# American Institute of Mathematical Sciences

January  2015, 11(1): 145-170. doi: 10.3934/jimo.2015.11.145

## Modeling and solving alternative financial solutions seeking

 1 Université de Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France 2 MGDIS, Parc d'Innovation de Bretagne Sud, F-56038 Vannes, France, France

Received  April 2013 Revised  December 2013 Published  May 2014

In this paper we model the working of local community finances. As a result of this first step, we obtain a systemic model that is used to formalize the problem of Alternative Financial Solutions Seeking, which consists in building a collection of Alternative Multi-Year Prospective Budgets from two Multi-Year Prospective Budgets built by a finance expert. The modeling and formalization steps are led in a way that allows us to implement a software code for Alternative Financial Solutions Seeking based on a Genetic Like Algorithm.
Citation: Emmanuel Frénod, Jean-Philippe Gouigoux, Landry Touré. Modeling and solving alternative financial solutions seeking. Journal of Industrial and Management Optimization, 2015, 11 (1) : 145-170. doi: 10.3934/jimo.2015.11.145
##### References:
 [1] La Qualité Comptable au service d'une gestion performante des collectivités locales - Guide des bonnes pratiques Num 18, Technical report, Académie des sciences et techniques comptables financières. [2] Annexe Num 1: Plan de comptes développé des communes de 500 habitants et plus au 1ier janvier 2009, Technical report, Plan M14 de Comptabilité, French State Secretary for Finance, (http://www.collectivites-locales.gouv.fr/files/files/plan_m14d_2009_2. pdf), 2009. [3] D. Beasley, D. Bull and R. Martin, An overview of genetic algorithms. part 1, fundamentals, University Computing, 15 (1993), 58-69. [4] D. Beasley, D. Bull and R. Martin, An overview of genetic algorithms. part 2, research topics, University Computing, 15 (1993), 170-181. [5] C. Castro, C. Antònio and L. Sousa, Optimisation of shape and process parameters in metal forging using genetic algorithms, Journal of Materials Processing Technology, 146 (2004), 356-364, URL http://www.sciencedirect.com/science/article/pii/S0924013603010525. doi: 10.1016/j.jmatprotec.2003.11.027. [6] L. Davis, Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, 1991. [7] K. De Jong, Proceedings of the Evolutionary Algorithms in Engineering Computer Science (EUROGEN99), chapter Evolutionary computation: Recent developments and open issues, 43-54, University of Jyvskyl Finland, Wiley, Chichester, 1999. [8] E. Fama, Market efficiency, long-term returns, and behavioral finance, Journal of Financial Economics, 49 (1998), 283-306, URL http://www.sciencedirect.com/science/article/pii/S0304405X98000269. doi: 10.2139/ssrn.15108. [9] P. Fourie and A. Groenwold, The particle swarm optimization algorithm in size and shape optimization, Structural and Multidisciplinary Optimization, 23 (2002), 259-267, URL http://dx.doi.org/10.1007/s00158-002-0188-0. doi: 10.1007/s00158-002-0188-0. [10] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, 1st edition, Addison-Wesley Professional, 1989, URL http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20 &path=ASIN/0201157675. [11] V. Goodman and J. G. Stampfli, The Mathematics of Finance: Modeling and Hedging, American Mathematical Society, 2001. [12] K. Ilinski, Physics of Finance : Gauge Modelling in Non-Equilibrium Pricing, Wiley, 2001. [13] C. Mattheck and S. Burkhardt, A new method of structural shape optimization based on biological growth, International Journal of Fatigue, 12 (1990), 185-190. doi: 10.1016/0142-1123(90)90094-U. [14] R. Musgrave, The Theory of Public Finance : A Study in Public Economy, McGraw-Hill, 1959. [15] H. S. Rosen, Public finance, The Encyclopedia of Public Choice, (2004), 252-262. URL http://dx.doi.org/10.1007/978-0-387-75870-1_22. doi: 10.1007/978-0-306-47828-4_21. [16] Chen S.-H. (ed.), Genetic Algorithms and Genetic Programming in Computational Finance, Kluwer Academic Publishers, 2002. [17] C. Soh and J. Yang, Fuzzy controlled genetic algorithm search for shape optimization, Journal of Computing in Civil Engineering, 10 (1996), 143-150. doi: 10.1061/(ASCE)0887-3801(1996)10:2(143). [18] C. Tiebout, A pure theory of local expenditures, Journal of Political Economy, 64 (1956), 416-424. doi: 10.1086/257839.

