Method For Solution Of Problems Research Articles

Integration of Efficient Techniques Based on Endpoints in Solution Method for Lifelong Multiagent Pickup and Delivery Problem

We investigate the integration of several additional efficient techniques that improve a solution method for the lifelong multiagent pickup-and-delivery (MAPD) problem to reduce the redundancy in the concurrent task execution and space usage of a warehouse map. The lifelong MAPD problem is an extended class of iterative multiagent pathfinding problems where a set of shortest collision-free travel paths of multiple agents is iteratively planned. This problem models a system in automated warehouses with robot-carrier agents that are allocated to pickup-and-delivery tasks generated on demand. In the task allocation to agents, several solution methods for lifelong MAPD problems consider the endpoints of the agents’ travel paths to avoid the deadlock situations among the paths due to the conflict of the endpoints. Since redundancies are found in the problem settings themselves and the concurrency of allocated tasks, several additional techniques have been proposed to reduce them in solution methods. However, there should be opportunities to investigate the integration of additional techniques with improvements for more practical solution methods. As analysis and an improved understanding of the additional solution techniques based on endpoints, we incrementally integrate the techniques and experimentally investigate their contributions to the quality of task allocation and the paths of the agents. Our result reveals significant complementary effects of the additionally integrated techniques and trade-offs among them in several different problem settings.

Solving Maxmin Optimization Problems via Population Games

Population games are games with a finite set of available strategies and an infinite number of players, in which the reward for choosing a given strategy is a function of the distribution of players over strategies. The paper shows that, in a certain class of maxmin optimization problems, it is possible to associate a population game to a given maxmin problem in such a way that solutions to the optimization problem are found from Nash equilibria of the associated game. Iterative solution methods for maxmin optimization problems can then be derived from systems of differential equations whose trajectories are known to converge to Nash equilibria. In particular, we use a discrete-time version of the celebrated replicator equation of evolutionary game theory, also known in machine learning as the exponential multiplicative weights algorithm. The resulting algorithm can be viewed as a generalization of the Iteratively Reweighted Least Squares (IRLS) method, which is well known in numerical analysis as a useful technique for solving Chebyshev function approximation problems on a finite grid. Examples are provided to show the use of the generalized IRLS method in collective investment and in decision making under model uncertainty.

Three-step Collocation Method for Solution of Third Derivative Initial Value Problem

In this research paper, we introduce a novel three-step block method designed to directly tackle third-order initial value problems. This method is crafted through an interpolation and collocation approach, leveraging power series analysis. We conduct a comprehensive examination of the proposed method, ensuring it meets all requisite conditions for rigorous analysis. To assess its efficacy and validity, we employ the method on both highly stiff linear and nonlinear initial value problems, juxtaposing our findings with established approaches in the literature. Our results highlight that the new method exhibits faster convergence compared to existing methods, underscoring its superior performance. Initial value problems, Interpolation and collocation procedure, Three step, Third order

On mathematical problems of two-coefficient inverse problems of ultrasonic tomography

This paper proves the theorem of uniqueness for the solution of a coefficient inverse problem for the wave equation in (with two unknown coefficients: speed of sound and absorption. The original nonlinear coefficient inverse problem is reduced to an equivalent system of two uniquely solvable linear integral equations of the first kind with respect to the sound speed and absorption coefficients. Estimates are made, substantiating the multistage method for two unknown coefficients. These estimates show that given sufficiently low frequencies and small inhomogeneities, the residual functional for the nonlinear inverse problem approaches a convex one. This solution method for nonlinear coefficient inverse problems is not linked to the limit approach as frequency tends to zero, but assumes solving the inverse problem using sufficiently low, but not zero, frequencies at the first stage. For small inhomogeneities that are typical, for instance, for medical tasks, carrying out real experiments at such frequencies does not present major difficulties. The capabilities of the method are demonstrated on a model inverse problem with unknown sound speed and absorption coefficients. The method effectively solves the nonlinear problem with parameter values typical for tomographic diagnostics of soft tissues in medicine. A resolution of approximately 2 mm was achieved using an average sounding pulse wavelength of 5 mm.

