Solution Of Optimization Problem Research Articles

A Reinforcement Learning-Based Multiobjective Heuristic Algorithm for Multiple-Truck Routing Problems with Heterogeneous Drones

As a result of new technological developments, drone usage has become common in last-mile logistics activities. Owing to the limited flight range of drones, drones may service customers by using trucks as hubs. Although the truck routing problem with drones (TRP-D) has been studied frequently, studies that have addressed this problem in a multiobjective manner are rare. In this study, multiobjective TRP-D is discussed. In this problem, multiple trucks are considered. Each truck is equipped with multiple heterogeneous drones. A multiobjective mixed-integer linear programming (MILP) model is proposed. Since the problem is NP-hard, a reinforcement learning (RL)-based multiobjective heuristic algorithm is proposed to obtain solutions in large-scale cases. A three-phase heuristic feasible-solution-generation algorithm is proposed. The variable neighbourhood descent (VND) algorithm with RL is proposed as a local search algorithm for the multiobjective optimization problem. The results of the proposed heuristic algorithm are compared with the Pareto optimal solutions for small-sized test problems via the augmented ε-constraint (AUGMECON) method and the CPLEX solver. The proposed algorithm is also compared with state-of-the-art multiobjective heuristic algorithms for large-scale problems. According to the results, the proposed algorithm is an efficient multiobjective heuristic algorithm for the addressed problem.

A Second-Order Numerical Method for a Class of Optimal Control Problems

The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the class of control actions used. The first one is that controls are searched for in a given class of functions, which depend on unknown parameters to be found by minimizing an objective functional. The parameter values, in general, may be different at different time intervals. The second feature of the considered problem is that the boundaries of time intervals are also optimized with fixed values of the parameters of the control actions in each of the intervals. The special cases of the problem under study are relay control problems with optimized switching moments. In this work, formulas for the gradient and the Hessian matrix of the objective functional with respect to the optimized parameters are obtained. For this, the technique of fast differentiation is used. A comparison of numerical experiment results obtained with the use of first- and second-order optimization methods is presented.

A Fast iterative shrinkage and threshold algorithm-based least-squares deconvolution technique with application to bearing fault signals

Bearings are commonly subjected to load, transmission, and impact during operation, resulting in bearing failure that ultimately leads to mechanical breakdown. The low energy level of fault-induced impulsive signals, however, renders it vulnerable to being masked by environmental noise and other disturbances present in the vibration signal. To cope with this issue, this paper investigates the application of the finite impulse response (FIR) filter for bearing fault detection. In this work, the estimation of the FIR is formulated as a least squares optimization problem, aiming to minimize the l 2 norm of the FIR and effectively suppress noise and interference sources. The solutions of the least squares optimization problem are obtained using the fast iterative shrinkage–thresholding (FISTA) algorithm. Furthermore, to better select the regularization parameter in our method, an improved gray wolf optimizer (I–GWO) is employed to conduct the parameter selection. Based on these improvements, the proposed FISTA–LSD technique enables rapid and precise detection of fault characteristics upon their occurrence, thereby mitigating the propagation of faults and preventing accidents from happening. Furthermore, with this automated selection process, engineers can save valuable time that would otherwise be spent on trial-and-error approaches. Through its rapid response capabilities and precise fault detection abilities enabled by the FISTA–LSD technique along with I–GWO integration for automatic parameter selection; this FISTA–LSD technique greatly enhances its practical value. The proposed technique is validated through the utilization of both numerical and experimental data.

Solving MADM Problems based on Matrix Games with a New Defuzzification Method for Triangular Intuitionistic Fuzzy Numbers

Abstract: The paper discusses about a new defuzzification method called the Comprehensive Li-Samuel ranking for Triangular Intuitionistic Fuzzy Numbers (TrIFNs) which is improved from the Li-Samuel ranking method associated with membership function and Li-Samuel ranking method associated with non-membership function. The Comprehensive Li-Samuel ranking for TrIFNs is utilised to derive the weights for the Multiple Attribute Decision Making (MADM) problems under TrIFN. The MADM problem is solved based on two-person zero-sum game which is converted into a pair of LPP by using Comprehensive Li-Samuel ranking. The process of transforming decision matrix into a matrix game and deriving decision maker’s and attribute weights from the matrix game are discussed. Numerical illustration is given to justify the viability and effectiveness of the proposed method and comparisons are made with existing ranking methods. The comparison study reveals that the proposed method provides the best maximum optimal solution for the decision problem than the existing methods

