On some multiobjective optimization problems arising in biology

References

• Arbel , A. and Oren , S. S. 1986 . Generating search directions in multiobjective linear programming using the analytic search hierarchy process . Socio. Econ. Plann. Sci. , 20 : 369 – 373 .
   Google Scholar
• Balas , E. 1965 . An additive algorithm for solving linear programs with zero-one variables . Oper. Res. , 13 : 517 – 546 .
   Web of Science ®Google Scholar
• Bao , T. Q. and Mordukhovich , B. S. 2010 . Pareto minimizers for multiobjective problems: Existence and optimality conditions . Math. Program. , 122 : 301 – 347 .
   Web of Science ®Google Scholar
• Bazaraa , M. S. , Jarvis , J. J. and Sherali , H. D. 1990 . Linear Programming and Network Flows , 2 , New York : John Wiley & Sons .
   Google Scholar
• Bitran , G. R. 1979 . Theory of algorithms for linear multiple objective programs with zero-one variables . Math. Program. , 17 : 362 – 390 .
   Web of Science ®Google Scholar
• Cherruault , Y. 1991 . New deterministic methods for global optimization and applications to biomedicine . Int. J. Biomed. Comput. , 27 : 215 – 229 .
   Google Scholar
• Cherruault , Y. 1994 . Global optimization in biology and medicine . Math. Comput. Modelling , 20 : 119 – 132 .
   Google Scholar
• Deckro , R. F. and Winkofsky , E. P. 1983 . Solving zero-one multiple objective programs through implicit enumeration . Eur. J. Oper. Res. , 12 : 362 – 374 .
   Google Scholar
• Ecker , J. G. , Kupferschmid , M. , Lawrence , C. E. , Reilly , A. A. and Scott , A. C.H. 2002 . An application of nonlinear optimization in molecular biology . Eur. J. Oper. Res. , 138 : 452 – 458 .
   Google Scholar
• Ehrgott , M. 2005 . Multicriteria Optimization , 2 , Berlin : Springer .
   Google Scholar
• Festa , P. 2007 . On some optimization problems in molecular biology . Math. Biosci. , 207 : 219 – 234 .
   Google Scholar
• Frances , M. and Litman , A. 1997 . On covering problems of codes . Theory Comput. Syst. , 30 ( 2 ) : 113 – 119 .
   Web of Science ®Google Scholar
• Geoffrion , A. 1968 . Proper efficiency and the theory of vector maximization . J. Math. Anal. Appl. , 22 : 618 – 630 .
   Web of Science ®Google Scholar
• Gomes , F. C. , Meneses , C. N. , Pardalos , P. M. and Viana , G. V.R. 2008 . A parallel multistart algorithm for the closest string problem . Comput. Oper. Res. , 35 : 3636 – 3643 .
   Web of Science ®Google Scholar
• Greenberg , H. J. , Hart , W. E. and Lancia , G. 2004 . Opportunities for combinatorial optimization in computational biology . INFORMS J. Comput. , 16 ( 3 ) : 211 – 231 .
   Google Scholar
• Jahanshahloo , G. R. and Foroughi , A. A. 2004 . Finding a weights-restricted efficient (extreme) point and using it for solving MOLP problems . Appl. Math. Comput. , 150 : 203 – 211 .
   Google Scholar
• Kostreva , M. M. , Ogryczak , W. and Tonkyn , D. W. 1999 . Relocation problems arising in conservation biology . Comput. Math. Appl. , 37 : 135 – 150 .
   Google Scholar
• Lanctot , J. , Li , M. , Ma , B. , Wang , S. and Zhang , L. Distinguishing string selection problems . Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) . Baltimore, Maryland. pp. 633 – 642 .
   Google Scholar
• Lanctot , J. , Li , M. , Ma , B. , Wang , S. and Zhang , L. 2003 . Distinguishing string selection problems . Inform. Comput. , 185 : 41 – 55 .
   Google Scholar
• Li , M. , Ma , B. and Wang , L. Finding similar regions in many strings . Proceedings of the Annual ACM Symposium on Theory of Computing . Atlanta, Georgia. pp. 473 – 482 .
   Google Scholar
• Liu , P.-K. and Wang , F.-S. 2008 . Inverse problems of biological systems using multi-objective optimization . J. Chin. Inst. Chem. Eng. , 39 : 399 – 406 .
