Abstract-We consider the competitive facility location problem in which two competing sides (the Leader and the Follower) open in succession their facilities, and each consumer chooses one of the open facilities basing on its own preferences. The problem amounts to choosing the Leader's facility locations so that to obtain maximal profit taking into account the subsequent facility location by the Follower who also aims to obtain maximal profit. We state the problem as a two-level integer programming problem. A method is proposed for calculating an upper bound for the maximal profit of the Leader. The corresponding algorithm amounts to constructing the classical maximum facility location problem and finding an optimal solution to it. Simultaneously with calculating an upper bound we construct an initial approximate solution to the competitive facility location problem. We propose some local search algorithms for improving the initial approximate solutions. We include the results of some simulations with the proposed algorithms, which enable us to estimate the precision of the resulting approximate solutions and give a comparative estimate for the quality of the algorithms under consideration for constructing the approximate solutions to the problem.
The problem of searching for organic compounds with a specified biological activity is one of the most important challenges facing modern organic chemistry. The QSAR methodology is, as has been shown in practice, one of the rather efficient approaches to the solution of this problem [1]. The essence of this method is the following: First, using experimental data on biological activities for a series of compounds, the so-called QSAR equation is formulated, which makes it possible to predict the activities of related compounds. Then, it is decided what structural features can be inherent in compounds with the desired properties and a structure generation task is designed. In accordance with this task, a generator program generates a set of molecular graphs. Then, the activities of the compounds corresponding to the generated molecular graphs are estimated using the QSAR model and the most promising compounds are selected for synthesis and further studies.In the past two decades, different research teams have developed a number of generation algorithms and programs for solving problems in different areas of chemistry [2][3][4][5][6][7]. However, only a few generators are suitable for QSAR studies. The QSAR model is often used to describe the properties of derivatives of some parent compound. In this case, the most suitable are generators that generate structures by adding substituents to a central fragment. The GOLD generator developed in [8,9] belongs to this type. However, this generator has some limitations caused by the limited power of computers at the time of its development. In particular, GOLD involves manual coding of fragments represented in the Wiswesser line notation (WLN) [10] and does not automatically perform fragment symmetry analysis.In this work, we suggest an efficient method of completely automatic generation of structures for QSAR studies.The basic principle of generation is to form a set of substituents from molecular fragments specified by the user and add them to the central fragment (Fig. 1). Any fragment can be represented as a molecular graph that can contain, in addition to the vertices corresponding to non-hydrogen atoms, specific vertices, namely, sinks and sources, used for linking the fragments. Generated substituents can be both unit fragments and allowable combinations of several fragments. A substituent can contain several identical fragments. Inasmuch as substituents are created from separate fragments, a rather large number of substituents can be formed.In this method, not all the possible combinations of fragments are allowable. The combinations that lead to the appearance of rings composed of separate fragments are forbidden. This limitation is caused by the fact that ring formation can result in generation of structures that differ noticeably from the structures used for formulating the QSAR equation and the prediction of the activity of these compounds by means of the QSAR model can lead to wrong results.The generator is classified with deterministic generators. It generates ...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.