Optimal Design of a Sensor Network for Guided Wave-Based Structural Health Monitoring Using Acoustically Coupled Optical Fibers

Guided waves (GW) allow fast inspection of a large area and hence have received great interest from the structural health monitoring (SHM) community. Fiber Bragg grating (FBG) sensors offer several advantages but their use has been limited for the GW sensing due to its limited sensitivity. FBG sensors in the edge-filtering configuration have overcome this issue with sensitivity and there is a renewed interest in their use. Unfortunately, the FBG sensors and the equipment needed for interrogation is quite expensive, and hence their number is restricted. In the previous work by the authors, the number and location of the actuators was optimized for developing a SHM system with a single sensor and multiple actuators. But through the use of the phenomenon of acoustic coupling, multiple locations on the structure may be interrogated with a single FBG sensor. As a result, a sensor network with multiple sensing locations and a few actuators is feasible and cost effective. This paper develops a two-step methodology for the optimization of an actuator–sensor network harnessing the acoustic coupling ability of FBG sensors. In the first stage, the actuator–sensor network is optimized based on the application demands (coverage with at least three actuator–sensor pairs) and the cost of the instrumentation. In the second stage, an acoustic coupler network is designed to ensure high-fidelity measurements with minimal interference from other bond locations (overlap of measurements) as well as interference from features in the acoustically coupled circuit (fiber end, coupler, etc.). The non-sorting genetic algorithm (NSGA-II) is implemented for finding the optimal solution for both problems. The analytical implementation of the cost function is validated experimentally. The results show that the optimization does indeed have the potential to improve the quality of SHM while reducing the instrumentation costs significantly.

An accurate wavelets‐collocation technique for neutral delay distributed‐order fractional optimal control problems

AbstractIn this study, a new class of optimal control problems called neutral delay distributed‐order fractional optimal control problems is introduced, this problem is solved based on an efficient computational scheme. To solve the problem, we derive an exact formula for the Riemann–Liouville fractional integral operator of Genocchi wavelets based on beta functions for the first time. By taking into account this operator, collocation method, and Gauss–Legendre integration formula, the solution of fractional optimal control problems (FOCPs) under consideration is converted to a nonlinear programming one to which existing well‐developed algorithms may be applied. The mentioned scheme is applied to both FOCPs with or without delay. Error analysis associated with the proposed idea is also investigated under several mild conditions. The effectiveness of the strategy is showed by several illustrative examples, furthermore, a comparison with the previous methods highlights the preference of this scheme.

Partially observable optimal control using exponential cost criterion

We consider a partially observable optimal control model in which the system and observation noises are correlated, and the cost criterion is in the form of an exponential of an integral. A new minimum principle criterion is derived and applied to compute the explicit solution of linear exponential Gaussian optimisation problem with correlated noises.

PROBLEMS OF FREIGHT CAR FLOWS DISTRIBUTION ON RAILWAY NETWORKS

Purpose. The purpose of the article is a critical analysis of the existing methods of freight car flows distribution on the railway network and the determination of the directions of these methods adaptation to the operating conditions of the Ukrainian railway transport. Methodology. The research was carried out on the basis of the processing of literary sources in the scientometric databases Scopus and Google Scholar. Results. The distribution of car flows on the railway network is one of the stages of developing a plan for the trains formation. The methods of solving this problem, which are currently used in the practical work of railway transport, were developed during the time of the planned state economy. They are based on the solution of a single-criterion optimization problem aimed at finding such a distribution of car flows on the network that minimizes the cost of transportation for the railway. Reforming the railway transport market with the aim of introducing competition requires the complication of methods of solving the problem of distribution of car flows to take into account the conflicting goals of independent participants in the transport process. The conducted studies showed that the main method of modeling the structure of the railway transport network and the volumes of car flows in it is the theory of graphs; determination of the carrying capacity of elements of the railway network is carried out by the methods of the theory of railway operation, simulation modeling and correlation analysis; determination of the optimal distribution of bandwidth is carried out by comparing competing options, as well as by linear and non-linear programming methods, adaptive control methods using neural networks; the behavior of participants in the transportation process during the allocation of bandwidth is investigated by game theory methods. It has been established that in modern conditions, the task of determining the criterion of equal access to congested sections on the branched railway network and the task of distributing car flows on the network in conditions of fluctuating car flows during transportation by regular trains and trains to order require additional research. Originality. The scientific novelty of the work consists in the critical analysis and generalization of modern methods used to solve the problem of distribution freight car flows distribution on railway networks. Practical value. The practical significance of the results lies in determining the inconsistency of the methods that are practically used on the railways of Ukraine for the distribution of car flows, with the modern conditions of operation of railway transport. Scientific methods have been established that allow to improve approaches to solving the problem of rational distribution of car flows, taking into account the interests of various participants in the transportation process.

