Mortar-Based Contact Formulation for Large Deformations

The discontinuities due to the discretization lead to some challenges. First, the normal direction of the contact surface is not steady because the discrete surface is only C₀ continuous. One might smooth the normal vector field. Second, the question of contact enforcement has to be cleared. Contact forces can be modeled with either a Lagrange multiplier method or a penalty formulation to prevent penetration. Third, there must be developed a integration scheme which is able to handle the non-steady boundary. Last, there is a strong discontinuity in measuring the penetration, where different criteria for enabling or disabling contact can be found (active set strategy). In this work, different approaches to solve this tasks are presented and brought into context. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sequence searching and evaluation: a unified approach for aircraft arrival sequencing and scheduling problems

Arrival sequencing and scheduling (ASS) is an important part of air traffic control. In the literature, various formulations of the ASS problems have been established by taking different scheduling requirements into account, and various methods have been developed to cope with these ASS problems. However, it is usually uneasy to generalize a method designed for one ASS formulation to another, while an approach that is able to handle different ASS problems is of great significance since air traffic controllers may need to switch among different scheduling requirements in practice. Motivated by this observation, an approach that is applicable to a number of different problem formulations of ASS is proposed in this paper. Specifically, the ASS problems that include different objective functions and constraints are firstly abstracted as a constrained permutation-based problem. After that, a Sequence Searching and Evaluation (SSE) approach is developed for the constrained permutation-based problem. The SSE solves different ASS problems by separating the sequence searching in one stage using an Estimation of Distribution Algorithm framework, and evaluating sequences in the second stage. Experiment results show that SSE is capable of obtaining competitive solutions for a variety of ASS problems.     

Time-step selection algorithms: Adaptivity,control, and signal processing

The efficiency of numerical time-stepping methods for dynamical systems is greatly enhanced by automatic time step variation. In this paper we present and discuss three different approaches to step size selection: (i) control theory (to keep the error in check); (ii) signal processing (to produce smooth step size sequences and improve computational stability); and (iii) adaptivity, in the sense that the time step should be covariant or contravariant with some prescribed function of the dynamical system's solution. Examples are used to demonstrate the different advantages in different applications. The main ideas are further developed to approach some open problems that are subject to special requirements.     

A logarithmic method for eliminating binary variables and constraints for the product of free-sign discrete functions

In this paper, a logarithmic method was developed to solve optimization problems containing the product of free-sign discrete functions (PFDF). The current deterministic methods used to handle these problems are based on the concept of continuous variables; therefore, the methods always transform the original model into another programming model (e.g., DC programming, convex programming) and solve them with a commercial solver. As the nature of a discrete variable is quite different from that of a continuous one, developing a novel method to address the above mentioned problems is necessary. This study proposes a concise and efficient method that linearizes PFDF term into a set of linear inequalities directly without redundant transformation. Further, the proposed method only requires the logarithmic numbers of binary variables and constraints. Numerical examples demonstrate that the proposed formulation significantly outperforms current approaches.     

MIP-based approaches for the container loading problem with multi-drop constraints

In this paper, we present approaches based on a mixed integer linear programming model (MIP) for the problem of packing rectangular boxes into a container or truck, considering multi-drop constraints. We assume that the delivery route of the container is already known in advance and that the volume of the cargo is less than or equal to the container volume. Considering the sequence that the boxes should be unloaded, the aim is to avoid additional handling when each drop-off point of the route is reached, as well as ensuring that the boxes do not overlap each other and the cargo loading is stable. Computational tests with the proposed model and the approaches were performed with randomly generated instances and instances from the literature using an optimization solver embedded into a modeling language. The results validate the model and the approaches, but indicate that they are able to handle only problems of a moderate size. However, the model and the approaches can be useful to motivate future research to solve larger problems, as well as to solve more general problems considering integrated vehicle routing and container loading problems.     

A hybrid optimization approach for multi-level capacitated lot-sizing problems

Solving multi-level capacitated lot-sizing problems is still a challenging task, in spite of increasing computational power and faster algorithms. In this paper a new approach combining an ant-based algorithm with an exact solver for (mixed-integer) linear programs is presented. A MAX–MIN ant system is developed to determine the principal production decisions, a LP/MIP solver is used to calculate the corresponding production quantities and inventory levels. Two different local search methods and an improvement strategy based on reduced mixed-integer problems are developed and integrated into the ant algorithm. This hybrid approach provides superior results for small and medium-sized problems in comparison to the existing approaches in the literature. For large-scale problems the performance of this method is among the best.     

