Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Cross inhibition improves activity selection when switching incurs time costs
2015
Abstract We consider a behavioural model of an animal choosing between two activities, based on positive feedback, and examine the effect of introducing cross inhibition between the motivations for the two activities. While cross-inhibition has previously been included in models of decision making, the question of what benefit it may provide to an animal’s activity selection behaviour has not previously been studied. In neuroscience and in collective behaviour cross-inhibition, and other equivalent means of coupling evidence-accumulating pathways, have been shown to approximate statistically-optimal decision-making and to adaptively break deadlock, thereby improving decision performance. Sw…
Variational Approximations for Generalized Linear Latent Variable Models
2017
Generalized linear latent variable models (GLLVMs) are a powerful class of models for understanding the relationships among multiple, correlated responses. Estimation, however, presents a major challenge, as the marginal likelihood does not possess a closed form for nonnormal responses. We propose a variational approximation (VA) method for estimating GLLVMs. For the common cases of binary, ordinal, and overdispersed count data, we derive fully closed-form approximations to the marginal log-likelihood function in each case. Compared to other methods such as the expectation-maximization algorithm, estimation using VA is fast and straightforward to implement. Predictions of the latent variabl…
Density Flow in Dynamical Networks via Mean-Field Games
2016
Current distributed routing control algorithms for dynamic networks model networks using the time evolution of density at network edges, while the routing control algorithm ensures edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We rearrange the density model to recast the problem within the framework of mean-field games. In doing that, we illustrate an extended state-space solution approach and we study the stochastic case where the density evolution is driven by a Brownian motion. Further, we investigate the case where the density evolution is perturbed by a bounded adversarial disturbance. For both the stochastic a…
A Pareto optimal design approach for simultaneous control of thinning and springback in stamping processes
2009
One of the most relevant research issues in automotive field is focused on the reduction of stamped parts weight also increasing their strength. In this way, a strong research effort is developed on high strength steels which are widely utilized and they require a proper springback control. Springback reduction in sheet metal forming is a typical goal to be pursued which is conflicting with thinning reduction for instance. Thus, such problems can be considered as multi-objective ones characterized by conflicting objectives. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one, particularly in an indu…
Decorous combinatorial lower bounds for row layout problems
2020
Abstract In this paper we consider the Double-Row Facility Layout Problem (DRFLP). Given a set of departments and pairwise transport weights between them the DRFLP asks for a non-overlapping arrangement of the departments along both sides of a common path such that the weighted sum of the center-to-center distances between the departments is minimized. Despite its broad applicability in factory planning, only small instances can be solved to optimality in reasonable time. Apart from this even deriving good lower bounds using existing integer programming formulations and branch-and-cut methods is a challenging problem. We focus here on deriving combinatorial lower bounds which can be compute…
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…