A grammar-based technique for genetic search and optimization

The genetic algorithm (GA) is a robust search technique which has been theoretically and empirically proven to provide efficient search for a variety of problems. Due largely to the semantic and expressive limitations of adopting a bitstring representation, however, the traditional GA has not found wide acceptance in the Artificial Intelligence community. In addition, binary chromosones can unevenly weight genetic search, reduce the effectiveness of recombination operators, make it difficult to solve problems whose solution schemata are of high order and defining length, and hinder new schema discovery in cases where chromosome-wide changes are required.;The research presented in this dissertation describes a grammar-based approach to genetic algorithms. Under this new paradigm, all members of the population are strings produced by a problem-specific grammar. Since any structure which can be expressed in Backus-Naur Form can thus be manipulated by genetic operators, a grammar-based GA strategy provides a consistent methodology for handling any population structure expressible in terms of a context-free grammar.;In order to lend theoretical support to the development of the syntactic GA, the concept of a trace schema--a similarity template for matching the derivation traces of grammar-defined rules--was introduced. An analysis of the manner in which a grammar-based GA operates yielded a Trace Schema Theorem for rule processing, which states that above-average trace schemata containing relatively few non-terminal productions are sampled with increasing frequency by syntactic genetic search. Schemata thus serve as the building blocks in the construction of the complex rule structures manipulated by syntactic GAs.;As part of the research presented in this dissertation, the GEnetic Rule Discovery System (GERDS) implementation of the grammar-based GA was developed. A comparison between the performance of GERDS and the traditional GA showed that the class of problems solvable by a syntactic GA is a superset of the class solvable by its binary counterpart, and that the added expressiveness greatly facilitates the representation of GA problems. to strengthen that conclusion, several experiments encompassing diverse domains were performed with favorable results

High-Quality Hypergraph Partitioning

This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer $k$, partition its vertex set into $k$ disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. Since the problem is computationally intractable, heuristics are used in practice - the most prominent being the three-phase multi-level paradigm: During coarsening, the hypergraph is successively contracted to obtain a hierarchy of smaller instances. After applying an initial partitioning algorithm to the smallest hypergraph, contraction is undone and, at each level, refinement algorithms try to improve the current solution. With this work, we give a brief overview of the field and present several algorithmic improvements to the multi-level paradigm. Instead of using a logarithmic number of levels like traditional algorithms, we present two coarsening algorithms that create a hierarchy of (nearly) $n$ levels, where $n$ is the number of vertices. This makes consecutive levels as similar as possible and provides many opportunities for refinement algorithms to improve the partition. This approach is made feasible in practice by tailoring all algorithms and data structures to the $n$-level paradigm, and developing lazy-evaluation techniques, caching mechanisms and early stopping criteria to speed up the partitioning process. Furthermore, we propose a sparsification algorithm based on locality-sensitive hashing that improves the running time for hypergraphs with large hyperedges, and show that incorporating global information about the community structure into the coarsening process improves quality. Moreover, we present a portfolio-based initial partitioning approach, and propose three refinement algorithms. Two are based on the Fiduccia-Mattheyses (FM) heuristic, but perform a highly localized search at each level. While one is designed for two-way partitioning, the other is the first FM-style algorithm that can be efficiently employed in the multi-level setting to directly improve $k$-way partitions. The third algorithm uses max-flow computations on pairs of blocks to refine $k$-way partitions. Finally, we present the first memetic multi-level hypergraph partitioning algorithm for an extensive exploration of the global solution space. All contributions are made available through our open-source framework KaHyPar. In a comprehensive experimental study, we compare KaHyPar with hMETIS, PaToH, Mondriaan, Zoltan-AlgD, and HYPE on a wide range of hypergraphs from several application areas. Our results indicate that KaHyPar, already without the memetic component, computes better solutions than all competing algorithms for both the cut-net and the connectivity metric, while being faster than Zoltan-AlgD and equally fast as hMETIS. Moreover, KaHyPar compares favorably with the current best graph partitioning system KaFFPa - both in terms of solution quality and running time