Search results for "Mathematic"
showing 10 items of 24974 documents
Mathematical models for a cutting problem in the glass manufacturing industry
2021
Abstract The glass cutting problem proposed for the ROADEF 2018 challenge is a two-dimensional, three-stage guillotine cutting process, with an additional cut to obtain pieces in some specific situations. However, it is not a standard problem because it includes specific constraints. The sheets produced in the glass manufacturing process have defects that make them different and have to be used in order. The pieces to be cut are grouped into subsets and the pieces from each subset must be cut in order. We approach the problem by developing and solving integer linear models. We start with the basic model, which includes the essential features of the problem, as a classical three-stage cuttin…
Sampled Fictitious Play on Networks
2019
We formulate and solve the problem of optimizing the structure of an information propagation network between multiple agents. In a given space of interests (e.g., information on certain targets), each agent is defined by a vector of their desirable information, called filter, and a vector of available information, called source. The agents seek to build a directed network that maximizes the value of the desirable source-information that reaches each agent having been filtered en route, less the expense that each agent incurs in filtering any information of no interest to them. We frame this optimization problem as a game of common interest, where the Nash equilibria can be attained as limit…
A strategic oscillation simheuristic for the Time Capacitated Arc Routing Problem with stochastic demands
2021
Abstract The Time Capacitated Arc Routing Problem (TCARP) extends the classical Capacitated Arc Routing Problem by considering time-based capacities instead of traditional loading capacities. In the TCARP, the costs associated with traversing and servicing arcs, as well as the vehicle’s capacity, are measured in time units. The increasing use of electric vehicles and unmanned aerial vehicles, which use batteries of limited duration, illustrates the importance of time-capacitated routing problems. In this paper, we consider the TCARP with stochastic demands, i.e.: the actual demands on each edge are random variables which specific values are only revealed once the vehicle traverses the arc. …
Meta-heuristic Algorithms for Nesting Problem of Rectangular Pieces
2017
Abstract Nesting problems consist of placing multiple items onto larger shapes finding a good arrangement. The goal of the nesting process is to minimize the waste of material. It is common to assume, as in the present work, that the stock sheet has fixed width and infinite height, since in the real world a company may have to cut pieces from a roll of material. The complexity of such problems is often faced with a two-stage approach, so-called “hybrid algorithm”, combining a placement routine and a meta-heuristic algorithm. Starting from a given positioning sequence, the placement routine generates a non-overlapping configuration. The encoded solution is manipulated and modified by the met…
Forecasting portfolio returns using weighted fuzzy time series methods
2016
We propose using weighted fuzzy time series (FTS) methods to forecast the future performance of returns on portfolios. We model the uncertain parameters of the fuzzy portfolio selection models using a possibilistic interval-valued mean approach, and approximate the uncertain future return on a given portfolio by means of a trapezoidal fuzzy number. Introducing some modifications into the classical models of fuzzy time series, based on weighted operators, enables us to generate trapezoidal numbers as forecasts of the future performance of the portfolio returns. This fuzzy forecast makes it possible to approximate both the expected return and the risk of the investment through the value and a…
Optimal control of discrete-time interval type-2 fuzzy-model-based systems with D-stability constraint and control saturation
2016
This paper investigates the optimal control problem for discrete-time interval type-2 (IT2) fuzzy systems with pole constraints. An IT2 fuzzy controller is characterized by two predefined functions, and the membership functions and the premise rules of the IT2 fuzzy controller can be chosen freely. The pole assignment is considered, which is constrained in a presented disk region. Based on Lyapunov stability theory, sufficient conditions of asymptotic stability with an H ∞ performance are obtained for the discrete-time IT2 fuzzy model based (FMB) system. Based on the criterion, the desired IT2 state-feedback controller is designed to guarantee that the closed-loop system is asymptotically s…
Modeling and control of uncertain nonlinear systems
2018
A survey of the methodologies associated with the modeling and control of uncertain nonlinear systems has been given due importance in this paper. The basic criteria that highlights the work is relied on the various patterns of techniques incorporated for the solutions of fuzzy equations that corresponds to fuzzy controllability subject. The solutions which are generated by these equations are considered to be the controllers. Currently, numerical techniques have come out as superior techniques in order to solve these types of problems. The implementation of neural networks technique is contributed in the complex way of dealing the appropriate coefficients and solutions of the fuzzy systems.
Bio-inspired evolutionary dynamics on complex networks under uncertain cross-inhibitory signals
2019
Given a large population of agents, each agent has three possiblechoices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a distributed way. The more popular an option is, the more likely it is to be chosen by uncommitted agents. Agents committed to one option can be attracted by those committed to the other option through a cross-inhibitory signal. This model originates in the context of honeybee swarms, and we generalize it to duopolistic competition and opinion dynamics. The contributions of this work include (i) the formulation of a model to explain the behavioral traits of the ho…
A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms
2017
Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approxim…
A Methodology for Modeling and Optimizing Social Systems
2020
[EN] A system methodology for modeling and optimizing social systems is presented. It allows constructing dynamical models formulated stochastically, i.e., their results are given by confidence intervals. The models provide optimal intervention ways to reach the stated objectives. Two optimization methods are used: (1) to test strategies and scenarios and (2) to optimize with a genetic algorithm. The application case presented is a small nonformal education Spanish business. First, the model is validated in the 2008-2012 period, and subsequently, the optimal way to obtain a maximum profit in the 2013-2025 period is obtained using the two methods.