This presentation discusses a practical solution approach to a challenging inventory routing problem. In particular, we discuss the case of a company distributing essential, but low-value goods to customers having a relatively stable demand rate. We propose a long-term, cyclic planning approach using new solution constructs. The concepts of �multi-tours� and �multi-frequency multi-tours� are used in a multi-start savings heuristic framework. Results show that using �multi-frequency multi-tour� patterns leads to considerable cost savings, mostly as a result of a significant reduction in the required vehicle fleet.

Nowadays, simulation in shipbuilding becomes more and more important. The use of simulation-based design and virtual reality technologies facilitates higher efficiency in terms of work strategy planning, and offers, as a result, significant productivity gains. Such gains can not be easily obtained only by using the simulation tools. It is required to link the simulation model with an optimization package.

Simulation is used in many different sectors � as automotive industry � but not yet so much in shipbuilding industry. This is due to the complexity and specifications of the work: almost each ship to build is unique and in consequence automation � and thus simulation � is quite difficult. In consequence, optimization linked to such simulation model is rare in industry. The project was to try to use simulation to model a shipbuilding workshop and linked it to an optimization tool.

The optimization is a sequence optimization: assemblies have to be built in a certain order that can be optimized in respect to various constraints. We have used genetic algorithm to find the best sequence. Obviously, a crucial problem was to reduce calculation time to reasonable levels.

A local search method has been developed for nonlinear mixed integer problems with implicit constraints. This formulation appears in structural optimization problems where the complexity of the models leads to implicit relationships between the variables. The evaluation of the implicit constraints for any given solution is possible only at an expensive computing cost using finite element or analytical methods. Approximation methods may be used to find local optima of structural problems with all real variables.

We present a mixed integer model where some variables have to take their values in discrete sets and the others have real values. We develop a method that combines a local search algorithm with an existing solver based on approximation methods. This solver is used as a black-box. The local search algorithm allows an effective exploration of the solution space by setting the values of some discrete variables at each run of the black-box solver. The local search algorithm can be considered as a multi-start procedure for the black-box solver. Tests have shown that the combination of a local search procedure and an approximation method performs very well for mixed integer nonlinear problems with implicit constraints.

The recent advances in simulation technologies like CFD, FEM, thermal analysis and unsteady flow, combined with the emergence of improved optimization algorithms make now possible the development and use of automatic optimization software and methodologies for complex multi-disciplinary aeronautical applications. In this context, the MAX optimization software developed at CENAERO has been successfully applied to various industrial problems. This code performs derivative-free optimization with very few calls to the computer intensive simulation software. Practically, the method is based on the use of a genetic algorithm using real coded variables and combined with an approximate model built through radial basis function (RBF) networks. Several applications have already been performed using this optimization technology, especially for the design of turbomachinery blades. Other studies include parameter identification for structural material law, design optimization of heat pipes in satellites, noise reduction of civil aircraft liners, etc.

Mechanics of multibody systems deals with the dynamic, kinematical or geometrical behaviour of systems composed of articulated rigid bodies like robots, vehicles, human body, machine tools, etc... Such analyses require the simulation of these systems and lead to the characterization of their performances. Some of these performances obviously constitute interesting objectives to optimize. One of the main issues in the optimization of multibody systems concerns transient motion problems, costly to evaluate and closed-loop topologies. Contrary to open topologies, they involve algebraic constraint equations between the coordinates of the bodies. Depending on the used formalism, their resolution and their impact on the optimization problem are strongly different. The applications of multibody optimization are various, from robotics to biomechanics, through automotive. Many examples will be described with different objectives: isotropy of parallel manipulators, design of planar mechanisms, identification of biomechanical models and ride or handling of road vehicles.

Convex optimization problems constitute a (nonlinear) generalization of linear optimization problems for which every local optimum is a global optimum, which can therefore be found very efficiently using dedicated algorithms. Optimization problems belonging to this class are, for instance, linear programs (LPs), second-order cone programs (SOCPs) and semidefinite programs (SDPs). In this talk we introduce two mechanical engineering applications of convex optimization techniques.

The first application is counterweight balancing, that is, the problem of determining counterweights for a linkage, such that it exerts smaller forces and moments on its supporting frame. It is shown that determining the optimal counterweight parameters can be formulated as an SOCP for planar mechanisms and an SDP for spatial mechanisms.

As a second, bio-mechanical application, we consider dynamic musculoskeletal analysis, that is, the problem of determining the muscle forces that underly some experimentally observed human motion. It is shown that this challenging, large-scale, nonconvex optimization problem can be solved in an efficient manner by using convex optimization techniques. That is, an approximate, convex program is formulated and solved, in order to provide a hot-start for the exact, nonconvex program. The key element in this approximation is a (global) linearization of muscle physiology, based on techniques from experimental system identification. This approach is applied to the study of muscle forces during gait.