A New Method to Solve Matrix Game with Interval Payoffs and its MATLAB Code

Game theory is of substantial significance in diverse domains, acting as a potent instrument to comprehend and assess strategic engagements among rational decision-makers. It formulates mathematical models to represent strategic interactions among rational decision-makers in the competitive world. Due to ambiguity in the real-world problems, acquiring the precise payoff values of a matrix game proves challenging. However, in numerous scenarios, these payoffs fluctuate within specific ranges, making them suitable for consideration as interval numbers. This leads to the formulation of a special form of game problem known as the interval valued game problem (IVGP). Some methodologies exist in the literature to find the optimal strategies as well as the value of game for IVGP, but most of them possess some limitations, resulting in the need for proposing a new methodology to find the optimal strategies and value of game. Thus, in this paper, a new solution method for game problems with payoffs represented as interval numbers is presented, utilizing the fuzzy concept. The process begins by transforming the interval payoffs into fuzzy numbers using a ranking function. Subsequently, these fuzzy payoffs are converted into crisp values, leading to the formulation of the crisp matrix game. The resulting crisp matrix game is then solved using linear programming approach. Additionally, MATLAB code for the proposed method is developed and proposed to streamline the computation process, enhancing comparison and decision-making efficiency, particularly when dealing with large payoff matrices. Furthermore, three numerical examples are provided to illustrate the validity of the proposed approach as well as its MATLAB code. A real-life example of IVGP in the realm of tourism industry is also provided. Finally, a comparative analysis is conducted, comparing the proposed method with some existing methods.

Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems

In this paper, we compare the performances of two Butcher-based block hybrid methods for the numerical integration of initial value problems. We compare the condition numbers of the linear system of equations arising from both methods and the absolute errors of the solution obtained. The results of the numerical experiments illustrate that the better conditioned method outperformed its less conditioned counterpart based on the absolute errors. In addition, after applying our method on some examples, it was discovered that the absolute errors in this work were better than those of a recent study in the literature. Hence, we recommend this method for the numerical solution of stiff and non-stiff initial value problems.

A modified algebraic method of mathematical signal processing in radar problems

A new method for approximate solution of ill-posed inverse problems of reconstructing images of objects with angular resolution exceeding the Rayleigh criterion is proposed and justified, i.e. with super resolution. Angular super-resolution allows you to obtain images of objects with increased clarity and distinguish previously invisible details of images of complex objects. In addition, on this basis, the probability of correct solutions to problems of object recognition and identification increases. Mathematically, the problem is reduced to solving the linear Fredholm integral equation of the first kind of convolution type. Solutions are sought with additional conditions in the form of restrictions on the location and size of the desired radiation source, which makes it possible to regularize the problem. The method is a development of one of the parameterization methods the algebraic method. The solution is sought in the form of a representation of the desired function in the area where the source is located in the form of a series expansion over the input sequence of orthogonal functions with unknown coefficients. Thus, the inverse problem is parameterized and reduced to searching for expansion coefficients. The presented method is based on the use of a priori information about the localization area of the radiation source, or on an estimate of the location and size of this area obtained by scanning the viewing sector with a goniometer system. Using zero values of the function describing the source outside this region, for systems based on antenna arrays it is possible to find tens and even hundreds of expansion coefficients of the desired function in a Fourier series. The solution is constructed in the form of an iterative process with a consistent increase in the number of functions used in the expansion until the solution remains stable. The adequacy and stability of the solutions was verified during numerical experiments using a mathematical model. The results of numerical studies show that the presented methods of digital processing of received signals make it possible to achieve an effective angular resolution 3–10 times higher than the Rayleigh criterion. The proposed method makes it possible to miniaturize the antenna system without degrading its characteristics. Compared to known ones, it is relatively simple, which allows it to be used by systems in real time.

