On the Impact of Multiobjective Scalarizing Functions

Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood. In this paper, we investigate the behavior of different scalarizing functions and their parameters. We thereby abstract firstly from any specific algorithm and only consider the difficulty of the single scalarized problems in terms of the search ability of a (1+lambda)-EA on biobjective NK-landscapes. Secondly, combining the outcomes of independent single-objective runs allows for more general statements on set-based performance measures. Finally, we investigate the correlation between the opening angle of the scalarizing function's underlying contour lines and the position of the final solution in the objective space. Our analysis is of fundamental nature and sheds more light on the key characteristics of multiobjective scalarizing functions.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Liger : a cross-platform open-source integrated optimization and decision-making environment

Real-world optimization problems involving multiple conflicting objectives are commonly best solved using multi-objective optimization as this provides decision-makers with a family of trade-off solutions. However, the complexity of using multi-objective optimization algorithms often impedes the optimization process. Knowing which optimization algorithm is the most suitable for the given problem, or even which setup parameters to pick, requires someone to be an optimization specialist. The lack of supporting software that is readily available, easy to use and transparent can lead to increased design times and increased cost. To address these challenges, Liger is presented. Liger has been designed for ease of use in industry by non-specialists in optimization. The user interacts with Liger via a visual programming language to create an optimization workflow, enabling the user to solve an optimization problem. Liger contains a novel optimization library known as Tigon. The library utilizes the concept of design patterns to enable the composition of optimization algorithms by making use of simple reusable operator nodes. The library offers a varied range of multi-objective evolutionary algorithms which cover different paradigms in evolutionary computation; and supports a wide variety of problem types, including support for using more than one programming language at a time to implement the optimization model. Additionally, Liger functionality can be easily extended by plugins that provide access to state-of-the-art visualization tools and are responsible for managing the graphical user interface. Lastly, new user-driven interactive capabilities are shown to facilitate the decision-making process and are demonstrated on a control engineering optimization problem

Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes

It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves

Magnetic shocks and substructures excited by torsional Alfvén wave interactions in merging expanding flux tubes

Vortex motions are frequently observed on the solar photosphere. These motions may play a key role in the transport of energy and momentum from the lower atmosphere into the upper solar atmosphere, contributing to coronal heating. The lower solar atmosphere also consists of complex networks of flux tubes that expand and merge throughout the chromosphere and upper atmosphere. We perform numerical simulations to investigate the behaviour of vortex driven waves propagating in a pair of such flux tubes in a non-force-free equilibrium with a realistically modelled solar atmosphere. The two flux tubes are independently perturbed at their footpoints by counter-rotating vortex motions. When the flux tubes merge, the vortex motions interact both linearly and nonlinearly. The linear interactions generate many small-scale transient magnetic substructures due to the magnetic stress imposed by the vortex motions. Thus, an initially monolithic tube is separated into a complex multi-threaded tube due to the photospheric vortex motions. The wave interactions also drive a superposition that increases in amplitude until it exceeds the local Mach number and produces shocks that propagate upwards with speeds of approximately $50$ km s$^{-1}$. The shocks act as conduits transporting momentum and energy upwards, and heating the local plasma by more than an order of magnitude, with peak temperature approximately $60,000$ K. Therefore, we present a new mechanism for the generation of magnetic waveguides from the lower solar atmosphere to the solar corona. This wave guide appears as the result of interacting perturbations in neighbouring flux tubes. Thus, the interactions of photospheric vortex motions is a potentially significant mechanism for energy transfer from the lower to upper solar atmosphere

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided

An efficient application of goal programming to tackle multiobjective problems with recurring fitness landscapes

