Laura Barbulescu

Scheduling Space–Ground Communications for the Air Force Satellite Control Network

We present the first coupled formal and empirical analysis of the Satellite Range Scheduling application. We structure our study as a progression; we start by studying a simplified version of the problem in which only one resource is present. We show that the simplified version of the problem is equivalent to a well-known machine scheduling problem and use this result to prove that Satellite Range Scheduling is NP-complete. We also show that for the one-resource version of the problem, algorithms from the machine scheduling domain outperform a genetic algorithm previously identified as one of the best algorithms for Satellite Range Scheduling. Next, we investigate if these performance results generalize for the problem with multiple resources. We exploit two sources of data: actual request data from the U.S. Air Force Satellite Control Network (AFSCN) circa 1992 and data created by our problem generator, which is designed to produce problems similar to the ones currently solved by AFSCN. Three main results emerge from our empirical study of algorithm performance for multiple-resource problems. First, the performance results obtained for the single-resource version of the problem do not generalize: the algorithms from the machine scheduling domain perform poorly for the multiple-resource problems. Second, a simple heuristic is shown to perform well on the old problems from 1992; however it fails to scale to larger, more complex generated problems. Finally, a genetic algorithm is found to yield the best overall performance on the larger, more difficult problems produced by our generator.

Properties of Gray and Binary Representations

Representations are formalized as encodings that map the search space to the vertex set of a graph. We define the notion of bit equivalent encodings and show that for such encodings the corresponding Walsh coefficients are also conserved. We focus on Gray codes as particular types of encoding and present a review of properties related to the use of Gray codes. Gray codes are widely used in conjunction with genetic algorithms and bit-climbing algorithms for parameter optimization problems. We present new convergence proofs for a special class of unimodal functions; the proofs show that a steepest ascent bit climber using any reflected Gray code representation reaches the global optimum in a number of steps that is linear with respect to the encoding size. There are in fact many different Gray codes.Shifting is defined as a mechanism for dynamically switching from one Gray code representation to another in order to escape local optima. Theoretical results that substantially improve our understanding of the Gray codes and the shifting mechanism are presented. New proofs also shed light on the number of unique Gray code neighborhoods accessible via shifting and on how neighborhood structure changes during shifting. We show that shifting can improve the performance of both a local search algorithm as well as one of the best genetic algorithms currently available.

Satellite Range Scheduling: A Comparison of Genetic, Heuristic and Local Search

Three algorithms are tested on the satellite range scheduling problem, using data from the U.S. Air Force Satellite Control Network; a simple heuristic, as well as local search methods, are compared against a genetic algorithm on old benchmark problems as well as problems produced by a generator we recently developed. The simple heuristic works well on the old benchmark, but fails to scale to larger, more complex problems produced by our generator. The genetic algorithm yields the best overall performance on larger, more difficult problems.

Testing, Evaluation and Performance of Optimization and Learning Systems

Benchmarks and test suites are widely used to evaluate optimization and learning systems. The advantage is that these test problems provide an objective means of comparing systems. The potential disadvantage is that systems can become overfitted to work well on benchmarks and therefore that good performance on benchmarks does not generalize to real world problems. The meaning and significance of benchmarks is examined in light of theoretical results such as “No Free Lunch.” The “structure” of common benchmarks is also explored.

Comparing heuristic search methods and genetic algorithms for warehouse scheduling

We compare several techniques for scheduling shipment of customer orders for the Coors Brewing warehouse and production line. The goal is to minimize time at dock for trucks and railcars while also minimizing inventory. The techniques include a genetic algorithm, local search operators, heuristic rules, systematic search and hybrid approaches. Initial results show a hybrid genetic algorithm to be superior to the other methods. The evaluation function is a fast approximate form of a warehouse simulation. We also assess the sensitivity of the search algorithms to noise in an approximate evaluation function using a more detailed (and costly) simulation.