An algebraic framework for multi-objective and robust variants of path problems

It is well known that various types of path problems in graphs can be treated together within a common algebraic framework. Thereby each type is characterized by a different ``path algebra", i.e., a different instance of the same abstract algebraic structure. This paper demonstrates that the common algebraic framework, although originally intended for conventional problem variants, can be extended to cover multi-objective and robust variants. Thus the paper is mainly concerned with constructing and justifying new path algebras that correspond to such more complex problem varieties. A consequence of the obtained algebraic formulation is that multi-objective or robust problem instances can be solved by well-known general algorithms designed to work over an arbitrary path algebra. The solutions obtained in this way comprise all paths that are efficient in the Pareto sense. The efficient paths are by default described only implicitly, as vectors of objective-function values. Still, it is shown in the paper that, with slightly extended versions of the involved algebras, the same paths can also be identified explicitly. Also, for robust problem instances it is possible to select only one ``robustly optimal" path according to a generalized min-max or min-max regret criterion

Independent sets and vertex covers considered within the context of robust optimization

This paper studies robust variants of the maximum weighted independent set problem and the minimum weighted vertex cover problem, respectively. Both problems are posed in a vertex-weighted graph. The paper explores whether the complement of a robustly optimal independent set must be a robustly optimal vertex cover, and vice-versa

Solving Robust Variants of Integer Flow Problems with Uncertain Arc Capacities

This paper deals with robust optimization and network flows. Several robust variants of integer flow problems are considered. They assume uncertainty of network arc capacities as well as of arc unit costs (where applicable). Uncertainty is expressed by discrete scenarios. Since the considered variants of the maximum flow problem are easy to solve, the paper is mostly concerned with NP-hard variants of the minimum-cost flow problem, thus proposing an approximate algorithm for their solution. The accuracy of the proposed algorithm is verified by experiments

Experimental Evaluation of a Parallel Max-Flow Algorithm

The maximum flow problem has been studied for over forty years. One of the methods for solving this problem is the generic push-relabel algorithm. In this paper we develop a parallel version of this sequential algorithm. Our assumed model of computation is a shared-memory multiprocessor. We describe a concrete implementation of the algorithm based on the PVM package, and present the obtained numerical results

A distributed evolutionary algorithm with a superlinear speedup for solving the vehicle routing problem

In this paper we present a distributed evolutionary algorithm for solving the capacitated vehicle routing problem. Our algorithm consists of autonomous processes that create heterogeneous evolutionary environments, perform evolution on separate populations of chromosomes, and communicate asynchronously through occasional migrations of chromosomes. The paper also presents experiments where the algorithm has been tested on some benchmark problem instances. By measuring the effects of distribution on solution quality and on computing time, the experiments confirm that the algorithm achieves a superlinear speedup

Solving Sparse Symmetric Path Problems on a Network of Computers

We present an optimized version of a previously studied distributed algorithm for solving path problems in graphs. The new version is designed for sparse symmetric path problems, i.e. for graphs that are both sparse and undirected. We report on experiments where the new version has been implemented and evaluated with the PVM package

Multilayer Perceptrons and Data Compression

This paper investigates the feasibility of using artificial neural networks as a tool for data compression. More precisely, the paper measures compression capabilities of the standard multilayer perceptrons. An outline of a possible "neural'' data compression method is given. The method is based on training a perceptron to reproduce a given data file. Experiments are presented, where the outlined method has been simulated by using differently configured perceptrons and various data files. The best compression rates obtained in the experiments are listed, and compared with similar results produced in a previous paper by holographic neural networks