Fractional logarithmic Chebyshev cardinal functions: Application for Caputo–Hadamard fractional optimal control problems

This study investigates a specific type of fractional optimization problems, subject to a dynamical system including the Caputo–Hadamard fractional differentiation. In this way, a novel class of basis functions known as the fractional logarithmic Chebyshev cardinal functions is introduced. An operational matrix regarding the Hadamard fractional integral of these fractional functions is derived and employed to develop an efficient numerical method for the provided problem. The established algorithm converts the solution of the primary fractional optimization problem into the solution of an algebraic system of equations by representing the state and control variables via the introduced fractional functions. Two test problems are considered to confirm the effectiveness of the suggested method. The derived outcomes of solving these examples highlight the satisfactory accuracy and efficiency of the designed method.

Doctor and Nurse Scheduling in Emergency Room Using Firefly Algorithm

The Emergency Room (ER) is a part of the hospital responsible for providing initial treatment to patients with life-threatening conditions. The operational hours of the ER follow the schedule set by the hospital. ER must be ready to serve emergency patients 24 hours a day and 7 days a week. Therefore, the scheduling of doctors and nurses in the ER needs to be well-managed to enhance the efficiency of doctors and nurses in responding emergency patients quickly and effectively. In this study, the problem of doctors and nurses scheduling in the ER is solved using the Firefly Algorithm, in which doctors and nurses represented as fireflies. This algorithm is chosen since its ability to find optimal solutions for complex optimization problems. In this research, doctors and nurses can submit schedule requests to improve job satisfaction. The optimization model is constructed by a number of constraints including the availability of doctors and nurses, schedule requests, and the operational needs of the ER. The Firefly Algorithm is applied to find the optimal solution for the model. Simulation results show that this algorithm can produce an optimal schedule, in which 70.6% of doctors' schedule requests and 98.2% of nurses' schedule requests are being fulfilled.

Turret-index optimisation with mathematical programming and metaheuristic approaches

This paper addresses the turret-index optimisation problem by proposing two mathematical programming approaches based on quadratic programming (QP) and constraint programming (CP). In addition, a metaheuristic algorithm based on weighted superposition attraction (WSA) is developed due to the combinatorial complexity of the problem. Despite attempting to linearise the QP formulation for problem resolution, both the QP and Linearized QP models prove ineffective for medium and larger-sized instances, providing solutions only for small-sized problems. In the second mathematical programming approach, a novel CP model is introduced in the literature. While CP can rapidly offer optimal solutions for small-sized problems, it only provides satisfactory solutions for medium and larger-sized problems within the predetermined computational time limits and does not guarantee optimal results. On the other hand, through computational analysis and relevant statistical tests, the proposed WSA algorithm provides the best solutions for all test problems within a reasonable computational time.

Integrated aircraft routing and cargo routing problem for combination airlines

The combination airlines operate both passenger aircraft and freighter aircraft to meet passenger and cargo demand. At present, combination airlines employ a sequential approach to allocating their capacity for passenger and cargo demand. Nevertheless, implementing an integrated resource allocation procedure has the potential to improve overall resource allocation efficiency. In this paper, we introduce an integrated model to help combination airlines integrate their aircraft routing and cargo routing decisions to maximize the expected overall profits derived from both passenger and cargo demand. We considered the stochastic nature of passenger baggage and proposed a set of individual chance constraints to ensure the robustness of the integrated solution. We reformulate the chance constraints using piecewise linear approximation to ensure solution efficiency. In addition, we proposed a column-and-row generation based solution approach that removes the through-connection related constraints at the beginning of the solution process and then adds the columns and rows during the iterations as needed. We proved that the proposed column-and-row generation approach can obtain an optimal solution for the LP relaxation problem. The model and the solution approach were tested in a number of scenarios obtained from a major Chinese combination airline. The computational results show that the combination airline can improve their expected profits by integrating capacity allocation. The results also demonstrated that the proposed column-and-row generation solution approach can decrease the solution time of the integrated model. These findings indicate that the model and the solution method are useful and efficient tools for combination airlines when planning their aircraft and cargo routes.

