Solution Of Optimization Problem Research Articles

Algorithm for solution of linear quadratic optimization problem with constraint in the form of equalities on control (pp.404-414)

Algorithm for solution of linear quadratic optimization problem with constraint in the form of equalities on control (pp.404-414)

Improvement of job shop scheduling method based on mathematical optimization and machine learning

This research is concerned with finding the optimal solution of a job shop scheduling problem (JSSP) in a shorter time. As a result of recent trends such as Industry 4.0, machine learning has received a lot of attention, and job shop scheduling methods using machine learning techniques have been developed. We have focused on hybridization of machine learning and mathematical optimization. A JSSP can be formulated as a 0-1 mixed integer programming, and it is expected that the optimal solution can be obtained in a shorter time by providing a good initial solution for the optimization algorithm by means of a learner constructed with data of scheduling performed previously. In our method based on this idea, the processing times of all operations are used as input features to predict a good value of each binary variable which represents the precedence relationship between two operations processed on the same machine. However, the information about the operations which are not related to the intended two operations may work as noise in learning and prediction. In this paper, two limitation methods of input features are proposed. In one of the methods, the processing times of only the operations processed on the same machine that the intended operations are processed are input to the learner. In the other methods, the processing times of those operations and their pre/post operations are input. Numerical experiments showed that these methods are effective at least from the point of view of efficient construction of a learner, because the number of nodes in the input and hidden layers can be reduced. From the aspect of better learning and prediction, both of the methods worked well, that is, they could find the optimal solution in a shorter time than the previous method in the cases where the previous method could not achieve good prediction and took a relatively long solution time. However, in the cases where the previous method could solve the problem in a relatively short time, the limitation methods could not predict a good initial solution and took a relatively long solution time. Between the results of the two limitation methods, there were no difference. These results imply that the processing times of the pre/post operations do not strongly affect performance on learning and prediction and that it is important to analyze what makes a difference between the two cases and utilize the proposed methods in the former case.

On approximate positively properly efficient solutions in nonsmooth semi-infinite multiobjective optimization problems with data uncertainty

On approximate positively properly efficient solutions in nonsmooth semi-infinite multiobjective optimization problems with data uncertainty

Stochastic Simulated Quantum Annealing for Fast Solution of Combinatorial Optimization Problems

Stochastic Simulated Quantum Annealing for Fast Solution of Combinatorial Optimization Problems

A multi-player game equilibrium problem based on stochastic variational inequalities

<p>In this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan's inequality and Lusin's theorem, considering the conditions of lower semi-continuity and concavity. Based on the study of the variational inequality method, we proposed a new algorithm to solve the problem. Furthermore, we analyzed the convergence of the algorithm. Finally, we applied the model to examine the economic benefits of digital currency issuance, corroborating the algorithm's effectiveness with a concrete numerical example.</p>

Distributed Safety Controller Synthesis for Unknown Interconnected Systems via Graph Neural Networks

This paper focuses on distributed controller synthesis for ensuring the safety of large-scale systems with unknown dynamics and known interconnection structures, employing control barrier certificates. Our approach centers on a distributed framework tailored to create control barrier certificates for safety, utilizing the interconnections within large-scale systems. We introduce a novel application of graph neural networks to synthesize these certificates and distributed controllers in a data-driven fashion. The formal correctness of trained networks is subsequently validated through data-driven techniques involving the solution of a sampling-based optimization problem. To illustrate the effectiveness of our methodology, we conduct experiments on a complex interconnected system comprising as many as 1000 components.

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 Cooperative Dynamic Game via Hypergraph Distributed Optimization

We propose a novel cooperative dynamic game with the use of distributed optimization methods. Each coalition has an objective function and the goal of all the coalitions is to optimize the summation of their objectives given the interactions of their agents. The internal interactions are described by a multigraph but we will use directly a stochastic matrix to describe them while the external interactions are described by a hypergraph. The objective functions are quadratic and they encompass information for both types of interactions to highlight their importance in the outcome for the coalitions. The problem is formulated by means of distributed optimization where the actions of the agents at each iteration are the optimum solutions of the sequential optimization problem and the game is evolving by using a tilted matrix mechanism. We show that the optimization problem at each iteration can be solved in one step via a dual decomposition algorithm by exploiting the hypergraph structure of the optimization problem. For the complete description of the dynamic game we propose a switched dynamical system and we demonstrate its convergence numerically.

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.