   Google Scholar
• Lotfi , V. , Yoon , Y. S. and Zionts , S. 1997 . Aspiration-based search algorithm for multiple objective linear programming problems: Theory and comparative tests . Manage. Sci. , 43 : 1047 – 1059 .
   Google Scholar
• Malakooti , B. 1988 . An exact interactive paired comparison method for exploring the efficient facets of MOLP problems with underlying quasi-concave utility functions . IEEE Trans. Syst. Man. Cybern. , 18 : 787 – 801 .
   Web of Science ®Google Scholar
• Malakooti , B. 2009 . Systematic decision process for intelligent decision making . J. Intell. Manuf. , (doi:10.1007/s10845-009-0327-1)
   Google Scholar
• Malakooti , B. 2010 . Independent, convergent, and divergent decision behavior for interactive multiple objective linear programming . Eng. Optim. , 42 : 325 – 346 .
   Web of Science ®Google Scholar
• Marín-Sanguino , A. and Torres , N. V. 2003 . Optimization of biochemical systems by linear programming and general mass action model representations . Math. Biosci. , 184 : 187 – 200 .
   PubMed Web of Science ®Google Scholar
• Meneses , C. N. , Oliveira , C. A.S. and Pardalos , P. M. 2005 . Optimization techniques for string selection and comparison problems in genomics . IEEE Eng. Med. Biol. , 24 : 81 – 87 .
   PubMed Web of Science ®Google Scholar
• Mordukhovich , B. S. 2006 . Variational Analysis and Generalized Differentiation, I: Basic Theory , Berlin : Springer . Grundlehren Series (Fundamental Principles of Mathematical Sciences)
   Google Scholar
• Mordukhovich , B. S. 2006 . Variational Analysis and Generalized Differentiation, II: Applications , Berlin : Springer . Grundlehren Series (Fundamental Principles of Mathematical Sciences)
   Google Scholar
• Pappas , J. L. 2006 . Biological taxonomic problem solving using fuzzy decision-making analytical tools . Fuzzy Sets Syst. , 157 : 1687 – 1703 .
   Google Scholar
• Pourkarimi , L. and Zarepisheh , M. 2007 . A dual-based algorithm for solving lexicographic multiple objective programs . Eur. J. Oper. Res. , 176 : 1348 – 1356 .
   Web of Science ®Google Scholar
• Rosen , J. B. , Phillips , A. T. , Oh , S. Y. and Dill , K. A. 2000 . A method for parameter optimization in computational biology . Biophys. J. , 79 : 2818 – 2824 .
   Google Scholar
• Saaty , T. L. 1980 . The Analytic Hierarchy Process , New York : McGraw-Hill .
   Google Scholar
• Saaty , T. L. 1986 . Axiomatic foundation of the analytic hierarchy process . Manage. Sci. , 32 : 841 – 855 .
   Web of Science ®Google Scholar
• Saaty , T. L. and Sodenkamp , M. 2008 . Making decisions in hierarchic and network systems . Int. J. Appl. Decis. Sci. , 1 : 24 – 79 .
   Google Scholar
• Shin , W. S. and Ravindran , A. 1991 . An interactive method for multiple-objective mathematical programming problems . J. Optim. Theory Appl. , 68 : 539 – 561 .
   Google Scholar
• Sim , J. S. and Park , K. Proceedings of the Annual Australasian Workshop on Combinatorial Algorithms (AWOCA) . The consensus string problem for a metric is NP-complete , pp. 107 – 113 . Perth, , Australia
   Google Scholar
• Soleimani-damaneh , M. 2007 . Multiple-objective programs in Banach spaces: Sufficiency for (proper) optimality . Nonlinear Anal. , 67 ( 3 ) : 958 – 962 .
   Google Scholar
• Steuer , R. E. 1986 . Multiple Criteria Optimization: Theory, Computation, and Application , New York : Wiley .
   Google Scholar
• Taha , H. A. 2007 . An Introduction to Operations Research , 8 , New Jersey : Pearson Education, Inc .
   Google Scholar
• Voit , E. O. 2002 . Models of data and models of processes in the post-genomic era . Math. Biosci. , 180 : 263 – 274 .
   PubMed Web of Science ®Google Scholar
• Zionts , S. and Wallenius , J. 1976 . An interactive programming method for solving the multiple criteria problem . Manage. Sci. , 22 : 652 – 663 .
   Web of Science ®Google Scholar