Mathematical Optimization and Algorithms for Offshore Wind Farm Design: An Overview

Wind energy is a fast evolving field that has attracted a lot of attention and investments in the last dec- ades. Being an increasingly competitive market, it is very important to minimize establishment costs and increase production profits already at the design phase of new wind parks. This paper is based on many years of collaboration with Vattenfall, a leading wind energy developer and wind power operator, and aims at giving an overview of the experience of using Mathematical Optimization in the field. The paper illustrates some of the practical needs defined by energy companies, showing how optimization can help the designers to increase production and reduce costs in the design of offshore parks. In particular, the study gives an overview of the individual phases of designing an offshore windfarm,andsomeoftheoptimizationproblemsinvolved. Finally it goes in depth with three of the most important optimization tasks: turbine location, electrical cable routing and foundation optimization. The paper is concluded with a discussion of future challenges

The two-dimensional bin packing problem with variable bin sizes and costs

AbstractThe two-dimensional variable sized bin packing problem (2DVSBPP) is the problem of packing a set of rectangular items into a set of rectangular bins. The bins have different sizes and different costs, and the objective is to minimize the overall cost of bins used for packing the rectangles. We present an integer-linear formulation of the 2DVSBPP and introduce several lower bounds for the problem. By using Dantzig–Wolfe decomposition we are able to obtain lower bounds of very good quality. The LP-relaxation of the decomposed problem is solved through delayed column generation, and an exact algorithm based on branch-and-price is developed. The paper is concluded with a computational study, comparing the tightness of the various lower bounds, as well as the performance of the exact algorithm for instances with up to 100 items

The Baggage Belt Assignment Problem

We consider the problem of assigning flights to baggage belts in the baggage reclaim area of an airport. The problem is originated by a real-life application in Copenhagen airport. The objective is to construct a robust schedule taking passenger and airline preferences into account. We consider a number of business and fairness constraints, avoiding congestions, and ensuring a good passenger flow. Robustness of the solutions is achieved by matching the delivery time with the expected arrival time of passengers, and by adding buffer time between two flights scheduled on the same belt. We denote this problem as the Baggage Belt Assignment Problem (BBAP). We first derive a general Integer Linear Programming (ILP) formulation for the problem. Then, we propose a Branch-and-Price (B&P) algorithm based on a reformulation of the ILP model tackled by Column Generation. Our approach relies on an effective dynamic programming algorithm for handling the pricing problems. We tested the proposed algorithm on a set of real-life data from Copenhagen airport as well as on a set of instances inspired by the real data. Our B&P scheme outperforms a commercial solver launched on the ILP formulation of the problem and is effective in delivering high quality solutions in limited computational times, making it possible its use in daily operations in medium-sized and large airports