Phase transitions in Pareto optimal complex networks

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem finding phase transitions of different kinds. Distinct phases are associated to different arrangements of the connections; but the need of drastic topological changes does not determine the presence, nor the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.Comment: 14 pages, 7 figure

Multi-objective optimal design of inerter-based vibration absorbers for earthquake protection of multi-storey building structures

In recent years different inerter - based vibration absorbers (IVAs) emerged for the earthquake protection of building structures coupling viscous and tuned - mass dampers with an inerter device . In the three most popular IVAs the inerter is functioning either as a motion amplifier [tuned - viscous - mass - damper (TVMD) configuration], mass amplifier [tuned - mass - damper - inerter (T MDI) configuration], or mass substitute [tuned - inerter - damper (TID) configuration]. Previous work has shown that through proper tuning , IVAs achieve enhanced earthquake - induced vibration suppression and/or weight reduction compared to conventional dampers/absorbers , but at the expense of increased control forces exerted from the IVA to the host building structure . These potentially large forces are typically not accounted for by current IVA tuning approaches. In this regard, a multi-objective IVA design approach is herein developed to identify the compromise between the competing objectives of (i) suppressing earthquake-induced vibrations in buildings, and (ii) avoiding development of excessive IVA (control) forces, while, simultaneously, assessing the appropriateness of different modeling assumptions for practical design of IVAs for earthquake engineering applications . The potential of the approach to pinpoint Pareto optimal IVA designs against the above objectives is illustrated for different IVA placements along the height of a benchmark 9-storey steel frame structure. Objective (i) is quantified according to current performanc e-based seismic design trends using first-passage reliability criteria associated with the probability of exceeding pre-specified thresholds of storey drifts and/or floor accelerations being the engineering demand parameters (EDPs) of interest . A variant, simpler, formulation is also considered using as performance quantification the sum of EDPs variances in accordance to traditional tuning methods for dynamic vibration absorbers. Objective (ii) is quantified through the variance of the IVA force. It is found that reduction of IVA control force of up to 3 times can be achieved with insignificant deterioration of building performance com pared to the extreme Pareto optimal IVA design targeting maximum vibration suppression , while TID and TMDI a chieve practically the same building performance and significantly outperform the TVMD. Moreover, it is shown that the simpler variant formulation may provide significantly suboptimal reliability performance . Lastly, it is verified that the efficacy of optimal IVA designs for stationary conditions is maintained for non-stationary stochastic excitation model capturing typical evolutionary features of earthquake excitations

Development of an automated aircraft subsystem architecture generation and analysis tool

Purpose – The purpose of this paper is to present a new computational framework to address future preliminary design needs for aircraft subsystems. The ability to investigate multiple candidate technologies forming subsystem architectures is enabled with the provision of automated architecture generation, analysis and optimization. Main focus lies with a demonstration of the frameworks workings, as well as the optimizers performance with a typical form of application problem. Design/methodology/approach – The core aspects involve a functional decomposition, coupled with a synergistic mission performance analysis on the aircraft, architecture and component levels. This may be followed by a complete enumeration of architectures, combined with a user defined technology filtering and concept ranking procedure. In addition, a hybrid heuristic optimizer, based on ant systems optimization and a genetic algorithm, is employed to produce optimal architectures in both component composition and design parameters. The optimizer is tested on a generic architecture design problem combined with modified Griewank and parabolic functions for the continuous space. Findings – Insights from the generalized application problem show consistent rediscovery of the optimal architectures with the optimizer, as compared to a full problem enumeration. In addition multi-objective optimization reveals a Pareto front with differences in component composition as well as continuous parameters. Research limitations/implications – This paper demonstrates the frameworks application on a generalized test problem only. Further publication will consider real engineering design problems. Originality/value – The paper addresses the need for future conceptual design methods of complex systems to consider a mixed concept space of both discrete and continuous nature via automated methods

An O(1)-Approximation for Minimum Spanning Tree Interdiction

Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is minimum spanning tree (MST) interdiction. Here, an undirected multigraph with nonnegative edge weights and positive interdiction costs on its edges is given, together with a positive budget B. The goal is to find a subset of edges R, whose total interdiction cost does not exceed B, such that removing R leads to a graph where the weight of an MST is as large as possible. Frederickson and Solis-Oba (SODA 1996) presented an O(log m)-approximation for MST interdiction, where m is the number of edges. Since then, no further progress has been made regarding approximations, and the question whether MST interdiction admits an O(1)-approximation remained open. We answer this question in the affirmative, by presenting a 14-approximation that overcomes two main hurdles that hindered further progress so far. Moreover, based on a well-known 2-approximation for the metric traveling salesman problem (TSP), we show that our O(1)-approximation for MST interdiction implies an O(1)-approximation for a natural interdiction version of metric TSP