Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping - Sonntag, Konstantin; Peitz, Sebastian (SIAM Journal on Optimization)
We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.
Keywords: multiobjective optimization; Pareto optimization; Lyapunov analysis; gradient-likedynamical systems; inertial dynamics; asymptotic vanishing damping; fast convergence

Optimization-based reliability control of mechatronic systems - Meyer, Tobias
Reliability-adaptive systems allow an adaptation of system behavior based on current system reliability. They can extend their lifetime at the cost of lowered performance or vice versa. This can be used to adapt failure behavior according to a maintenance plan, thus increasing availability while using up system capability fully. To facilitate setup, a control algorithm independent of a degradation model is desired. A closed loop control technique for reliability based on a health index, a measure for system degradation, is introduced. It uses self-optimization as means to implement behavior adaptation. This is based on selecting the priorities of objectives that the system pursues. Possible working points are computed beforehand using model-based multiobjective optimization techniques. The controller selects the priorities of objectives and this way balances reliability and performance. As exemplary application, an automatically actuated single plate dry clutch is introduced. The entire reliability control is setup and lifetime experiments are conducted. Results show that the variance of time to failure is reduced greatly, making the failure behavior more predictable. At the same time, the desired usable lifetime can be extended at the cost of system performance to allow for changed maintenance intervals. Together, these possibilities allow for greater system usage and better planning of maintenance.
Keywords: dependability; reliability; behavior adaptation; self-optimization; multiobjective optimization; optimal control; automotive drivetrain; clutch system; reliability-adaptive system

Formulation of reliability-related objective functions for design of intelligent mechatronic systems - Kaul, Thorben; Meyer, Tobias; Sextro, Walter (SAGE Journals)
State-of-the-art mechatronic systems offer inherent intelligence that enables them to autonomously adapt their behavior to current environmental conditions and to their own system state. This autonomous behavior adaptation is made possible by software in combination with complex sensor and actuator systems and by sophisticated information processing, all of which make these systems increasingly complex. This increasing complexity makes the design process a challenging task and brings new complex possibilities for operation and maintenance. However, with the risk of increased system complexity also comes the chance to adapt system behavior based on current reliability, which in turn increases reliability. The development of such an adaption strategy requires appropriate methods to evaluate reliability based on currently selected system behavior. A common approach to implement such adaptivity is to base system behavior on different working points that are obtained using multiobjective optimization. During operation, selection among these allows a changed operating strategy. To allow for multiobjective optimization, an accurate system model including system reliability is required. This model is repeatedly evaluated by the optimization algorithm. At present, modeling of system reliability and synchronization of the models of behavior and reliability is a laborious manual task and thus very error-prone. Since system behavior is crucial for system reliability, an integrated model is introduced that integrates system behavior and system reliability. The proposed approach is used to formulate reliability-related objective functions for a clutch test rig that are used to compute feasible working points using multiobjective optimization.
Keywords: Integrated model; reliability; system behavior; Bayesian network; multiobjective optimization

Method to Identify Dependability Objectives in Multiobjective Optimization Problem - Meyer , Tobias; Sondermann-Wölke, Christoph; Sextro, Walter (Conference Proceedings of the 2nd International Conference on System-Integrated Intelligence)
Intelligent mechatronic systems, such as self-optimizing systems, allow an adaptation of the system behavior at runtime based on the current situation. To do so, they generally select among several pre-defined working points. A common method to determine working points for a mechatronic system is to use model-based multiobjective optimization. It allows finding compromises among conflicting objectives, called objective functions, by adapting parameters. To evaluate the system behavior for different parameter sets, a model of the system behavior is included in the objective functions and is evaluated during each function call. Intelligent mechatronic systems also have the ability to adapt their behavior based on their current reliability, thus increasing their availability, or on changed safety requirements; all of which are summed up by the common term dependability. To allow this adaptation, dependability can be considered in multiobjective optimization by including dependability-related objective functions. However, whereas performance-related objective functions are easily found, formulation of dependability-related objective functions is highly system-specific and not intuitive, making it complex and error-prone. Since each mechatronic system is different, individual failure modes have to be taken into account, which need to be found using common methods such as Failure-Modes and Effects Analysis or Fault Tree Analysis. Using component degradation models, which again are specific to the system at hand, the main loading factors can be determined. By including these in the model of the system behavior, the relation between working point and dependability can be formulated as an objective function. In our work, this approach is presented in more detail. It is exemplified using an actively actuated single plate dry clutch system. Results show that this approach is suitable for formulating dependability-related objective functions and that these can be used to extend system lifetime by adapting system behavior.
Keywords: Self-optimization; multiobjective optimization; objective function; dependability; intelligent system; behavior adaptation

On the Properties of the R2 Indicator - Brockhoff, Dimo; Wagner, Tobias; Trautmann, Heike (Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation)
In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The R2 and the Hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the R2 indicator exist. In this paper, we thus perform a comprehensive investigation of the properties of the R2 indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of μ solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the R2 and HV indicator are presented.
Keywords: hypervolume indicator; multiobjective optimization; performance assessment; r2 indicator