Many real-world applications require decision-makers to assess the quality of solutions while considering multiple conflicting objectives. Obtaining good approximation sets for highly constrained many objective problems is often a difficult task even for modern multiobjective algorithms. In some cases, multiple instances of the problem scenario present similarities in their fitness landscapes. That is, there are recurring features in the fitness landscapes when searching for solutions to different problem instances. We propose a methodology to exploit this characteristic by solving one instance of a given problem scenario using computationally expensive multiobjective algorithms to obtain a good approximation set and then using Goal Programming with efficient single-objective algorithms to solve other instances of the same problem scenario. We use three goal-based objective functions and show that on benchmark instances of the multiobjective vehicle routing problem with time windows, the methodology is able to produce good results in short computation time. The methodology allows to combine the effectiveness of state-of-the-art multiobjective algorithms with the efficiency of goal programming to find good compromise solutions in problem scenarios where instances have similar fitness landscapes

Wave Damping Observed in Upwardly Propagating Sausage-mode Oscillations contained within a Magnetic Pore

We present observational evidence of compressible MHD wave modes propagating from the solar photosphere through to the base of the transition region in a solar magnetic pore. High cadence images were obtained simultaneously across four wavelength bands using the Dunn Solar Telescope. Employing Fourier and wavelet techniques, sausage-mode oscillations displaying significant power were detected in both intensity and area fluctuations. The intensity and area fluctuations exhibit a range of periods from 181 to 412 s, with an average period ~290 s, consistent with the global p-mode spectrum. Intensity and area oscillations present in adjacent bandpasses were found to be out of phase with one another, displaying phase angles of 6fdg12, 5fdg82, and 15fdg97 between the 4170 Å continuum–G-band, G-band–Na i D1, and Na i D1–Ca ii K heights, respectively, reiterating the presence of upwardly propagating sausage-mode waves. A phase relationship of ~0° between same-bandpass emission and area perturbations of the pore best categorizes the waves as belonging to the "slow" regime of a dispersion diagram. Theoretical calculations reveal that the waves are surface modes, with initial photospheric energies in excess of 35,000 W m−2. The wave energetics indicate a substantial decrease in energy with atmospheric height, confirming that magnetic pores are able to transport waves that exhibit appreciable energy damping, which may release considerable energy into the local chromospheric plasma

Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes

It has been increasingly reported that the multiobjective optimization evolutionary algorithm based on decomposition (MOEA/D) is promising for handling multiobjective optimization problems (MOPs). MOEA/D employs scalarizing functions to convert an MOP into a number of single-objective subproblems. Among them, penalty boundary intersection (PBI) is one of the most popular decomposition approaches and has been widely adopted for dealing with MOPs. However, the original PBI uses a constant penalty value for all subproblems and has difficulties in achieving a good distribution and coverage of the Pareto front for some problems. In this paper, we investigate the influence of the penalty factor on PBI, and suggest two new penalty schemes, i.e., adaptive penalty scheme and subproblem-based penalty scheme (SPS), to enhance the spread of Pareto-optimal solutions. The new penalty schemes are examined on several complex MOPs, showing that PBI with the use of them is able to provide a better approximation of the Pareto front than the original one. The SPS is further integrated into two recently developed MOEA/D variants to help balance the population diversity and convergence. Experimental results show that it can significantly enhance the algorithm�s performance. © 2016, Springer-Verlag Berlin Heidelberg

Dynamics of Ion Sound Waves in the Front of the Terrestrial Bow Shock

International audienceIon-sound turbulence played a crucial role in early models of anomalous processes in the shock front. Both the current and the gradient of electron temperature within the magnetic ramp region have been considered as sources of free energy for the ion sound instability in the shock front. Since the solar wind velocity upstream of the terrestrial bow shock usually exceeds the velocity of ion sound waves, these waves were expected to be observed in the region the ramp and downstream of it. However, the EFW instrument on board Cluster 3 measured ion sound wave packets in the upatream part of the foot region. These observations pose two questions, namely 'What is the generation mechanism of these waves?', and 'Why are ion sound waves observed as confined quasimonchromatic wave packets?'. The envelope of such wave packets results from nonlinearities in the wave dynamics. However, these nonlineararities do not appear in the solutions to the KdV equations which theoretically describe such wave packets. Internal burst mode data from the EFW instrument are used to separate spatial and temporal variations on a distance about 60 meters. Nonlinear frequency domain identification techniques have been applied to the observed ion sound waves. The results are used to identify possible wave sources and investigate their dynamics