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##### References:
 [1] La Qualité Comptable au service d'une gestion performante des collectivités locales - Guide des bonnes pratiques Num 18, Technical report, Académie des sciences et techniques comptables financières. [2] Annexe Num 1: Plan de comptes développé des communes de 500 habitants et plus au 1ier janvier 2009, Technical report, Plan M14 de Comptabilité, French State Secretary for Finance, (http://www.collectivites-locales.gouv.fr/files/files/plan_m14d_2009_2. pdf), 2009. [3] D. Beasley, D. Bull and R. Martin, An overview of genetic algorithms. part 1, fundamentals, University Computing, 15 (1993), 58-69. [4] D. Beasley, D. Bull and R. Martin, An overview of genetic algorithms. part 2, research topics, University Computing, 15 (1993), 170-181. [5] C. Castro, C. Antònio and L. Sousa, Optimisation of shape and process parameters in metal forging using genetic algorithms, Journal of Materials Processing Technology, 146 (2004), 356-364, URL http://www.sciencedirect.com/science/article/pii/S0924013603010525. doi: 10.1016/j.jmatprotec.2003.11.027. [6] L. Davis, Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, 1991. [7] K. De Jong, Proceedings of the Evolutionary Algorithms in Engineering Computer Science (EUROGEN99), chapter Evolutionary computation: Recent developments and open issues, 43-54, University of Jyvskyl Finland, Wiley, Chichester, 1999. [8] E. Fama, Market efficiency, long-term returns, and behavioral finance, Journal of Financial Economics, 49 (1998), 283-306, URL http://www.sciencedirect.com/science/article/pii/S0304405X98000269. doi: 10.2139/ssrn.15108. [9] P. Fourie and A. Groenwold, The particle swarm optimization algorithm in size and shape optimization, Structural and Multidisciplinary Optimization, 23 (2002), 259-267, URL http://dx.doi.org/10.1007/s00158-002-0188-0. doi: 10.1007/s00158-002-0188-0. [10] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, 1st edition, Addison-Wesley Professional, 1989, URL http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20 &path=ASIN/0201157675. [11] V. Goodman and J. G. Stampfli, The Mathematics of Finance: Modeling and Hedging, American Mathematical Society, 2001. [12] K. Ilinski, Physics of Finance : Gauge Modelling in Non-Equilibrium Pricing, Wiley, 2001. [13] C. Mattheck and S. Burkhardt, A new method of structural shape optimization based on biological growth, International Journal of Fatigue, 12 (1990), 185-190. doi: 10.1016/0142-1123(90)90094-U. [14] R. Musgrave, The Theory of Public Finance : A Study in Public Economy, McGraw-Hill, 1959. [15] H. S. Rosen, Public finance, The Encyclopedia of Public Choice, (2004), 252-262. URL http://dx.doi.org/10.1007/978-0-387-75870-1_22. doi: 10.1007/978-0-306-47828-4_21. [16] Chen S.-H. (ed.), Genetic Algorithms and Genetic Programming in Computational Finance, Kluwer Academic Publishers, 2002. [17] C. Soh and J. Yang, Fuzzy controlled genetic algorithm search for shape optimization, Journal of Computing in Civil Engineering, 10 (1996), 143-150. doi: 10.1061/(ASCE)0887-3801(1996)10:2(143). [18] C. Tiebout, A pure theory of local expenditures, Journal of Political Economy, 64 (1956), 416-424. doi: 10.1086/257839.
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