The design (synthesis) of analog electrical circuits starts with a highlevel statement of the circuit's desired behavior and requires creating a circuit that satisfies the specified design goals. Analog circuit synthesis entails the creation of both the topology and the sizing (numerical values) of all of the circuit's components. The difficulty of the problem of analog circuit synthesis is well known and there is no previously known general automated technique for synthesizing an analog circuit from a high-level statement of the circuit's desired behavior. This paper presents a single uniform approach using genetic programming for the automatic synthesis of both the topology and sizing of a suite of eight different prototypical analog circuits, including a lowpass filter, a crossover (woofer and tweeter) filter, a source identification circuit, an amplifier, a computational circuit, a timeoptimal controller circuit, a temperature-sensing circuit, and a voltage reference circuit. The problem-specific information required for each of the eight problems is minimal and consists primarily of the number of inputs and outputs of the desired circuit, the types of available components, and a fitness measure that restates the highlevel

Motivated by applications in robotics, we formulate the problem of minimizing the total angle cost of a TSP tour for a set of points in Euclidean space, where the angle cost of a tour is the sum of the direction changes at the points. We establish the NP-hardness of both this problem and its relaxation to the cycle cover problem. We then consider the issue of designing approximation algorithms for these problems and show that both problems can be approximated to within a ratio of O(log n) in polynomial time. We also consider the problem of simultaneously approximating both the angle and the length measure for a TSP tour. In studying the resulting tradeoff, we choose to focus on the sum of the two performance ratios and provide tight bounds on the sum. Finally, we consider the extremal value of the angle measure and obtain essentially tight bounds for it. In this extended abstract we restrict our attention to the planar setting, but all our results are easily extended to higher dimensio...

For a given set A ` (\Gamma; +] of angles, the problem "Angle-Restricted Tour" (ART) is to decide whether a set P of n points in the Euclidean plane allows a closed directed tour consisting of straight line segments, such that all angles between consecutive line segments are from the set A. We present a variety of algorithmic and combinatorial results on this problem. In particular, we show that any finite set of at least five points allows a "pseudoconvex" tour (i. e. a tour where all angles are nonnegative), and we derive a fast algorithm for constructing such a tour. Moreover, we give a complete classification (from the computational complexity point of view) for the special cases where the tour has to be part of the orthogonal grid.

Genetic programming is an automatic programming technique that evolves computer programs to solve, or approximately solve, problems. This paper presents two examples in which genetic programming creates a computer program for controlling a robot so that the robot moves to a specified destination point in minimal time. In the first approach, genetic programming evolves a computer program composed of ordinary arithmetic operations and conditional operations to implement a time-optimal control strategy. In the second approach, genetic programming evolves the design of an analog electrical circuit consisting of transistors, diodes, resistors, and power supplies to implement a near-optimal control strategy. 1.

Most problem-solving techniques used by engineers involve the introduction of analytical and mathematical representations and techniques that are entirely foreign to the problem at hand. Genetic programming offers the possibility of solving problems in a more direct way using the given ingredients of the problem. This idea is explored by considering the problem of designing an electrical controller to implement a solution to the time-optimal fly-to control problem. 1.