Multi-objective optimization for a composite pressure vessel with unequal polar openings

Multi-objective parametric optimization problem is presented for overwrapped composite pressure vessels under internal pressure for storage and heating water. It is solved using the developed iterative optimization algorithm. Optimal values of design parameters for the vessel are obtained by varying the set of parameters for composite layers, such as the thickness of layers and radii of polar openings, which influence the distribution of fiber angles along the vessel. The suggested optimization methodology is based on the mechanical solution for composite vessels and the satisfaction of the main failure criteria. An innovative approach lies in the possibility of using the developed optimization methodology for designing vessels with non-symmetrical filament winding, which have unequal polar openings on the domes. This became possible due to the development of a special numerical mechanical finite element model of a composite vessel. A specific Python program provides the creation of a model and controls the exchange of data between the modules of the iterative optimization process. The numerical model includes the determination of the distribution of fiber angles on the domes and cylindrical part of the vessel as well as changes in layer thicknesses. The optimization problem solution is provided using a Multi-Island Genetic Algorithm, this type of method showed its efficiency for such applications, by allowing to avoid local solutions. Thus, optimal parameters of a composite vessel were found by minimizing composite mass and thickness and maximizing the strain energy. Test solutions using the developed methodology are presented for three types of composite materials to evaluate their possibility for integration into the vessel design model.

Theory of classical and modified spaceborne synthetic aperture radar imaging

This paper presents a novel method for spaceborne synthetic aperture radar (SAR) imaging, achieved through the statistical solution of the inverse optimization problem of image reconstruction, specifically focusing on radar cross-section (RCS). The proposed method improves upon traditional techniques by incorporating signal decorrelation, implemented via inverse filtering. A comparative analysis is provided between the modified method and the classical aperture synthesis approach, both of which are grounded in the optimization problem solution within the theory of the maximum likelihood method.

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.

Some new results on rough interval linear programming problems and their application to scheduling and fixed-charge transportation problems

This paper focuses on linear programming problems in a rough interval environment. By introducing four linear programming problems, an attempt is being made to propose some results on optimal value of a linear programming problem with rough interval parameters. To obtain optimal solutions of a linear programming problem with rough interval data, constraints of the four proposed linear problems are applied. In this regard, firstly, the largest and the smallest feasible spaces for a linear constraint set with rough interval coefficients and parameters are introduced. Then, a rough interval for optimal value of such problems is obtained. Further, an upper approximation interval and a lower approximation interval as the optimal solutions of linear programming problems with rough interval parameters are achieved. Moreover, two solution concepts, surely and possibly solutions, are defined. Some numerical examples demonstrate the validity of the results. In particular, a scheduling problem and a fixed-charge transportation problem (FCTP) under rough interval uncertainty are investigated.

A Tree Seed Algorithm with Multi-Strategy for Parameter Estimation of Solar Photovoltaic Models

Tree seed algorithm (TSA), which is one of the metaheuristics algorithms recently proposed for the solution of continuous optimization problems, has an effective algorithmic structure inspired by the relation between trees and seeds. At the same time, the use of two different solution generation mechanisms by depending on the control parameter in TSA aims to balance the exploration and exploitation capabilities of the algorithm. However, when the structure of the algorithm is examined in detail, it is seen that there are some disadvantages such as loss of population diversity and getting stuck in local minimums. To overcome these disadvantages in the basic algorithm, three different approaches (self-adaptive weighting mechanism, chaotic elite learning approach and experience-based learning method) were proposed to TSA under the name of multi-strategies in this study. The algorithm improved with these approaches is named as the multi-strategy-based tree seed algorithm (MS-TSA). MS-TSA was first tested on CEC2017 functions. Then MS-TSA was applied to the problems in the CEC2020 competition and compared with the results of the best performing algorithms in this competition. As a result of the comparisons, MS-TSA was found to be a competitive method on solving benchmark functions. Then, parameter estimation of single diode, double diode and photovoltaic module models using the input data of various solar panels was carried out by the MS-TSA. The results obtained with MS-TSA were compared with both the results of the basic TSA and the results of well-known algorithms in the literature. As a result of the comparative analysis, it was seen that the lowest RMSE value between the simulation data obtained with the proposed MS-TSA and the standard data was obtained by the MS-TSA. In addition, comprehensive performance analyzes of the algorithms were made with the convergence curve, boxplots, current (I) - voltage (V) and power (P) - voltage (V) characteristic curves obtained according to the experimental results. As a result of the experiments and analyses, MS-TSA was found to be a more successful method than the compared algorithms in parameter estimation of PV models.

