Evolutionary Algorithms for Quantum Computers

In this article, we formulate and study quantum analogues of randomized search heuristics, which make use of Grover search (in Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 212–219. ACM, New York, 1996) to accelerate the search for improved offsprings. We then specialize the above formulation to two specific search heuristics: Random Local Search and the (1+1) Evolutionary Algorithm. We call the resulting quantum versions of these search heuristics Quantum Local Search and the (1+1) Quantum Evolutionary Algorithm. We conduct a rigorous runtime analysis of these quantum search heuristics in the computation model of quantum algorithms, which, besides classical computation steps, also permits those unique to quantum computing devices. To this end, we study the six elementary pseudo-Boolean optimization problems OneMax, LeadingOnes, Discrepancy, Needle, Jump, and TinyTrap. It turns out that the advantage of the respective quantum search heuristic over its classical counterpart varies with the problem structure and ranges from no speedup at all for the problem Discrepancy to exponential speedup for the problem TinyTrap. We show that these runtime behaviors are closely linked to the probabilities of performing successful mutations in the classical algorithms.     

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Efficient workspace generation for binary manipulators with many actuators

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators with binary actuators have a finite number of states. Major benefits of binary actuation are that extensive feedback control is not required, task repeatability can be very high, and two-state actuators are generally very inexpensive, thus resulting in low-cost robotic mechanisms. Determining the workspace of a binary manipulator is of great practical importance for a variety of applications. For instance, a representation of the workspace is essential for trajectory tracking, motion planning, and the optimal design of binary manipulators. Given that the number of configurations attainable by binary manipulators grows exponentially in the number of actuated degrees of freedom, 0(2), brute force representation of binary manipulator workspaces is not feasible in the highly actuated case. This article describes an algorithm that performs recursive calculations starting at the end-effector and terminating at the base. The implementation of these recursive calculations is based on the macroscopically serial structure and the discrete nature of the manipulator. As a result, the method is capable of approximating the workspace in linear time, O(n), where the slope depends on the acceptable error. © 1995 John Wiley b Sons, Inc.     

Absorption and Metabolism of <Emphasis Type="Italic">cis</Emphasis>-9,<Emphasis Type="Italic">trans</Emphasis>-11-CLA and of Its Oxidation Product 9,11-Furan Fatty Acid by Caco-2 Cells

Furan fatty acids (furan-FA) can be formed by auto-oxidation of conjugated linoleic acids (CLA) and may therefore be ingested when CLA-containing foodstuff is consumed. Due to the presence of a furan ring structure, furan-FA may have toxic properties, however, these substances are toxicologically not well characterized so far. Here we show that 9,11-furan-FA, the oxidation product of the major CLA isomer cis-9,trans-11-CLA (c9,t11-CLA), is not toxic to human intestinal Caco-2 cells up to a level of 100 μM. Oil-Red-O staining indicated that 9,11-furan-FA as well as c9,t11-CLA and linoleic acid are taken up by the cells and stored in the form of triglycerides in lipid droplets. Chemical analysis of total cellular lipids revealed that 9,11-furan-FA is partially elongated probably by the enzymatic activity of cellular fatty acid elongases whereas c9,t11-CLA is partially converted to other isomers such as c9,c11-CLA or t9,t11-CLA. In the case of 9,11-furan-FA, there is no indication for any modification or activation of the furan ring system. From these results, we conclude that 9,11-furan-FA has no properties of toxicological relevance at least for Caco-2 cells which serve as a model for enterocytes of the human small intestine.     

Evaluating efficiency of self-reconfiguration in a class of modular robots

In this article we examine the problem of dynamic self-reconfiguration of a class of modular robotic systems referred to as metamorphic systems. A metamorphic robotic system is a collection of mechatronic modules, each of which has the ability to connect, disconnect, and climb over adjacent modules. A change in the macroscopic morphology results from the locomotion of each module over its neighbors. Metamorphic systems can therefore be viewed as a large swarm of physically connected robotic modules that collectively act as a single entity. What distinguishes metamorphic systems from other reconfigurable robots is that they possess all of the following properties: (1) a large number of homogeneous modules; (2) a geometry such that modules fit within a regular lattice; (3) self-reconfigurability without outside help; (4) physical constraints which ensure contact between modules. In this article, the kinematic constraints governing metamorphic robot self-reconfiguration are addressed, and lower and upper bounds are established for the minimal number of moves needed to change such systems from any initial to any final specified configuration. These bounds are functions of initial and final configuration geometry and can be computed very quickly, while it appears that solving for the precise number of minimal moves cannot be done in polynomial time. It is then shown how the bounds developed here are useful in evaluating the performance of heuristic motion planning/reconfiguration algorithms for metamorphic systems. © 1996 John Wiley & Sons, Inc.