In our paper we analysed algorithms that seek the optimal routing configuration in backbone networks with capacity constraints. We investigated a special case when multiple full mesh demand sets (forming Virtual Private Networks (VPNs)) have to be built. We examined the pro-active path based shared protection scheme and investigated heuristic algorithms to calculate the paths. We analysed two d...

Solving scheduling problems with Constraint Satisfaction Problems (CSP’s) techniques implies a wide space search with a large number of variables, each one of them with a wide interpretation domain. This paper discusses the application of CSP heuristic techniques (based on the concept of slack of activities) for variable and value ordering on a special type of job-shop scheduling problems in wh...

The multi-homogeneous B ezout number of a polynomial system is the number of paths that one has to follow in computing all its isolated solutions with continuation method. Each partition of variables corresponds to a multi-homogeneous B ezout number. It is a challenging problem to find a partition with minimal multi-homogeneous B ezout number. Two heuristic numerical methods for computing the m...

Algorithms which seek global optima are computationally expensive. Alternatively, heuristic methods have been proposed to find approximate solutions. Because heuristic algorithms do not always deliver exact solutions it is difficult to verify the computed solutions. Such a problem is known as the oracle problem. In this paper, we propose to apply Metamorphic Testing (MT) in such situations beca...

Constructing a small BDD from a given boolean formula depends on finding a good variable ordering. Finding a good order is NP-complete. In the past, methods based on heuristic analysis and formula (circuit) rewriting have shown to be useful for specific problem domains. We show that these methods need to be integrated: heuristic analysis can drive rewriting, which in turn simplifies analysis. W...

In this paper, we consider a variation of the Euclidean Steiner Tree Problem in which the space underlying the set of nodes has a specified non-uniform cost structure. This problem is significant in many practical situations, such as laying cable networks, where the cost for laying a cable can be highly dependent on the location and the nature of the area through which it is to be laid. We empi...

Some engineering applications of heuristic multilevel optimization methods are presented and the discussion focuses on the dependency matrix that indicates the relationship between problem functions and variables. Decompositions are identified with dependency matrices that are full, block diagonal and block triangular with coupling variables. Coordination of the subproblem optimizations is show...

We investigate the stochastic flow shop problem with m machines and general distributions for processing times. No analytic method exists for solving this problem, so we looked instead at heuristic methods. We devised three constructive procedures with modest computational requirements, each based on approaches that have been successful at solving the deterministic counterpart. We compared the ...