Heuristics with constant error guarantees for the design of tree networks

Article Abstract:

The Capacitated Minimal Spanning Tree Problem is examined. A tree network is a group of trees rooted at a shared central node. Several types of network design problems can be seen as needed for the formation of a spanning tree network of a minimum length, subject to a bound on the total of 'weights' on the nodes of a given component tree. Such problems are NP-complete, and it has been demonstrated in the past that only miniscule examples can be solved to optimality. An efficient heuristic algorithm is presented, based on cutting up a 'traveling salesman' tour. The heuristic finds a solution whose expense is at most 3-2-K times the minimum when all the nodes have a unit weight and the capacity restriction is K.

Heuristic programming

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An approximate algorithm for multidimensional zero-one knapsack problems - a parametric approach

Article Abstract:

A new approximate algorithm is offered to address multi-dimensional, zero-one knapsack problems with positive coefficients. The technique is governed by three parameters, which alter the trade-off between computation time and solution quality, and whose values are established by users. The solution found on average was 0.34% of the best for 48 test problems with five to 20 constraints and six to 500 variables. Computation time was most brief compared with three other well-known heuristics.

Models, Scheduling (Management), Integer programming

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