A non-parametric approach to demand forecasting in revenue management

In revenue management, the profitability of the inventory and pricing decisions rests on the accuracy of demand forecasts. However, whenever a product is no longer available, true demand may differ from registered bookings, thus inducing a negative bias in the estimation figures, as well as an artificial increase in demand for substitute products. In order to address these issues, we propose an original Mixed Integer Nonlinear Program (MINLP) to estimate product utilities as well as capturing seasonal effects. This behavioral model solely rests on daily registered bookings and product availabilities. Its outputs are the product utilities and daily potential demands, together with the expected demand of each product within any given time interval. Those are obtained via a tailored algorithm that outperforms two well-known generic software for global optimization.     

Mathematical representation of radiality constraint in distribution system reconfiguration problem

Distribution systems are most commonly operated in a radial configuration for a number of reasons. In order to impose radiality constraint in the optimal network reconfiguration problem, an efficient algorithm is introduced in this paper based on graph theory. The paper shows that the normally followed methods of imposing radiality constraint within a mixed-integer programming formulation of the reconfiguration problem may not be sufficient. The minimum-loss network reconfiguration problem is formulated using different ways to impose radiality constraint. It is shown, through simulations, that the formulated problem using the proposed method for representing radiality constraint can be solved more efficiently, as opposed to the previously proposed formulations. This results in up to 30% reduction in CPU time for the test systems used in this study.     

A nature-inspired firefly algorithm based approach for nanoscale leakage optimal RTL structure

Optimization of leakage power is essential for nanoscale CMOS (nano-CMOS) technology based integrated circuits for numerous reasons, including improving battery life of the system in which they are used as well as enhancing reliability. Leakage optimization at an early stage of the design cycle such as the register-transfer level (RTL) or architectural level provides more degrees of freedom to design engineers and ensures that the design is optimized at higher levels before proceeding to the next and more detailed phases of the design cycle. In this paper, an RTL optimization approach is presented that targets leakage-power optimization while performing simultaneous scheduling, allocation and binding. The optimization approach uses a nature-inspired firefly algorithm so that large digital integrated circuits can be effectively handled without convergence issues. The firefly algorithm optimizes the cost of leakage delay product (LDP) under various resource constraints. As a specific example, gate-oxide leakage is optimized using a 45 nm CMOS dual-oxide based pre-characterized datapath library. Experimental results over various architectural level benchmark integrated circuits show that average leakage optimization of 90% can be obtained. For a comparative perspective, an integer linear programming (ILP) based algorithm is also presented and it is observed that the firefly algorithm is as accurate as ILP while converging much faster. To the best of the authors׳ knowledge, this is the first ever paper that applies firefly based algorithms for RTL optimization.     

Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

On control of transport in Brownian ratchet mechanisms

Engineered transport of material at the nano/micro scale is essential for the manufacturing platforms of the future. Unlike conventional transport systems, at the nano/micro scale, transport has to be achieved in the presence of fundamental sources of uncertainty such as thermal noise. Remarkably, it is possible to extract useful work by rectifying noise using an asymmetric potential; a principle used by Brownian ratchets. In this article a systematic methodology for designing open-loop Brownian ratchet mechanisms that optimize velocity and efficiency is developed. In the case where the particle position is available as a measured variable, closed loop methodologies are studied. Here, it is shown that methods that strive to optimize velocity of transport may compromise efficiency. A dynamic programming based approach is presented which yields up to three times improvement in efficiency over optimized open loop designs and 35% better efficiency over reported closed loop strategies that focus on optimizing velocities.     

