Michael Schyns

Simulated Annealing for Complex Portfolio Selection Problems

Abstract This paper describes the application of a simulated annealing approach to the solution of a complex portfolio selection model. The model is a mixed integer quadratic programming problem which arises when Markowitz’ classical mean–variance model is enriched with additional realistic constraints. Exact optimization algorithms run into difficulties in this framework and this motivates the investigation of heuristic techniques. Computational experiments indicate that the approach is promising for this class of problems.

Automatic Aircraft Cargo Load Planning

The goal of this paper is the development of a new mixed integer linear program designed for optimally loading a set of containers and pallets into a compartmentalised cargo aircraft. It is based on real-world problems submitted by a professional partner. This model takes into account strict technical and safety constraints. In addition to the standard goal of optimally positioning the centre of gravity, we also propose a new approach based on the moment of inertia. This double goal implies an increase in aircraft efficiency and a decrease in fuel consumption. Cargo loading generally remains a manual, or at best a computer-assisted, and time-consuming task. A fully automatic software was developed to quickly compute optimal solutions. Experimental results show that our approach achieves better solutions than manual planning, within only a few seconds.

An ant colony system for responsive dynamic vehicle routing

We present an algorithm based on an ant colony system to deal with a broad range of Dynamic Capacitated Vehicle Routing Problems with Time Windows, (partial) Split Delivery and Heterogeneous fleets (DVRPTWSD). We address the important case of responsiveness. Responsiveness is defined here as completing a delivery as soon as possible, within the time window, such that the client or the vehicle may restart its activities. We develop an interactive solution to allow dispatchers to take new information into account in real-time. The algorithm and its parametrization were tested on real and artificial instances. We first illustrate our approach with a problem submitted by Liege Airport, the 8th biggest cargo airport in Europe. The goal is to develop a decision system to optimize the journey of the refueling trucks. We then consider some classical VRP benchmarks with extensions to the responsiveness context.

A mixed integer programming formulation for the three‐dimensional bin packing problem deriving from an air cargo application

The present paper discusses the problem of optimizing the loading of boxes into containers. The goal is to minimize the unused volume. This type of problem belongs to the family of multiple bin size bin packing problems (MBSBPP). The approach includes an extensive set of constraints encountered in real-world applications in the three-dimensional case: the stability, the fragility of the items, the weight distribution, and the possibility to rotate the boxes. It also includes the specific situation in which containers are truncated parallelepipeds. This is typical in the field of air transportation. While most papers on cutting and packing problems describe ad hoc procedures, this paper proposes a mixed integer linear program. The validity of this model is tested on small instances.

The Airline Container Loading Problem with Pickup and Delivery

This paper considers the loading optimization problem for a set of containers and pallets transported into a cargo aircraft that serves multiple airports. Because of pickup and delivery operations that occur at intermediate airports, this problem is simultaneously a Weight, and Balance Problem and a Sequencing Problem. Our objective is to minimize fuel and handling operation costs. This problem is shown to be NP-hard. We resort to a mixed integer linear program. Based on real-world data from a professional partner (TNT Airways), we perform numerical experiments using a standard B, and C library. This approach yields better solutions than traditional manual planning, which results in substantial cost savings.

A relaxed approach to combinatorial problems in robustness and diagnostics

A range of procedures in both robustness and diagnostics require optimisation of a target functional over all subsamples of given size. Whereas such combinatorial problems are extremely difficult to solve exactly, something less than the global optimum can be ‘good enough’ for many practical purposes, as shown by example. Again, a relaxation strategy embeds these discrete, high-dimensional problems in continuous, low-dimensional ones. Overall, nonlinear optimisation methods can be exploited to provide a single, reasonably fast algorithm to handle a wide variety of problems of this kind, thereby providing a certain unity. Four running examples illustrate the approach. On the robustness side, algorithmic approximations to minimum covariance determinant (MCD) and least trimmed squares (LTS) estimation. And, on the diagnostic side, detection of multiple multivariate outliers and global diagnostic use of the likelihood displacement function. This last is developed here as a global complement to Cook’s (in J. R. Stat. Soc. 48:133–169, 1986) local analysis. Appropriate convergence of each branch of the algorithm is guaranteed for any target functional whose relaxed form is—in a natural generalisation of concavity, introduced here—‘gravitational’. Again, its descent strategy can downweight to zero contaminating cases in the starting position. A simulation study shows that, although not optimised for the LTS problem, our general algorithm holds its own with algorithms that are so optimised. An adapted algorithm relaxes the gravitational condition itself.