Limited memory quasi-newton method for large-scale linearly equality-constrained minimization

1. IntroductionConsider the following linearly constrained nonlinear programming problemwhere x e R", A E Rmxn and f E C2. We are interested in the case when n and m arelarge and when the Hessian matrix of f is difficult to compute or is dense. It is ajssumed thatA is a matrix of full row rank and that the level set S(xo) = {x: f(x) 5 f(xo), Ax ~ b} isnonempty and compact.In the past few years j there were two kinds of methods for solving the large-scaleproblem (1.1). FOr the one kind, pr…     

Optimality conditions for mixed discrete bilevel optimization problems

In this article, we consider bilevel optimization problems with discrete lower level and continuous upper level problems. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. In the case where the lower level is a parametric linear problem, the bilevel problem is transformed into a continuous one. After that, we are able to discuss local optimality conditions using tools of variational analysis for each of the different approaches. Finally, we consider a simple application of our results namely the bilevel programming problem with the minimum spanning tree problem in the lower level.     

Report on the activities of the working group on discrete mathematics

In the past decade there have been significant developments in computer technology and solution techniques for analysing business and industrial decision problems. In recent years good modelling systems have become available to ease the burden of model communication. Currently the single most important barrier to increased use of structured approaches to decision modelling is the acquisition of the necessary skills to initially develop models of complex decision systems. This paper examines the modelling process with reference to linear programming. Two related production planning problems are presented and their associated models developed. The relationship between the two problems is such that student modellers are forced to become involved in the important details of the problems and, by examining the nature of solution spaces in constrained optimisation, students are able to rapidly gain confidence and skills in modelling.     

The Application of Preprocessing and Cutting Plane Techniques for a Class of Production Planning Problems

This paper investigates properties of integer programming models for a class of production planning problems. The models are developed within a decision support system to advise a sales team of the products on which to focus their efforts in gaining new orders in the short term. The products generally require processing on several manufacturing cells and involve precedence relationships. The cells are already (partially) committed with products for stock and to satisfy existing orders and therefore only the residual capacities of each cell in each time period of the planning horizon are considered. The determination of production recommendations to the sales team that make use of residual capacities is a nontrivial optimization problem. Solving such models is computationally demanding and techniques for speeding up solution times are highly desirable. An integer programming model is developed and various preprocessing techniques are investigated and evaluated. In addition, a number of cutting plane approaches have been applied. The performance of these approaches which are both general and application specific is examined.     

不完全偏好信息下房地产投资的模糊优选

解决了不完全偏好信息下含有模糊决策元素的房地产投资方案的优选问题.分析形成了房地产投资方案的评价指标体系,并在Hamming距离与Euclidean距离测度的基础上,建立了不完全偏好信息下的模糊多属性决策模型,能处理决策元素为一般模糊数的决策问题,同时提供了所建非线性规划模型的交叉迭代解法.实际算例的比较结果表明,本文提出的决策模型及算法优于文献中关于偏好信息完全确知的经典模型与算法.     

Metaheuristics for multiobjective optimisation

This is a summary of the author’s PhD thesis supervised by Laetitia Jourdan and El-Ghazali Talbi and defended on 8 December 2009 at the Université Lille 1. The thesis is written in French and is available from . This work deals with the design, implementation and experimental analysis of metaheuristics for solving multiobjective optimisation problems, with a particular interest on hard and large combinatorial problems from the field of logistics. After focusing on a unified view of multiobjective metaheuristics, we propose new cooperative, adaptive and parallel approaches. The performance of these methods are experimented on a scheduling and a routing problem involving two or three objective functions. We finally discuss how to adapt such metaheuristics during the search process in order to handle uncertainty that may occur from many different sources.     

Rigorous filtering using linear relaxations

This paper presents rigorous filtering methods for continuous constraint satisfaction problems based on linear relaxations, designed to efficiently handle the linear inequalities coming from a linear relaxation of quadratic constraints. Filtering or pruning stands for reducing the search space of constraint satisfaction problems. Discussed are old and new approaches for rigorously enclosing the solution set of linear systems of inequalities, as well as different methods for computing linear relaxations. This allows custom combinations of relaxation and filtering. Care is taken to ensure that all methods correctly account for rounding errors in the computations. The methods are implemented in the GloptLab environment for solving quadratic constraint satisfaction problems. Demonstrative examples and tests comparing the different linear relaxation methods are also presented.     

Numerical Solution of Riemann–Hilbert Problems: Random Matrix Theory and Orthogonal Polynomials

Recently, a general approach to solving Riemann–Hilbert problems numerically has been developed. We review this numerical framework and apply it to the calculation of orthogonal polynomials on the real line. Combining this numerical algorithm with the approach of Bornemann to compute Fredholm determinants, we are able to calculate spectral densities and gap statistics for a broad class of finite-dimensional unitary invariant ensembles. We show that the accuracy of the numerical algorithm for approximating orthogonal polynomials is uniform as the degree grows, extending the existing theory to handle g-functions. As another example, we compute the Hastings–McLeod solution of the homogeneous Painlevé II equation.     

