Finding the optimal locations under non-submodular cannibalization: when the personal movement flow matters

Due to the ever-growing city scale, the fierce competition among businesses, and residents’ strong willingness to chase a better quality of life, it is crucial for companies and governments to devote more effort to city planning that will benefit neighborhoods and the people who live there. Therefore, the facility location problem attracts considerable attention from academia and industry. It aims to model complex real-world scenarios and solve various facility location applications in promoting social benefits or saving costing. As a result, several models have been proposed, such as the P-center model, P-medium model, Set Covering model, and hierarchical model, to better match the reality; tons of brilliant work has been proposed by researchers under variant models and complex settings to pursue a more accurate problem formulation. On the other hand, with its immense complexity, the real world tends to defy carefully designed complex settings and problem formulation, which poses challenges for accurately capturing application characteristics, not to mention further effectively and efficiently finding the optimal locations. This thesis will tackle these challenges on three unexplored flow-capturing problems and try to answer three research questions, including non-submodular cannibalization, coverage maximization for the seekers against lost minimization for the host, and cost minimization for nonuniform probabilistic equal covering. First, we study the flow-capturing problem under a scenario of deploying out-of-home billboards displaying advertising to affect individual decisions, where the influence of advertising on customers measures the coverage. A particular situation in this work is the non-submodular cannibalization, which is caused by the Sigmoid function used to measure the advertising influence from out-of-home billboards on a customer. The non-submodular cannibalization makes this NP-hard problem to be more challenging. Therefore, we propose a novel tangent-line-based algorithm to compute a submodular function to estimate the upper bound of influence. Henceforth, we introduce a branch-and-bound framework with an early termination condition. However, this framework is time-consuming when the Set of potential locations is enormous. Thus, we further optimize it with a progressive pruning upper bound estimation approach, which achieves a better approximation ratio and significantly decreases the running time. Second, we study how to deal with multiple resource seekers and a source provider, where each seeker requests a certain amount of demands. This is similar to the multi-objective facility location problem, in which we need to minimize the wasted source by just satisfying seekers’ demands since the wasted source can be allocated to future demands, which maximizes the earned profit for the source provider. Under such a scenario, we formulate the wasted source and the earned profit together, namely regret, as our objective function which, however, is neither monotone nor submodular. Therefore, we propose a randomized local search framework with two neighborhood search strategies and prove that the worst case is bounded. Last, we investigate an important but rarely studied problem, i.e., how to place facilities such that (1) it ensures the likelihood of facilities covering every person can meet a threshold at least, and (2) the total cost of placement is minimized. Unlike the first two problems in which the profit-push goal forces the solution to focus on high-cost-efficiency persons but ignore others, this work provides equal attention for everyone. However, the covering goal based on the check-in probability causes non-submodular cannibalization. Therefore, based on a greedy-based solution, we transform the covering goal to a logarithmic form and then propose a multi-selection branch-and-bound-based frame, which can trade off efficiency and effectiveness. Next, in order to improve the scalability of handling a large-scale dataset, we further propose a hybrid-greedy solution to improve efficiency. To summarize, this thesis proposes novel variant models based on the flow-capturing problem to more accurately simulate different situations and further explore how to find the locations for the proposed problems formulated upon the proposed model.