Computational geometry

Hybrid metaheuristics have received considerable interest these recent years in the field of combinatorial optimization. A wide variety of hybrid approaches have been proposed in the literature. In this paper, a taxonomy of hybrid metaheuristics is presented in an attempt to provide a common terminology and classification mechanisms. The taxonomy, while presented in terms of metaheuristics, is also applicable to most types of heuristics and exact optimization algorithms.

As an illustration of the usefulness of the taxonomy an annoted bibliography is given which classifies a large number of hybrid approaches according to the taxonomy.

A Taxonomy of Hybrid Metaheuristics

Metaheuristics are the most exciting development in approximate optimization techniques of the last two decades. They have had widespread successes in attacking a variety of difficult combinatorial optimization problems that arise in many practical areas. This bibliography provides a classification of a comprehensive list of 1380 references on the theory and application of metaheuristics. Metaheuristics include but are not limited to constraint logic programming; greedy random adaptive search procedures; natural evolutionary computation; neural networks; non-monotonic search strategies; space-search methods; simulated annealing; tabu search; threshold algorithms and their hybrids. References are presented in alphabetical order under a number of subheadings.

Metaheuristics: A bibliography

Publisher Summary This chapter presents three mathematical tools that can be used to describe graph-grammars and the sets generated by them. The chapter describes graph properties by logical formulas and presents a comparison of the powers of several logical languages. The chapter discusses first-order logic, second-order logic, and monadic second-order logic, together with a few variants and restrictions of these three languages. It presents algebraic techniques that are useful for defining and studying graph rewriting rules and context-free graph-grammars. The chapter also presents the use of category theory for specifying graph rewriting rules in a precise and concise way, and for properly defining the least or rather the initial solution of a system of graph equations. It presents some links between the context-free graph-grammars and monadic second-order logic. Some applications to the definition of sets of graphs by forbidden configurations and to the theory of NP-completeness are also presented in the chapter.

Graph Rewriting: An Algebraic and Logic Approach.

In this paper we study the effect of using information about (partial) symmetries for the minimization of reduced ordered binary decision diagrams (ROBDD's). The influence of symmetries for the integration in dynamic variable ordering is studied for both completely and incompletely specified Boolean functions. The problems above are studied from a theoretical and practical point of view. Statistical results and benchmark results are reported to underline the efficiency of the approach. They prove that our techniques lead to improvements of the ROBDD sizes by up to 70%.

BDD minimization using symmetries

We present a new algorithm for k-layer straightline crossing minimization which is based on sifting that is a heuristic for dynamic reordering of decision diagrams used during logic synthesis and formal verification of logic circuits. The experiments prove sifting to be very efficient. In particular it outperforms the traditional layer by layer sweep based heuristics known from literature by far when applied to k-layered graphs with k ≥ 3.

/pdf/using-sifting-for-k-layer-straightline-crossing-minimization-3z59i3qpxv.pdf

Using sifting for k-layer straightline crossing minimization

This paper addresses problems that arise while checking the equivalence of two Boolean functions under arbitrary input permutations The permutation problem has several applications in the synthesis and verification of combinational logic: it arises in the technology mapping stage of logic synthesis and in logic verification A popular method to solve it is to compute a signature for each variable that helps to establish a correspondence between the variables Several researchers have suggested a wide range of signatures that have been used for this purpose However, for each choice of signature, there remain variables that cannot be uniquely identified Our research has shown that, for a given example, this set of problematic variables tends to be the same-regardless of the choice of signatures The paper investigates this problem

http://cs.ecs.baylor.edu/~maurer/CSI5346/LimSigs.pdf

Limits of using signatures for permutation independent Boolean comparison

Discrete wavelet transformations (DWT) followed by embedded zerotree encoding is a very efficient technique for image compression \cite{TenLectures, Shapiro, Spiht}. However, the algorithms proposed in literature assume random access to the whole image. This makes the algorithms unsuitable for hardware solutions because of extensive access to external memory. Here, we present an efficient architecture for computing DWT of images, which is based on a partitioned approach for lossy image compression~\cite{Ritter}. The architecture achieves its computational power by using pipelining and taking advantage of the flexible memory configurations available in FPGA's.

/pdf/a-pipelined-architecture-for-partitioned-dwt-based-lossy-1lft662q1b.pdf

Paul Molitor

Papers

BDD minimization using symmetries

Using sifting for k-layer straightline crossing minimization

Limits of using signatures for permutation independent Boolean comparison

A pipelined architecture for partitioned DWT based lossy image compression using FPGA's

Exact algorithms and heuristics for the Quadratic Traveling Salesman Problem with an application in bioinformatics