A perspective-based convex relaxation for switched-affine optimal control

We consider the switched-affine optimal control problem, i.e., the problem of selecting a sequence of affine dynamics from a finite set in order to minimize a sum of convex functions of the system state. We develop a new reduction of this problem to a mixed-integer convex program (MICP), based on perspective functions. Relaxing the integer constraints of this MICP results in a convex optimization problem, whose optimal value is a lower bound on the original problem value. We show that this bound is at least as tight as similar bounds obtained from two other well-known MICP reductions (via conversion to a mixed logical dynamical system, and by generalized disjunctive programming), and our numerical study indicates it is often substantially tighter. Using simple integer-rounding techniques, we can also use our formulation to obtain an upper bound (and corresponding sequence of control inputs). In our numerical study, this bound was typically within a few percent of the optimal value, making it attractive as a stand-alone heuristic, or as a subroutine in a global algorithm such as branch and bound. We conclude with some extensions of our formulation to problems with switching costs and piecewise affine dynamics.     

Sample re-weighting hyper box classifier for multi-class data classification

In this work, we propose two novel classifiers for multi-class classification problems using mathematical programming optimisation techniques. A hyper box-based classifier (Xu & Papageorgiou, 2009) that iteratively constructs hyper boxes to enclose samples of different classes has been adopted. We firstly propose a new solution procedure that updates the sample weights during each iteration, which tweaks the model to favour those difficult samples in the next iteration and therefore achieves a better final solution. Through a number of real world data classification problems, we demonstrate that the proposed refined classifier results in consistently good classification performance, outperforming the original hyper box classifier and a number of other state-of-the-art classifiers.Furthermore, we introduce a simple data space partition method to reduce the computational cost of the proposed sample re-weighting hyper box classifier. The partition method partitions the original dataset into two disjoint regions, followed by training sample re-weighting hyper box classifier for each region respectively. Through some real world datasets, we demonstrate the data space partition method considerably reduces the computational cost while maintaining the level of prediction accuracies.     

Two stage stochastic bilevel programming model of a pre-established timberlands supply chain with biorefinery investment interests

This work studies the supply allocation problem, using a Stackelberg game, for an established timberlands supply chain with an additional decision of new biorefinery investments. In a timberlands system, harvester and manufacturer decision makers have separate objectives to maximize their respective profits. This interaction is represented with a turn based Stackelberg game. The harvesters decide first on the quantity harvested, and the manufacturers decide on how much to utilize. This game is modeled with a bilevel mathematical program. The novel feature of this paper's bilevel formulation is the inclusion of parametric uncertainty in a two stage model. The first stage problem involves logistical decisions around biorefinery investments, such as location and capacity, while the second stage problem involves a bilevel timberlands model with parameter uncertainty. Studying this problem formulation revealed interesting insights for solving multiperiod problems with bilevel stages as well as the decision maker's behavior for the timberlands model.     

Optimal scheduling of single stage batch plants with direct heat integration

This paper addresses the multi-objective optimization problem arising in the operation of heat integrated batch plants, where makespan and utility consumption are the two conflicting objectives. A new continuous-time MILP formulation with general precedence variables is proposed to simultaneously handle decisions related to timing, product sequencing, heat exchanger matches (selected from a two-stage superstructure) and their heat loads. It features a complex set of timing constraints to synchronize heating and cooling tasks, derived from Generalized Disjunctive Programming. Through the solution of an industrial case study from a vegetable oil refinery, we show that major savings in utilities can be achieved while generating the set of Pareto optimal solutions through the ɛ-constraint method.     

p-Median and p-dispersion problems: A bi-criteria analysis

Given a collection of n locations and a symmetric measure of distance (difference) between each pair of locations, we seek to identify (select) a subset of p locations so as to achieve two distinct objectives. The first objective is to use the selected locations as centers (medians) of p groups that would partition the entire collection and minimize the total distance between the locations and their respective group medians. The second objective is to maximize the minimum distance (diversity) among the selected locations themselves. We study this problem as a multi-objective optimization problem and propose an iterative algorithm to obtain its non-dominated frontier. At each iteration we construct and solve a 0–1 integer programming problem. Through a computational experiment we show that this algorithm is computationally effective for small to medium size instances of the problem. We also propose a Lagrangian heuristic algorithm for solving larger instances of this problem.