Advanced method for solving the transportation problem

Transportation problem is one of the predominant areas of operations research. It is a type of linear programming problem designed to minimize the cost of distributing a single product from m sources to n destinations. Transportation problem is widely used as a decision making tool in different fields such as engineering, business management and many others. These types of problems can be solved by general network methods. In this paper The Advanced Method for Solving the Transportation Problem (AMSTP) is proposed to find initial basic feasible solution and optimal solution of transportation problem and compared its results with other existing methods.

Bobcat Optimization Algorithm: an effective bio-inspired metaheuristic algorithm for solving supply chain optimization problems

Supply chain efficiency is a major challenge in today’s business environment, where efficient resource allocation and coordination of activities are essential for competitive advantage. Traditional efficiency strategies often struggle for resources for the complex and dynamic network. In response, bio-inspired metaheuristic algorithms have emerged as powerful tools to solve these optimization problems. Referring to the random search nature of metaheuristic algorithms and emphasizing that no metaheuristic algorithm is the best optimizer for all optimization applications, the No Free Lunch (NFL) theorem encourages researchers to design newer algorithms to be able to provide more effective solutions to optimization problems. Motivated by the NFL theorem, the innovation and novelty of this paper is in designing a new meta-heuristic algorithm called Bobcat Optimization Algorithm (BOA) that imitates the natural behavior of bobcats in the wild. The basic inspiration of BOA is derived from the hunting strategy of bobcats during the attack towards the prey and the chase process between them. The theory of BOA is stated and then mathematically modeled in two phases (i) exploration based on the simulation of the bobcat’s position change while moving towards the prey and (ii) exploitation based on simulating the bobcat’s position change during the chase process to catch the prey. The performance of BOA is evaluated in optimization to handle the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100, as well as to address CEC 2020. The optimization results show that BOA has a high ability in exploration, exploitation, and balance them during the search process in order to achieve a suitable solution for optimization problems. The results obtained from BOA are compared with the performance of twelve well-known metaheuristic algorithms. The findings show that BOA has been successful in handling the CEC 2017 test suite in 89.65, 79.31, 93.10, and 89.65% of the functions for the problem dimension equal to 10, 30, 50, and 100, respectively. Also, the findings show that in order to handle the CEC 2020 test suite, BOA has been successful in 100% of the functions of this test suite. The statistical analysis confirms that BOA has a significant statistical superiority in the competition with the compared algorithms. Also, in order to analyze the efficiency of BOA in dealing with real world applications, twenty-two constrained optimization problems from CEC 2011 test suite and four engineering design problems have been selected. The findings show that BOA has been successful in 90.90% of CEC2011 test suite optimization problems and in 100% of engineering design problems. In addition, the efficiency of BOA to handle SCM applications has been challenged to solve ten case studies in the field of sustainable lot size optimization. The findings show that BOA has successfully provided superior performance in 100% of the case studies compared to competitor algorithms.

Interval-Valued Multiobjective Programming Problems Based on Convex Cones

The new solution concepts of interval-valued multiobjective optimization problems using ordering cone are proposed in this paper. An equivalence relation is introduced to divide the collection of all bounded closed intervals into the equivalence classes. The family of all equivalence classes is also called a quotient set. In this case, this quotient set can turn into a vector space under some suitable settings for vector addition and scalar multiplication. The notions of ordering cone and partial ordering on a vector space are essentially equivalent. It means that an ordering in the quotient set can be defined to study the Pareto optimal solution in multiobjective optimization problems. In this paper, we consider the multiobjective optimization problem such that its coefficients are taken to be the bounded closed intervals. With the help of the convex cone, we can study the Pareto optimal solutions of the multiobjective optimization problem with interval-valued coefficients.