A tabu search procedure based on a random Roulette diversification for the weighted maximal planar graph problem

An efficient and effective tabu search implementation for the weighted maximal planar graph problem is proposed. The search incorporates a number of novel features including: the introduction of a new set of two-move operators; a move-cache-memory structure for efficiently searching the neighbourhood space; and a random roulette selection from a ranked list of best moves for diversification. The effects of these and other features on solution quality are investigated. Computational results are reported on a set of 100 benchmark instances of sizes varying from 20 to 100 vertices. The results demonstrate that the new probabilistic tabu search algorithm is very competitive with state of the art algorithms in the literature in terms of both solution quality and computational effort. Scope The weighted maximal planar graph (WMPG) problem seeks to find a sub-graph from a given weighted complete graph such that the subgraph is planar, i.e., it can be embedded on the plane without any edges intersecting. It is maximal, i.e., no additional edge can be added to the sub-graph without destroying its planarity and it has also the maximal sum of edge weights. The WMPG problem has applications in modern manufacturing systems, e.g., arranging rooms within a building floor plan, and placing machines on a factory floor or components on a circuit board. The WMPG problem is NP-Hard. In the absence of a polynomial-time algorithm to solve it exactly, it still attracts research on approximate approaches.