Importance The article addresses optimization of marketing activities in social networks, particularly, the determination of groups for advertising based on its cost and characteristics that determine information dissemination about products and services among users. Objectives The aims are to develop a model to select groups of a social network for advertising, to modify and implement stochastic algorithms to solve the integer programming problems and compare their characteristics. Methods To develop optimization models, I use methods of operations research. The study also employs methods of random search for boundary points to solve the problem of integer programming, in particular, a simple random search, adaptive search and a search with varying probabilities. The multidimensional comparative analysis is applied to formulate integral characteristics of arguments that are used in the adaptive search algorithm. Results I developed models to select groups of social network for advertising, modified the adaptive search algorithm for boundary points, implying the calculation of an integral indicator of each variable in the problem based on normalized values, performed computational experiments and comparison of results obtained through the considered algorithms. The most accurate solution is obtained using the adaptive algorithm; the simplest to implement is a random search algorithm. Conclusions Economic agents may use the developed models to select groups of social network for advertising. The presented modification of adaptive search algorithm enables to solve integer programming problems.
Keywords: integer programming, social network, advertising, random search
Goyal S., Gagnon J. Social networks and the firm. Revista de Adminstração, 2016, vol. 51, no.2, pp. 240–243. doi: 10.5700/rausp1237
Gribanova E.B., Katasonova A.V. [A model to evaluate social network groups for marketing activities implementation]. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki = Proceedings of Tomsk State University of Control Systems and Radioelectronics, 2017, no. 2, pp. 68–72. (In Russ.)
Antamoshkin A.N., Masich I.S. [Search Algorithms for Constrained Pseudo-Boolean Optimization]. Sistemy upravleniya, svyazi i bezopasnosti = Systems of Control, Communication and Security, 2016, no. 1, pp. 103–145. (In Russ.) URL: Link
Bradley S., Hax A., Magnanti T. Applied Mathematical Programming. Addison-Wesley, 1977, 716 p.
Burkova I.V. [Method of network programming in problems of discrete optimization]. Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta = The Bulletin of Voronezh State Technical University, 2010, no. 8, pp. 154–159. (In Russ.)
Kaufman L., Vanden M., Hansen P. A plant and warehouse location problem. Journal of Operation Research Society, 1977, vol. 28, iss. 3, pp. 547–554. doi: 10.1057/jors.1977.104
Čejka J. Transport planning realized through the optimization models. Procedia Engineering, 2016, vol. 161, pp. 1187–1196. doi: 10.1016/j.proeng.2016.08.538
Ming Yan, Yurong Yuan. A multi-attribute reverse auction decision making model based on linear programming. Systems Engineering Procedia, 2012, vol. 4, pp. 372–378. doi: 10.1016/j.sepro.2011.11.089
Masich I.S. [Combinatorial optimization in foundry production planning]. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta = Vestnik SibGAU, 2009, no. 2, pp. 40–44. (In Russ.)
Zabudskii G.G., Alekseenko I.V. [Optimization of technological schemes of processes of manufacturing fur products]. Nauchnyi vestnik Novosibirskogo gosudarstvennogo tekhnicheskogo universiteta = Science Bulletin of NSTU, 2008, no. 1, pp. 25–33. (In Russ.)
Moutaz J., Romanchenko O.A., Tolstikova O.N. [Locating a public service object based on the discrete optimization method]. Upravlenie bol'shimi sistemami, 2006, no. 14, pp. 123–134. (In Russ.) URL: Link
Ovchinnikov V.A. [Systematization of exact methods of discrete optimization]. Nauka i Obrazovanie, 2015, no. 6, pp. 288–304. (In Russ.)
Antamoshkin A.N., Masich I.S. [Greedy algorithms and local search for conditional pseudo-Boolean optimization]. Issledovano v Rossii, 2003, no. 177, pp. 2143–2149. URL: Link (In Russ.)
Rastrigin L.A. Adaptatsiya slozhnykh sistem [Adaptation of complex systems]. Riga, Zinatne Publ., 1981, 375 p.
Grinchenko S.N. [Trial and error method and search optimization: Analysis, classification, interpretation of the natural selection concept]. Issledovano v Rossii, 2003, no. 104, pp. 1228–1271. (In Russ.) URL: Link
Glover F. Tabu search. Part I. INFORMS Journal on Computing, 1989, vol. 1, pp. 190–206. doi: 10.1287/ijoc.1.3.190
Pedroso J.P. An evolutionary solver for linear integer programming. BSIS Technical Reports, 1998, no. 98-7, pp. 1–15.
Jansen T., Wegener I. A comparison of simulated annealing with a simple evolutionary algorithm on pseudo-boolean functions of unitation. Theoretical Computer Science, 2007, vol. 386, iss. 1-2, pp. 73–93. doi: 10.1016/j.tcs.2007.06.003
Galushin P.V., Semenkina O.E. [Development and evaluation of evolutionary algorithms for discrete optimization]. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta = Vestnik SibGAU, 2011, no. 5, pp. 25–29. (In Russ.)
Kazakovtsev L.A., Stupina A.A. [Parallel implementation of the changing probabilities method]. Sovremennye Problemy Nauki i Obrazovaniya, 2012, no. 4.URL: Link (In Russ.)