The results presented comprise joint work with Goele Pipeleers, Myriam Verschuure, Dimitri Coemelck, Jan De Caigny, Friedl De Groote, Erwin Aertbeli�en, Jan Swevers, Joris De Schutter (all affiliated with the Mech. Eng. Dept., PMA Division) Pieter Spaepen (Mech. Eng. Dept., BMGO Division), Ilse Jonkers (Dept. of Kinesiology) and Lieven Vandenberghe (University of California Los Angeles -- Electrical Engineering Dept.).

B. Demeulenaere is a Postdoctoral Fellow of the Research Foundation--Flanders. Part of the presented research has been carried out during a visiting scholarship (2004--2005) at UCLA's EE Dept., with the financial aid of the Research Foundation--Flanders and under the supervision of L. Vandenberghe. This work is supported by K.U.Leuven-BOF EF/05/006 Center-of-Excellence Optimization in Engineering, F.W.O. project G.0462.05 `Development of a powerful dynamic optimization framework for mechanical and biomechanical systems based on convex optimization techniques' and I.W.T. project 040444 'Dynamic balancing of weaving machines'.

Although offering significant improvements with respect to the second generation (namely, GSM), the third generation (3G) of mobiles (known in Europe under the acronym UMTS) guarantees only a limited transmission rate and hence fails to provide high-rate demanding services for instance high definition videoconferencing. Two easy ways to increase the rates is either to increase either the transmission power or the bandwidth. However, on the one hand, both environmental concerns and battery autonomy issues prevent a raise of the transmission power. On the other hand, bandwidth (spectrum) is a scarce resource, legally regulated. Recently, MIMO (Multiple Input Multiple Output) systems arising from the use of several antennas both at the transmit side and the receive side have been proposed as a possible candidate for the next generation (4G). By sending several information streams in parallel, the MIMO systems allow to increase the rates, improve the robustness and/or to increase the number of users that can be simultaneously accommodated.

The purpose of the talk is twofold. Firstly, we introduce the MIMO wireless paradigm and emphasize the key challenges designers are confronted with. Secondly, we present some solutions we have adopted to solve specific optimization problems arising when several users are simultaneously communicating.

A systematic approach is proposed, allowing the design of a sensor network able to identify all key variables of a process with a prescribed accuracy, at the lowest cost, and to preserve the redundancy of the measurement system, even in case of failure of a single sensor. The proposed method is based on a linearised process model, derived automatically from a general, non-linear validation model. A genetic algorithm is used to select the sensor types and locations.

To reduce the solution time, two ways of parallelizing the algorithm have been compared: the global parallelization and the distributed genetic algorithms. Both techniques allow reducing the elapsed time but the second one is more efficient.

Typical results are presented for an ammonia synthesis loop.

A general convex interior point method is presented for solving under Matlab the lower bound (or static) approach of limit analysis (LA) in order to determine limit loadings of mechanical structures. The method is tested in the case of a von Mises material by comparison with those obtained using first a pre-linearization, second a direct SOCP formulation solved with the MOSEK code. The same problems are solved afterwards for a Gurson material, the non-classical objective of the work, where SOCP does not apply.

In a second step, thanks to a variational formulation based on the virtual power principle and convexity properties, a stress-based upper bound method is proposed, using continuous or discontinuous, linear or quadratic velocity fields as virtual variables, and stress fields as real parameters. This numerical method presents an analogy with the static approach, only the linear conditions are changed; it is tested on the same previous mechanical problems for both cases of von Mises and Gurson materials. Finally, we present different methods to circumvent the shortcomings of the direct methods used for solving the systems of linear equations required in the aforementioned approaches.

Nowadays, the demand for robust and efficient optimization algorithms to solve mixed integer and nonconvex problems is continuously increasing. In this talk, we present a problem of that kind arising in electrical supply networks and called "Tertiary Voltage Control" problem (TVC). This problem is very hard because of its strong nonconvexity due to equality constraints involving trigonometric functions (among others).

The method we propose consists in solving a succession of appropriate linear relaxation problems articulated in a branch-and-bound tree. As the speed of convergence of the method depends on the quality of the relaxations, we design relaxations as tight as possible. To this aim, we use piecewise approximations based on special ordered sets for each nonlinear component of the initial problem, and modify these approximations to obtain valid lower and upper approximations. If the relaxation problem is not close enough to the initial problem, we further refine it by dividing the feasible domain of relaxation, hence creating two new subproblems. In that way, we ensure the convergence of the method to the global optimum of the initial problem as far as the feasible domain of the latter is bounded. We terminate this talk by presenting some preliminary numerical experiments on a toy problem having the main characteristics of the TVC problem.