Applications – OR and Management Sciences

A Computational Framework for Uncertainty Quantification and Stochastic Optimization in Unit Commitment with Wind Power Generation

Categories Control Applications, Scheduling, Stochastic Programming Tags , , ,

We present a computational framework for integrating a state-of-the-art numerical weather prediction (NWP) model in stochastic unit commitment/energy dispatch formulations that account for wind power uncertainty. We first enhance the NWP model with an ensemble-based uncertainty quantification strategy implemented in a distributed-memory parallel computing architecture. We discuss computational issues arising in the implementation of the … Read more

Exact Solution of Emerging Quadratic Assignment Problems

Categories Applications - OR and Management Sciences, Combinatorial Optimization, Facility Planning and Design Tags , , ,

We report on a growing class of assignment problems that are increasingly of interest and very challenging in terms of the difficulty they pose to attempts at exact solution. These problems address economic issues in the location and design of factories, hospitals, depots, transportation hubs and military bases. Others involve improvements in communication network design. … Read more

Resource Allocation with Time Intervals

Categories Combinatorial Optimization, Scheduling Tags , ,

We study a resource allocation problem where jobs have the following characteristics: Each job consumes some quantity of a bounded resource during a certain time interval and induces a given profit. We aim to select a subset of jobs with maximal total profit such that the total resource consumed at any point in time remains … Read more

A continuous model for open pit mine planning

Categories Applications - OR and Management Sciences, Global Optimization, Infinite Dimensional Optimization Tags , ,

This paper proposes a new mathematical model for the open pit mine planning problem, based on continuous functional analysis. The traditional models for this problem have been constructed by using discrete 0-1 decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming (MIP) problems. Instead, we use a continuous approach which allows for a … Read more

Hager-Zhang Active Set Algorithm for Large-Scale Continuous Knapsack Problems

Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Nonlinear Optimization Tags , , , , , ,

The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly called as continuous knapsack problems. Since there are efficient methods to solve large-scale bound constrained nonlinear programs, it is desirable to … Read more

Applying a global optimisation algorithm to Fund of Hedge Funds portfolio optimisation

Categories Applications - OR and Management Sciences, Finance and Economics, Global Optimization Tags , , ,

Portfolio optimisation for a Fund of Hedge Funds (“FoHF”) has to address the asymmetric, non-Gaussian nature of the underlying returns distributions. Furthermore, the objective functions and constraints are not necessarily convex or even smooth. Therefore traditional portfolio optimisation methods such as mean-variance optimisation are not appropriate for such problems and global search optimisation algorithms could … Read more

Worst-Case Value-at-Risk of Non-Linear Portfolios

Categories Finance and Economics, Robust Optimization Tags , , , ,

Portfolio optimization problems involving Value-at-Risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR … Read more

On the Solution of Complementarity Problems Arising in American Options Pricing

Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Finance and Economics Tags , ,

In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution … Read more

The mesh adaptive direct search algorithm for periodic variables

Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization Tags , , , ,

This work analyzes constrained black box optimization in which the functions defining the problem are periodic with respect to some or all the variables. We show that the natural strategy of mapping trial points into the interval defined by the period in the Mesh Adaptive Direct Search (MADS) framework can be easily done in practice, … Read more

Algorithm 909: NOMAD: Nonlinear Optimization with the MADS algorithm

Categories Applications - OR and Management Sciences, Optimization Software and Modeling Systems Tags , , , ,

NOMAD is software that implements the MADS algorithm (Mesh Adaptive Direct Search) for black-box optimization under general nonlinear constraints. Blackbox optimization is about optimizing functions that are usually given as costly programs with no derivative information and no function values returned for a significant number of calls attempted. NOMAD is designed for such problems and … Read more