Quantum algorithms for multicriteria optimization of construction machine allocation among road facilities

Abstract

A road-building contractor that runs several sites at once has to reconcile three requirements that cannot be reduced to one another: short relocation runs, a shift capacity matched to the planned demand of every site, and no crowding of machines of one technological group onto a single work area. The calculations establish how circuit depth and criterion weights govern the allocation obtained in a model scheme. The material is a model scheme of three construction machines and three road facilities with disclosed relocation distances, shift capacities and planned demands; one machine attached to one facility serves as the modelling unit. A weighted convolution of three normalized criteria, extended by a penalty for violating single attachment, was recast as a quadratic binary problem and solved by exact state-vector simulation of a nine-qubit circuit with angles tuned by a grid pass and a Nelder-Mead search. At the base inputs the computed convolution of the selected allocation reached the exhaustive minimum of 0.2102, whereas attaching every machine to its closest facility exceeded that minimum by 129.44%. The calculated value of that probability was 1.013%, and raising the depth from one layer to five increased it by roughly an order of magnitude. Within the model scheme a moderate depth makes the optimal allocation the most probable admissible outcome, and the weight of the capacity-mismatch criterion governs the composition of the computed attachment far more strongly than the number of retained candidate allocations.