Optimal selection of a portfolio of options under Value-at-Risk constraints: a scenario approach

This paper introduces a multiperiod model for the optimal selection of a financial portfolio of options linked to a single index. The objective of the model is to maximize the expected return of the portfolio under constraints limiting its Value-at-Risk. We rely on scenarios to represent future security prices. The model contains several interesting features, like the consideration of transaction costs, bid-ask spreads, arbitrage-free option pricing, and the possibility to rebalance the portfolio with options introduced at the start of each period. The resulting mixed integer programming model is applied to realistic test instances involving options on the S&P500 index. In spite of the large size and of the numerical difficulty of this model, near-optimal solutions can be computed by a standard branch-and-cut solver or by a specialized heuristic. The structure and the financial features of the selected portfolios are also investigated.

MIP-based constructive heuristics for the three-dimensional Bin Packing Problem with transportation constraints

Abstract This article is about seeking a good feasible solution in a reasonable amount of computation time to the three-dimensional Multiple Bin Size Bin Packing Problem (MBSBPP). The MBSBPP studied considers additional constraints encountered in real world air transportation situations, such as cargo stability and the particular shape of containers. This MBSBPP has already been formulated as a Mixed Integer linear Programming problem, but as yet only poor results have been achieved for even fairly small problem sizes. The goal of the work this paper describes is to develop heuristics that are able to quickly provide good initial feasible solutions for the MBSBPP. Three methodologies are considered, which are based on the decomposition of the original problem into easier subproblems: the matheuristics Relax-and-Fix, Insert-and-Fix and Fractional Relax-and-Fix. They have been parametrised on real data sets and then compared to each other. In particular, two of these techniques show promising results in reasonable computational times.

Early detection of university students with potential difficulties

Abstract Using data mining methods, this paper presents a new means of identifying freshmens profiles likely to face major difficulties to complete their first academic year. Academic failure is a relevant issue at a time when post-secondary education is ever more critical to economic success. We aim at early detection of potential failure using student data available at registration, i.e. school records and environmental factors, with a view to timely and efficient remediation and/or study reorientation. We adapt three data mining methods, namely random forest, logistic regression and artificial neural network algorithms. We design algorithms to increase the accuracy of the prediction when some classes are of major interest. These algorithms are context independent and can be used in different fields. Real data pertaining to undergraduates at the University of Liege (Belgium), illustrates our methodology.

A tailored two-phase constructive heuristic for the three-dimensional Multiple Bin Size Bin Packing Problem with transportation constraints

This paper considers the three-dimensional Multiple Bin Size Bin Packing Problem which consists in packing a set of cuboid boxes into containers of various shapes, while minimising unused space. The problem is extended to air cargo where the bins are Unit Load Devices, specially designed for fitting in aircraft. We developed a fast constructive heuristic able to manage the constraints to be met in transportation. The heuristic is split into two distinct phases. The first phase deals with the packing of boxes into identical bins using an extension of the Extreme Points which describe the possible interesting positions to accommodate boxes. During this phase, the fragility, stability and orientation of the boxes are taken into account as well as the special shape of the bins and their weight capacity. The second phase considers the multiple types of available bins. If necessary, the best loading pattern identified is enhanced with respect to weight distribution in post processing. After the description of the parametrisation, computational experiments are performed on data sets specially designed for this application. The heuristic requires only few seconds to achieve promising results in terms of filling rate.