Green logistics park location selection with circular intuitionistic fuzzy CODAS method: The case of Istanbul

In this study, it is aimed to integrate CODAS method with circular intuitionistic fuzzy sets as a new solution method for MCDM problems. Containing a radius notation with degrees of central membership and non-membership degrees is the main advantage of circular intuitionistic fuzzy in decision making. On the other side, Combinative Distance-based Assessment (CODAS) method contains many advantages such as basing on two types of distance calculations (Euclidean and Taxicab distances) comparing with other MCDM methods. When the advantages of circular intuitionistic fuzzy sets and CODAS method are considered, proposed circular intuitionistic fuzzy CODAS method (CIFS-CODAS) presents many superiorities compared to other MCDM techniques. By this way, an application for green logistics park location selection will be handled by using CIFS-CODAS to show the validity of the methodology. After, a comparative analysis with intuitionistic fuzzy CODAS (IFS-CODAS), intuitionistic fuzzy TOPSIS (IFS-TOPSIS) and intuitionistic fuzzy EDAS (IFS-EDAS) methods will be performed for green logistics park location selection problem to confirm the robustness of presented method. Green logistics and Green Deal are also emphasized considering environmental factors as a scope of the article. Finally, the results will be evaluated in the context of the logistics sector and green logistics.

Analisis Sukuk Pada Keuangan Syariah di Indonesia : Systematic Literature Review

The capital market is one of the means used for investment but there are many capital market instruments that contain elements that are not halal (haram) according to Islamic law. This study aims to see Indonesia's position in the Islamic financial market through the role of sukuk. Because considering that Indonesia is a Muslim-majority country and investment in the capital market is the government's effort to encourage and strengthen Indonesia's position on the national and global Islamic financial markets. This research uses a Systematic Literature Review (SLR) approach to journal publications from 2012 to 2022. The results show that research on Islamic finance in Indonesia focuses on 3 topics and trends, namely SBSN, Green Sukuk and Sukuk from an Islamic perspective. And the most frequently used method is the library research method by 50%, the qualitative method by 40% and the Analytic Network Process Problem-Solution Method by 10%.

A graph theory-based solution method for capacitor bank and voltage regulator allocation problems in an unbalanced distribution system

This paper presents a graph theory-based method to solve voltage and reactive power (voltage/var) control problems for a three-phase unbalanced distribution system (UDS). Multi-point fixed and switched capacitor bank (CB), solar distributed generation (SDG) and voltage regulator (VR) location are determined by simple and straightforward graph theory-based measures. The main contribution of this paper is – a single-stage optimisation-based voltage/var control method for UDS unlike commonly used two-stage optimisation methods; to find the location and optimal size of the CB. As the proposed graph theory method used power flow outputs to determine the most suitable nodes for CB and SDG connection, optimisation is needed only for optimal sizing at a certain location which reduces the computational burden. Secondly, optimal placement of VR is used to maintain the voltage level/voltage unbalance of the system. Multiple test cases with optimal configurations of switched CBs and optimal power factor operation-based SDG are used to demonstrate the effectiveness of proposed optimal operation techniques for overall improvement of performance parameters of UDS.

Advances in partial disassembly line balancing: A state-of-the-art review

As sustainable manufacturing practices increasingly prioritize the efficient and environmentally conscious disassembly of products, understanding the nuances of partial disassembly line balancing (PDLB) becomes essential. In our study, we conducted an in-depth analysis of 53 PDLB studies, published from 2008 to 2024, to understand the current trends and gaps in this domain. Our research methodology involved a systematic collection of material, descriptive analysis, careful category selection, and rigorous material evaluation. This approach enabled us to construct a comprehensive taxonomy tailored to PDLB, distinguishing it from classical disassembly line balancing (DLB) literature. Our findings reveal a noticeable surge in PDLB research in the last three years, reflecting its growing relevance in sustainable manufacturing. The study highlights that deterministic disassembly conditions, economic performance indicators, and iterative heuristic approaches are the focal points in recent PDLB research. This insight is critical for guiding future investigations in the field. Our taxonomy not only categorizes existing research in PDLB but also sheds light on under-explored areas, offering a clear direction for upcoming studies. This paper contributes to the literature by providing a detailed review of PDLB-specific elements such as problem characteristics, disassembly levels, objectives, constraints, and solution methods, thus paving the way for further advancements in sustainable manufacturing practices.

