Set-based Multiobjective Fitness Landscapes: A Preliminary Study

Fitness landscape analysis aims to understand the geometry of a given optimization problem in order to design more efficient search algorithms. However, there is a very little knowledge on the landscape of multiobjective problems. In this work, following a recent proposal by Zitzler et al. (2010), we consider multiobjective optimization as a set problem. Then, we give a general definition of set-based multiobjective fitness landscapes. An experimental set-based fitness landscape analysis is conducted on the multiobjective NK-landscapes with objective correlation. The aim is to adapt and to enhance the comprehensive design of set-based multiobjective search approaches, motivated by an a priori analysis of the corresponding set problem properties

Chatter milling modeling of active magnetic bearing spindle in high-speed domain

A new dynamical modeling of Active Magnetic Bearing Spindle (AMBS) to identify machining stability of High Speed Milling (HSM) is presented. This original modeling includes all the minimum required parameters for stability analysis of AMBS machining. The stability diagram generated with this new model is compared to classical stability lobes theory. Thus, behavior’s specificities are highlighted, especially the major importance of forced vibrations for AMBS. Then a sensitivity study shows impacts of several parameters of the controller. For example, gain adjustment shows improvements on stability. Side milling ramp test is used to quickly evaluate the stability. Finally, the simulation results are then validated by HSM cutting tests on a 5 axis machining center with AMBS

Soft beams: when capillarity induces axial compression

We study the interaction of an elastic beam with a liquid drop in the case where bending and extensional effects are both present. We use a variational approach to derive equilibrium equations and constitutive relation for the beam. This relation is shown to include a term due to surface energy in addition of the classical Young's modulus term, leading to a modification of Hooke's law. At the triple point where solid, liquid, and vapor phases meet we find that the external force applied on the beam is parallel to the liquid-vapor interface. Moreover, in the case where solid-vapor and solid-liquid interface energies do not depend on the extension state of the beam, we show that the extension in the beam is continuous at the triple point and that the wetting angle satisfy the classical Young-Dupr\'e relation

Chatter Control by Spindle Speed Variation in High-Speed Milling

High-speed milling operations are often limited by regenerative vibrations. The aim of this paper is to analyze the effect of spindle speed variation on machine tool chatter in high-speed milling. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. Parametric studies show also the influence of the frequency and amplitude variation parameters. This modeling is validated experimentally by variable spindle speed cutting tests with a triangular shape. Stable and unstable tests are analyzed in term of amplitude vibration and surface roughness degradation. This work reveals that stability must be considered at period variation scale. It is also shown that spindle speed variation can be efficiently used to suppress chatter in the flip lobe area

An Analysis on Selection for High-Resolution Approximations in Many-Objective Optimization

This work studies the behavior of three elitist multi- and many-objective evolutionary algorithms generating a high-resolution approximation of the Pareto optimal set. Several search-assessment indicators are defined to trace the dynamics of survival selection and measure the ability to simultaneously keep optimal solutions and discover new ones under different population sizes, set as a fraction of the size of the Pareto optimal set.Comment: apperas in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes

In multiobjective combinatorial optimization, there exists two main classes of metaheuristics, based either on multiple aggregations, or on a dominance relation. As in the single objective case, the structure of the search space can explain the difficulty for multiobjective metaheuristics, and guide the design of such methods. In this work we analyze the properties of multiobjective combinatorial search spaces. In particular, we focus on the features related the efficient set, and we pay a particular attention to the correlation between objectives. Few benchmark takes such objective correlation into account. Here, we define a general method to design multiobjective problems with correlation. As an example, we extend the well-known multiobjective NK-landscapes. By measuring different properties of the search space, we show the importance of considering the objective correlation on the design of metaheuristics.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011