Knapsack problem with a single continuous variable (KPC) is a natural extension of the standard 0-1 knapsack problem. In the KPC, the capacity of the knapsack is not fixed, so it becomes more difficult to solve. Although several metaheuristics have been proposed to solve the KPC, their performances are not stable enough. This paper proposes a hybrid ant colony optimization (HACO) algorithm to solve the KPC. In the HACO algorithm, a simplified ACO algorithm is designed to search the optimal subset of items, and the mutation operator of differential evolution algorithm is used to search the optimal value of continuous variable. The parameter of the mutation operator is adaptively configured via an ACO algorithm. In the simplified ACO algorithm, an independent selection strategy and a pheromone-based selection strategy are designed to speed up the algorithm and simplify the tuning of parameters respectively. Personal best solutions constructed by each ant are used to deposit pheromone. Furthermore, a value-based greedy optimization strategy is introduced to enhance the solutions. The HACO algorithm is experimentally analyzed on 40 KPC instances. The experimental results show that the HACO algorithm is better than other competitors in terms of obtaining the best solution and the mean solution.

Summary This article focuses on how to design an efficient GPU‐based chicken swarm optimization (CSO) algorithm (GCSO), so as to improve diversity and speed up convergence by running a large number of populations in parallel. GCSO mainly improves the sequential CSO in three aspects: (i) GCSO modifies the location updating equation of the rooster and proposes a parallel iterative strategy to transform the sequential iteration process into a parallel iterative process, thereby achieving fine‐grained parallelism and improving the convergence speed. (ii) A multirange search strategy is proposed to build different neighborhoods for each flock on the graphic process units (GPU), so that each flock searched in their respective neighborhoods, thus increasing the density and diversity of the search, and making it not easy to fall into a local optimum. (iii) A new column storage structure is designed to meet the requirement of coalescent access on GPU. Twelve benchmark functions are selected to compare GCSO algorithm with some sequential intelligence optimization algorithms and the GPU‐based particle swarm algorithm. The results show that the GCSO is able to obtain a speedup up to 163.09× compared with the CSO and achieve better optimization results in terms of both optimization accuracy and convergence speed than some intelligence optimization algorithms.

As the volume of data and technical complexity of large-scale analysis increases, many domain experts desire a computational powerful but still familiar analysis interface to fully participate in the analysis workflow by just focusing on individual datasets, leaving the large-scale computation to the system. Towards this goal, we discuss Divide-and-Conquer strategies that can help domain experts perform large-scale simulations by scaling up their analysis code written in R, the most popuar data science and interactive analysis language. We then proceed to implementing the Divide-and-Conquer strategies as a dental imaging analysis framework, VisRden, that uses R as the analysis language, allowing advanced users to provide custom R scripts and variables to be fully embedded into the large-scale analysis workflow in R. VisRden can divide large-scale image processing tasks and conquer 3D reconstruction tasks with SGE (Sun Grid Engine) array jobs and R. Image-based operations and result aggregations are scheduled as array jobs in a parallel means to accelerate the knowledge discovery process. All these combine to provide a new analytics workflow for performing similar large-scale analysis loops where expert users only need to focus on the Divide-and-Conquer tasks with the domain knowledge.

In this paper we present a mathematical knot/braid diagram interface that exploits 3D computer graphics, interactive visualization, and multi-touch technology to enhance one's intuitive experience with mathematical theory of knots. Our interaction model is based on the clever but simple geometric construction named the Reide-meister moves, which allows 3D topological manipulations using rather simple 2D moves. Multi-touch interfaces can provide a natural way for us to interact with the extra degrees of freedom that characterize knots' mathematical, physical, and arithmetic properties. Relative to a specialized mouse-driven interface, the proposed multi-touch interface is easier and more intuitive to learn, and our pilot study shows that knot and braid manipulation with multi-touch is much faster and more efficient. All these combine to show that interactive computer graphics methods and computer interfaces can be used to construct virtual manipulatives and meet the challenge of exploring abstract mathematical worlds.

Many geometric problems of interest to mathematical visualization applications involve changing structures requiring mathematical simulations, such as the moves that transform one knot into an equivalent knot. In this paper, we propose to explore a unique paradigm that makes use of self-deformable object models embedded in mathematical space, supplemented by energy-driven relaxation and user-defined motion constraints to guide the simulation through the configuration space. Furthermore, we exploit web-based user interfaces and parallelization to accelerate mathematical simulations, and to extract key moments where successive terms in the sequence differ by one critical change to represent and analyze various mathematical evolutions. The presented work leverages the nature of the interrelationship between mathematics and computer science, especially computer graphics, graph algorithms, user interfaces, and accelerated computation.

Learning and interaction are viewed as two related but distinct topics in developmental robotics. Many studies focus solely on either building a robot that can acquire new knowledge and learn to perform new tasks, or designing smooth human-robot interactions with pre-acquired knowledge and skills. The present paper focuses on linking language learning with human-robot interaction, showing how better human-robot interaction can lead to better language learning by robot. Toward this goal, we developed a real-time human-robot interaction paradigm in which a robot learner acquired lexical knowledge from a human teacher through free-flowing interaction. With the same statistical learning mechanism in the robot's system, we systematically manipulated the degree of activity in human-robot interaction in three experimental conditions: the robot learner was either highly active with lots of speaking and looking acts, or moderately active with a few acts, or passive without actions. Our results show that more talking and looking acts from the robot, including those immature behaviors such as saying non-sense words or looking at random targets, motivated human teachers to be more engaged in the interaction. In addition, more activities from the robot revealed its robot's internal learning states in real time, which allowed human teachers to provide more useful and "on-demand" teaching signals to facilitate learning. Thus, compared with passive and batch-mode training, an active robot learner can create more and better training data through smooth and effective social interactions that consequentially lead to more successful language learning.

We present KnotPad, an interactive paper-like system for visualizing and exploring mathematical knots; we exploit topological drawing and math-aware deformation methods in particular to enable and enrich our interactions with knot diagrams. Whereas most previous efforts typically employ physically based modeling to simulate the 3D dynamics of knots and ropes, our tool offers a Reidemeister move based interactive environment that is much closer to the topological problems being solved in knot theory, yet without interfering with the traditional advantages of paper-based analysis and manipulation of knot diagrams. Drawing knot diagrams with many crossings and producing their equivalent is quite challenging and error-prone. KnotPad can restrict user manipulations to the three types of Reidemeister moves, resulting in a more fluid yet mathematically correct user experience with knots. For our principal test case of mathematical knots, KnotPad permits us to draw and edit their diagrams empowered by a family of interactive techniques. Furthermore, we exploit supplementary interface elements to enrich the user experiences. For example, KnotPad allows one to pull and drag on knot diagrams to produce mathematically valid moves. Navigation enhancements in KnotPad provide still further improvement: by remembering and displaying the sequence of valid moves applied during the entire interaction, KnotPad allows a much cleaner exploratory interface for the user to analyze and study knot equivalence. All these methods combine to reveal the complex spatial relationships of knot diagrams with a mathematically true and rich user experience.