A Model-Based Approach and Analysis for Multi-Period Networks

The aim of this contribution is to address a general class of network problems, very common in process systems engineering, where spoilage on arcs and storage in nodes are inevitable as time changes. Having a set of capacities, so-called horizon capacity which limits the total flow passing arcs over all periods, the min-cost flow problem in the discrete-time model with time-varying network parameters is investigated. While assuming a possibility of storage or and spoilage, we propose some approaches employing polyhedrals to obtain optimal solutions for a pre-specified planning horizon. Our methods describe some reformulations based on polyhedrals that lead to LP problems comprising a set of sparse subproblems with exceptional structures. Considering the sparsity and repeating structure of the polyhedrals, algorithmic approaches based on decomposition techniques of block-angular and block-staircase cases are proposed to handle the global problem aiming to reduce the computational resources required.     

Meta-heuristic approaches for minimizing total earliness and tardiness penalties of single-machine scheduling with a common due date

This study addresses a class of single-machine scheduling problems involving a common due date where the objective is to minimize the total job earliness and tardiness penalties. A genetic algorithm (GA) approach and a simulated annealing (SA) approach utilizing a greedy local search and three well-known properties in the area of common due date scheduling are developed. The developed algorithms enable the starting time of the first job not at zero and were tested using a set of benchmark problems. From the viewpoints of solution quality and computational expenses, the proposed approaches are efficient and effective for problems involving different numbers of jobs, as well as different processing time, and earliness and tardiness penalties.     

A heuristic for scheduling problems,especially for scheduling farm operations

Scheduling problems in agriculture are often solved using techniques such as linear programming (the multi-period formulation) and dynamic programming. But it is difficult to obtain an optimal schedule with these techniques for any but the smallest problems, because the model is unwieldly and much time is needed to solve the problem. Therefore, a new algorithm, a heuristic, has been developed to handle scheduling problems in agriculture. It is based on a search technique (i.e. hill-climbing) supported by a strong heuristic evaluation function. In this paper the heuristic performance is compared with dynamic programming. The heuristic offers near-optimal solutions and is much faster than the dynamic programming model. When tested against dynamic programming the difference in results was about 3%. This heuristic could probably also be applied in an industrial environment (e.g. agribusiness or road construction).     

A novel Lagrangian relaxation approach for a hybrid flowshop scheduling problem in the steelmaking-continuous casting process

One of the largest bottlenecks in iron and steel production is the steelmaking-continuous casting (SCC) process, which consists of steel-making, refining and continuous casting. The SCC scheduling is a complex hybrid flowshop (HFS) scheduling problem with the following features: job grouping and precedence constraints, no idle time within the same group of jobs and setup time constraints on the casters. This paper first models the scheduling problem as a mixed-integer programming (MIP) problem with the objective of minimizing the total weighted earliness/tardiness penalties and job waiting. Next, a Lagrangian relaxation (LR) approach relaxing the machine capacity constraints is presented to solve the MIP problem, which decomposes the relaxed problem into two tractable subproblems by separating the continuous variables from the integer ones. Additionally, two methods, i.e., the boundedness detection method and time horizon method, are explored to handle the unboundedness of the decomposed subproblems in iterations. Furthermore, an improved subgradient level algorithm with global convergence is developed to solve the Lagrangian dual (LD) problem. The computational results and comparisons demonstrate that the proposed LR approach outperforms the conventional LR approaches in terms of solution quality, with a significantly shorter running time being observed.     

A container yard storage strategy for improving land utilization and operation efficiency in a transshipment hub port

This paper studies the storage yard management problem in a busy transshipment hub, where intense loading and unloading activities have to be considered at the same time. The need to handle huge volumes of container traffic and the scarcity of land in the container port area pose serious challenges for the port operator to provide efficient services. A consignment strategy with a static yard template has been used to reduce the level of reshuffles in the yard, but it sacrifices on land utilization because of exclusive storage space reservation. Two space-sharing approaches are proposed to improve on the land utilization through dynamic reservation of storage space for different vessels during different shifts. Meanwhile, workload assignment among reserved spaces will also satisfy the high-low workload balancing protocol to reduce traffic congestion in the yard. A framework which integrates space reservation and workload assignment is proposed. Experimental results show that the framework is able to provide solutions for containers handling within much less storage space, while guarantee the least yard crane deployment.     

The production–inventory problem of a product with time varying demand,production and deterioration rates

In this paper, we consider the production–inventory problem in which the demand, production and deterioration rates of a product are assumed to vary with time. Shortages of a cycle are allowed to be backlogged partially. Two models are developed for the problem by employing different modeling approaches over an infinite planning horizon. Solution procedures are derived for determining the optimal replenishment policies. A procedure to find the near-optimal operating policy of the problem over a finite time horizon is also suggested.