On the construction of diagonally implicit two–step peer methods with RK stability

In this paper, diagonally implicit two–step peer methods for the numerical solution of initial value problems of order ordinary differential are divided into four types including the combination of explicit and implicit methods in a sequential or parallel environments. In this class of the methods, construction of implicit methods equipped with Runge–Kutta stability property together with A– or L–stability are investigated and examples of such methods are given up to order five. Finally, the efficiency and accuracy of the proposed methods are verified by applying them on some well–known stiff problems.

A solution method for stochastic multilevel programming problems. A systematic sampling evolutionary approach

Stochastic multilevel programming is a mathematical programming problem with some given number of hierarchical levels of decentralized decision makers and having some kind of randomness properties in the problem definition. The introduction of some randomness property in its hierarchical structure makes stochastic multilevel problems computationally challenging and expensive. In this article, a systematic sampling evolutionary method is adapted to solve the problem. The solution procedure is based on realization of the random variables and systematic partitioning of each hierarchical level’s decision space for searching an optimal reaction. The search goes sequentially upwards starting from the bottom up through the top hierarchical level problem. The existence of solution and convergence of the solution procedure is shown. The solution procedure is implemented and tested on some selected deterministic test problems from literature. Moreover, the proposed algorithm can be used to solve stochastic multilevel programming problems with additional complexity in their problem definition.

An exact solution method for seru scheduling problems considering past-sequence-dependent setup time and adjustment activities

An exact solution method for seru scheduling problems considering past-sequence-dependent setup time and adjustment activities

An exact solution method for seru scheduling problems with multiple rate-modifying activities and learning effect

An exact solution method for seru scheduling problems with multiple rate-modifying activities and learning effect

Solving the Stochastic Machine Assignment Problem with Probability-based Objectives: Problem Formulation, Solution Method, and Practical Applications

Solving the Stochastic Machine Assignment Problem with Probability-based Objectives: Problem Formulation, Solution Method, and Practical Applications

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning

A FAMILY OF 82Q EXPONENTIAL HYBRID METHODS FOR SOLVING IVPS IN ODES

In a recent paper, a new class of exponential general linear methods of second stage seventh order for the numerical solution of first order initial value problems in ordinary deferential equations was derived. In this paper, we derive the new class of higher order extended exponential general linear methods for the numerical solution of first order initial value problems in ordinary deferential equations. The numerical results obtained by the new method for some problems show its superiority in efficiency and accuracy for solving problems for which the proposed general linear method is appropriate

Hybrid Deep Learning and Sensitivity Operator-Based Algorithm for Identification of Localized Emission Sources

Hybrid approaches combining machine learning with traditional inverse problem solution methods represent a promising direction for the further development of inverse modeling algorithms. The paper proposes an approach to emission source identification from measurement data for advection–diffusion–reaction models. The approach combines general-type source identification and post-processing refinement: first, emission source identification by measurement data is carried out by a sensitivity operator-based algorithm, and then refinement is done by incorporating a priori information about unknown sources. A general-type distributed emission source identified at the first stage is transformed into a localized source consisting of multiple point-wise sources. The second, refinement stage consists of two steps: point-wise source localization and emission rate estimation. Emission source localization is carried out using deep learning with convolutional neural networks. Training samples are generated using a sensitivity operator obtained at the source identification stage. The algorithm was tested in regional remote sensing emission source identification scenarios for the Lake Baikal region and was able to refine the emission source reconstruction results. Hence, the aggregates used in traditional inverse problem solution algorithms can be successfully applied within machine learning frameworks to produce hybrid algorithms.

A solution method for mixed-variable constrained blackbox optimization problems

A solution method for mixed-variable constrained blackbox optimization problems