Incremental multiple objective genetic algorithms

This paper presents a new genetic algorithm approach to multi-objective optimization problemsIncremental Multiple Objective Genetic Algorithms (IMOGA). Different from conventional MOGA methods, it takes each objective into consideration incrementally. The whole evolution is divided into as many phases as the number of objectives, and one more objective is considered in each phase. Each phase is composed of two stages: first, an independent population is evolved to optimize one specific objective; second, the better-performing individuals from the evolved single-objective population and the multi-objective population evolved in the last phase are joined together by the operation of integration. The resulting population then becomes an initial multi-objective population, to which a multi-objective evolution based on the incremented objective set is applied. The experiment results show that, in most problems, the performance of IMOGA is better than that of three other MOGAs, NSGA-II, SPEA and PAES. IMOGA can find more solutions during the same time span, and the quality of solutions is better

Evolving dynamic multiple-objective optimization problems with objective replacement

This paper studies the strategies for multi-objective optimization in a dynamic environment. In particular, we focus on problems with objective replacement, where some objectives may be replaced with new objectives during evolution. It is shown that the Pareto-optimal sets before and after the objective replacement share some common members. Based on this observation, we suggest the inheritance strategy. When objective replacement occurs, this strategy selects good chromosomes according to the new objective set from the solutions found before objective replacement, and then continues to optimize them via evolution for the new objective set. The experiment results showed that this strategy can help MOGAs achieve better performance than MOGAs without using the inheritance strategy, where the evolution is restarted when objective replacement occurs. More solutions with better quality are found during the same time span

Determining the convergence of variance in Gaussian belief propagation via semi-definite programming

In order to compute the marginal distribution from a high dimensional distribution with loopy Gaussian belief propagation (BP), it is important to determine whether Gaussian BP would converge. In general, the convergence condition for Gaussian BP variance and mean are not necessarily the same, and this paper focuses on the convergence condition of Gaussian BP variance. In particular, by describing the message-passing process of Gaussian BP as a set of updating functions, the necessary and sufficient convergence condition of Gaussian BP variance is derived, with the converged variance proved to be independent of the initialization as long as it is greater or equal to zero. It is further proved that the convergence condition can be verified efficiently by solving a semi-definite programming (SDP) optimization problem. Numerical examples are presented to corroborate the established theories.published_or_final_versio

Pre-flare coronal dimmings

In this paper, we focus on the pre-flare coronal dimmings. We report our multiwavelength observations of the GOES X1.6 solar flare and the accompanying halo CME produced by the eruption of a sigmoidal magnetic flux rope (MFR) in NOAA active region (AR) 12158 on 2014 September 10. The eruption was observed by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamic Observatory (SDO). The photospheric line-of-sight magnetograms were observed by the Helioseismic and Magnetic Imager (HMI) aboard SDO. The soft X-ray (SXR) fluxes were recorded by the GOES spacecraft. The halo CME was observed by the white light coronagraphs of the Large Angle Spectroscopic Coronagraph (LASCO) aboard SOHO.} {About 96 minutes before the onset of flare/CME, narrow pre-flare coronal dimmings appeared at the two ends of the twisted MFR. They extended very slowly with their intensities decreasing with time, while their apparent widths (8$-$9 Mm) nearly kept constant. During the impulsive and decay phases of flare, typical fanlike twin dimmings appeared and expanded with much larger extent and lower intensities than the pre-flare dimmings. The percentage of 171 {\AA} intensity decrease reaches 40\%. The pre-flare dimmings are most striking in 171, 193, and 211 {\AA} with formation temperatures of 0.6$-$2.5 MK. The northern part of the pre-flare dimmings could also be recognized in 131 and 335 {\AA}.} To our knowledge, this is the first detailed study of pre-flare coronal dimmings, which can be explained by the density depletion as a result of the gradual expansion of the coronal loop system surrounding the MFR during the slow rise of the MFR.Comment: 6 pages, 8 figures, to be accepted for publication by A&

Convergence Analysis of the Variance in Gaussian Belief Propagation

It is known that Gaussian belief propagation (BP) is a low-complexity algorithm for (approximately) computing the marginal distribution of a high dimensional Gaussian distribu- tion. However, in loopy factor graph, it is important to determine whether Gaussian BP converges. In general, the convergence conditions for Gaussian BP variances and means are not nec- essarily the same, and this paper focuses on the convergence condition of Gaussian BP variances. In particular, by describing the message-passing process of Gaussian BP as a set of updating functions, the necessary and sufficient convergence conditions of Gaussian BP variances are derived under both synchronous and asynchronous schedulings, with the converged variances proved to be independent of the initialization as long as it is chosen from the proposed set. The necessary and sufficient convergence condition is further expressed in the form of a semi-definite programming (SDP) optimization problem, thus can be verified more efficiently compared to the existing convergence condition based on compu- tation tree. The relationship between the proposed convergence condition and the existing one based on computation tree is also established analytically. Numerical examples are presented to corroborate the established theories.published_or_final_versio