Learning Opposites with Evolving Rules

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their opposition-based version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type- I) opposition, that for each $x\in[a,b]$ assigns its opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been called type-II opposite in literature. In absence of any knowledge about a function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate $\breve{x}_I$ according to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ true opposites? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform opposition mining. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.Comment: Accepted for publication in The 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015), August 2-5, 2015, Istanbul, Turke

How to Speed up Optimization? Opposite-Center Learning and Its Application to Differential Evolution

This paper introduces a new sampling technique called Opposite-Center Learning (OCL) intended for convergence speed-up of meta-heuristic optimization algorithms. It comprises an extension of Opposition-Based Learning (OBL), a simple scheme that manages to boost numerous optimization methods by considering the opposite points of candidate solutions. In contrast to OBL, OCL has a theoretical foundation-the opposite center point is defined as the optimal choice in pair-wise sampling of the search space given a random starting point. A concise analytical background is provided. Computationally the opposite center point is approximated by a lightweight Monte Carlo scheme for arbitrary dimension. Empirical results up to dimension 20 confirm that OCL outperforms OBL and random sampling: the points generated by OCL have shorter expected distances to a uniformly distributed global optimum. To further test its practical performance, OCL is applied to differential evolution (DE). This novel scheme for continuous optimization named Opposite-Center DE (OCDE) employs OCL for population initialization and generation jumping. Numerical experiments on a set of benchmark functions for dimensions 10 and 30 reveal that OCDE on average improves the convergence rates by 38% and 27% compared to the original DE and the Opposition-based DE (ODE), respectively, while remaining fully robust. Most promising are the observations that the accelerations shown by OCDE and OCL increase with problem dimensionality

Differentiation signatures in the Flora region

Most asteroid families are very homogeneous in physical properties. Some show greater diversity, however. The Flora family is the most intriguing of them. The Flora family is spread widely in the inner main belt, has a rich collisional history, and is one of the most taxonomically diverse regions in the main belt. As a result of its proximity to the asteroid (4) Vesta (the only currently known intact differentiated asteroid) and its family, migration between the two regions is possible. This dynamical path is one of the counter arguments to the hypothesis that there may be traces of a differentiated parent body other than Vesta in the inner main belt region. We here investigate the possibility that some of the V- and A- types (commonly interpreted as basaltoids and dunites - parts of the mantle and crust of differentiated parent bodies) in the Flora dynamical region are not dynamically connected to Vesta.Comment: accepted to AA (28 09 2015

A new evolutionary search strategy for global optimization of high-dimensional problems

Global optimization of high-dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation. The weakness of randomization-based evolutionary algorithms in searching high-dimensional spaces is demonstrated in this paper. A new strategy, SP-UCI is developed to treat complexity caused by high dimensionalities. This strategy features a slope-based searching kernel and a scheme of maintaining the particle population's capability of searching over the full search space. Examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that SP-UCI surpasses two popular algorithms, particle swarm optimizer (PSO) and differential evolution (DE), on high-dimensional problems. Experimental results also corroborate the argument that, in high-dimensional optimization, only problems with well-formative fitness landscapes are solvable, and slope-based schemes are preferable to randomization-based ones. © 2011 Elsevier Inc. All rights reserved

A Wide-Field CCD Survey for Centaurs and Kuiper Belt Objects

A modified Baker-Nunn camera was used to conduct a wide-field survey of 1428 square degrees of sky near the ecliptic in search of bright Kuiper Belt objects and Centaurs. This area is an order of magnitude larger than any previously published CCD survey for Centaurs and Kuiper Belt Objects. No new objects brighter than red magnitude m=18.8 and moving at a rate 1"/hr to 20"/hr were discovered, although one previously discovered Centaur 1997 CU26 Chariklo was serendipitously detected. The parameters of the survey were characterized using both visual and automated techniques. From this survey the empirical projected surface density of Centaurs was found to be SigmaCentaur(m<18.8)=7.8(+16.0 -6.6)x10^-4 per square degree and we found a projected surface density 3sigma upper confidence limit for Kuiper Belt objects of SigmaKBO(m< 18.8)<4.1x10^-3 per square degree. We discuss the current state of the cumulative luminosity functions of both Centaurs and Kuiper Belt objects. Through a Monte Carlo simulation we show that the size distribution of Centaurs is consistent with a q=4 differential power law, similar to the size distribution of the parent Kuiper Belt Objects. The Centaur population is of order 10^7 (radius > 1 km) assuming a geometric albedo of 0.04. About 100 Centaurs are larger than 50 km in radius, of which only 4 are presently known. The current total mass of the Centaurs is 10^-4 Earth Masses. No dust clouds were detected resulting from Kuiper Belt object collisions, placing a 3sigma upper limit <600 collisionally produced clouds of m<18.8 per year.Comment: 13 pages, 5 figures, Accepted for Publication in A

Triplicity and Physical Characteristics of Asteroid (216) Kleopatra

To take full advantage of the September 2008 opposition passage of the M-type asteroid (216) Kleopatra, we have used near-infrared adaptive optics (AO) imaging with the W.M. Keck II telescope to capture unprecedented high resolution images of this unusual asteroid. Our AO observations with the W.M. Keck II telescope, combined with Spitzer/IRS spectroscopic observations and past stellar occultations, confirm the value of its IRAS radiometric radius of 67.5 km as well as its dog-bone shape suggested by earlier radar observations. Our Keck AO observations revealed the presence of two small satellites in orbit about Kleopatra (see Marchis et al., 2008). Accurate measurements of the satellite orbits over a full month enabled us to determine the total mass of the system to be 4.64+/-0.02 10^18 Kg. This translates into a bulk density of 3.6 +/-0.4 g/cm3, which implies a macroscopic porosity for Kleopatra of ~ 30-50%, typical of a rubble-pile asteroid. From these physical characteristics we measured its specific angular momentum, very close to that of a spinning equilibrium dumbbell.Comment: 35 pages, 3 Tables, 9 Figures. In press to Icaru

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte