splitting technique and local search

In the modern electricity market, solving the unit commitment (UC) problem becomes more challenging due to its large number of binary variables and coupling constraints. Therefore, the goal of this paper is to obtain nearly optimal solutions for such complex UC problems within specific time limits. To achieve this, a hybrid approach is presented in this paper, which incorporates a splitting technique and a local search for UC. The hybrid approach involves two steps. In the first step, the augmented Lagrange function (ALF) of UC is decomposed using a splitting technique based on the alternating direction method of multipliers (ADMM). The resulting sub-problems can be effectively solved in a distributed manner by utilizing Lagrange duality theory and binary variable characteristics. Additionally, the penalty parameters of the ALF are updated effectively with the sub-gradient method to diminish the influence of the initial penalty parameters on the algorithm. In the second step, the appropriate relaxation unit is selected using the binary variable characteristics in the current solution of ADMM. Further, the high-quality feasibility of the final solution is ensured through local search. The hybrid approach utilizes ADMM to quickly fix most binary variables in the UC model and then leverages the CPLEX solver to solve the mixed-integer linear programming (MILP) formulation of UC by fixing a large number of binary variables. Consequently, the CPLEX solver needs to branch fewer binary variables, reducing the local search time. The hybrid approach is applied to solve several power systems consisting of up to 1000 units. Compared with the CPLEX solver, the solution of the hybrid approach is found to be stable, and the relative gap of the solution is less than 1 %, demonstrating the effectiveness and performance of the proposed approach while meeting the time limit requirements of the power industry dispatching.

An efficient frame preemption algorithm for time-sensitive networks using enhanced graph convolutional network with particle swarm optimization

Numerous time-sensitive applications are being made possible by the Internet of Things (IoT) phenomenon, which calls for real-time transmission to provide communication services. Applications that depend on low latency have been made possible because of the 5G Ultra-Reliable and Low-Latency Communication (URLLC) scenario. Widely regarded as a possible paradigm for achieving the deterministic transmission guarantees for 5G, Time-Sensitive Networking (TSN) has gained much attention. TSN, on the other hand, is a hybrid traffic system that combines best-effort and time-sensitive traffic, necessitating efficient routing and frame preemption to provide a predictable and limited latency. On the other hand, time-sensitive and non-time-sensitive traffic optimization significantly broaden the issue area and increase the difficulty of establishing a solution. This research presents Enhanced Graph Convolutional Network-based Deep Reinforcement Learning (EGCN-based DRL) solutions for the joint optimization problem in real-world communication contexts. The EGCN is included in deep reinforcement learning to obtain the network's spatial dependency and enhance the generalization performance of the suggested technique (DRL). Specifically, the EGCN approximates the graph convolution kernel using the first-order Chebyshev polynomial, which reduces the complexity of the algorithm and improves the feasibility of the task. Particle Swarm Optimization (PSO) is also employed to hasten the convergence of the model training process. The objective of TSN is to provide deterministic and time-critical communication capabilities over Ethernet networks. TSN aims to enable reliable, low-latency, and synchronized communication between devices, ensuring that time-sensitive data and control messages are delivered with high precision and determinism. The suggested EGCN-based DRL algorithm surpasses cutting-edge techniques in terms of average end-to-end latency, and it also converges quickly, according to numerical simulations.

Estimates of matrix solutions of operator equations with random parameters under uncertainties

We investigate problems of estimating solutions of linear operator equations with random parameters under conditions of uncertainty. We establish that the guaranteed rms estimates of the matrices are found as solutions of special optimization problems under certain observations of the system state. As the output signals of the system, we have observations that are described by linear functions from the solutions of such equations with random right-hand sides, which have unknown second moments. Under the condition that the observation second moments of the right-hand parts and errors belong to certain sets, it is proved that the guaranteed estimates are expressed through solutions of operator equation systems. When the linear operator is given by the scalar product of rectangular matrices, a quasi-minimax estimate and its error are constructed. It is shown that the quasi-minimax estimation error tends to zero when the number of observations tends to infinity. An example of calculating the guaranteed rms estimate of the matrix's trace, which is a solution of a matrix equation with a random parameter, is given.

Giant Armadillo Optimization: A New Bio-Inspired Metaheuristic Algorithm for Solving Optimization Problems.

In this paper, a new bio-inspired metaheuristic algorithm called Giant Armadillo Optimization (GAO) is introduced, which imitates the natural behavior of giant armadillo in the wild. The fundamental inspiration in the design of GAO is derived from the hunting strategy of giant armadillos in moving towards prey positions and digging termite mounds. The theory of GAO is expressed and mathematically modeled in two phases: (i) exploration based on simulating the movement of giant armadillos towards termite mounds, and (ii) exploitation based on simulating giant armadillos' digging skills in order to prey on and rip open termite mounds. The performance of GAO in handling optimization tasks is evaluated in order to solve the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100. The optimization results show that GAO is able to achieve effective solutions for optimization problems by benefiting from its high abilities in exploration, exploitation, and balancing them during the search process. The quality of the results obtained from GAO is compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that GAO presents superior performance compared to competitor algorithms by providing better results for most of the benchmark functions. The statistical analysis of the Wilcoxon rank sum test confirms that GAO has a significant statistical superiority over competitor algorithms. The implementation of GAO on the CEC 2011 test suite and four engineering design problems show that the proposed approach has effective performance in dealing with real-world applications.

A monotone numerical integration method for mean–variance portfolio optimization under jump-diffusion models

We develop a highly efficient, easy-to-implement, and strictly monotone numerical integration method for Mean-Variance (MV) portfolio optimization. This method proves very efficient in realistic contexts, which involve jump-diffusion dynamics of the underlying controlled processes, discrete rebalancing, and the application of investment constraints, namely no-bankruptcy and leverage.A crucial element of the MV portfolio optimization formulation over each rebalancing interval is a convolution integral, which involves a conditional density of the logarithm of the amount invested in the risky asset. Using a known closed-form expression for the Fourier transform of this conditional density, we derive an infinite series representation for the conditional density where each term is strictly positive and explicitly computable. As a result, the convolution integral can be readily approximated through a monotone integration scheme, such as a composite quadrature rule typically available in most programming languages. The computational complexity of our proposed method is an order of magnitude lower than that of existing monotone finite difference methods. To further enhance efficiency, we propose an implementation of this monotone integration scheme via Fast Fourier Transforms, exploiting the Toeplitz matrix structure.The proposed monotone numerical integration scheme is proven to be both ℓ∞-stable and pointwise consistent, and we rigorously establish its pointwise convergence to the unique solution of the MV portfolio optimization problem. We also intuitively demonstrate that, as the rebalancing time interval approaches zero, the proposed scheme converges to a continuously observed impulse control formulation for MV optimization expressed as a Hamilton–Jacobi–Bellman Quasi-Variational Inequality. Numerical results show remarkable agreement with benchmark solutions obtained through finite differences and Monte Carlo simulation, underscoring the effectiveness of our approach.