This thesis describes a facility location problem in terms of transportation networks. Using an approach similar to the Thomson’s principle in electrical networks, we derive an equivalent lattice gas model with long range interactions, unveiling the nature of the quadratic transportation cost and providing alternative methods for optimizing the cost function other than the cavity approach used in previous studies. Optimal states of facility location in different scenarios are computed and analysed. Magnetized and antiferromagnetic domains coexist to balance coverage and energy saving in certain situations. The regimes with rugged energy landscape due to the competing interactions of the lattice gases are also identified, which impose difficulties on the ground state searching o...[ Read more ]

This thesis describes a facility location problem in terms of transportation networks. Using an approach similar to the Thomson’s principle in electrical networks, we derive an equivalent lattice gas model with long range interactions, unveiling the nature of the quadratic transportation cost and providing alternative methods for optimizing the cost function other than the cavity approach used in previous studies. Optimal states of facility location in different scenarios are computed and analysed. Magnetized and antiferromagnetic domains coexist to balance coverage and energy saving in certain situations. The regimes with rugged energy landscape due to the competing interactions of the lattice gases are also identified, which impose difficulties on the ground state searching of various local algorithms.