A compromise programming method using multibounds formulation and dual approach for multicriteria structural optimization
To enhance the reliability and efficiency of the multicriteria optimization procedure, a compromise programming method using multibounds formulation (MBF) is proposed in this paper. This method can be used either to obtain the Pareto optimum set or to find the ‘best’ Pareto optimum solution in the s...
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| Vydáno v: | International journal for numerical methods in engineering Ročník 58; číslo 4; s. 661 - 678 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Chichester, UK
John Wiley & Sons, Ltd
28.09.2003
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | To enhance the reliability and efficiency of the multicriteria optimization procedure, a compromise programming method using multibounds formulation (MBF) is proposed in this paper. This method can be used either to obtain the Pareto optimum set or to find the ‘best’ Pareto optimum solution in the sense of having the minimum distance to the utopia point. By introducing a set of artificial design variables, it is shown that a simplified and easy‐to‐use formulation can be established for practical applications. Particularly, this formulation is well adapted to the efficient dual solution approach due to the convexity of objective function. Theoretically, based on the Kuhn–Tucker optimality conditions, demonstrations show that the new formulation is equivalent to its original form and thus retains the basic properties of the latter. Numerical examples will be solved to show the capacity of this method. Copyright © 2003 John Wiley & Sons, Ltd. |
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| AbstractList | To enhance the reliability and efficiency of the multicriteria optimization procedure, a compromise programming method using multibounds formulation (MBF) is proposed in this paper. This method can be used either to obtain the Pareto optimum set or to find the ‘best’ Pareto optimum solution in the sense of having the minimum distance to the utopia point. By introducing a set of artificial design variables, it is shown that a simplified and easy‐to‐use formulation can be established for practical applications. Particularly, this formulation is well adapted to the efficient dual solution approach due to the convexity of objective function. Theoretically, based on the Kuhn–Tucker optimality conditions, demonstrations show that the new formulation is equivalent to its original form and thus retains the basic properties of the latter. Numerical examples will be solved to show the capacity of this method. Copyright © 2003 John Wiley & Sons, Ltd. To enhance the reliability and efficiency of the multicriteria optimization procedure, a compromise programming method using multibounds formulation (MBF) is proposed in this paper. This method can be used either to obtain the Pareto optimum set or to find the 'best' Pareto optimum solution in the sense of having the minimum distance to the Utopia point. By introducing a set of artificial design variables, it is shown that a simplified and easy-to-use formulation can be established for practical applications. Particularly, this formulation is well adapted to the efficient dual solution approach due to the convexity of objective function. Theoretically, based on the Kuhn-Tucker optimality conditions, demonstrations show that the new formulation is equivalent to its original form and thus retains the basic properties of the latter. Numerical examples will be solved to show the capacity of this method. |
| Author | Zhang, W. H. |
| Author_xml | – sequence: 1 givenname: W. H. surname: Zhang fullname: Zhang, W. H. email: zhangwh@nwpu.edu.cn organization: Sino-French Laboratory of Concurrent Engineering, Department of Aircraft Manufacturing Engineering, Northwestern Polytechnical University, 710072 Xi'an, Shaanxi, China |
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| Cites_doi | 10.1007/BF00934871 10.1115/1.2829440 10.1007/s00158-002-0185-3 10.1080/03052159608941404 10.1016/S0045-7949(01)00142-0 10.1002/cnm.1630010613 10.1007/BF00933599 10.1002/nme.229 10.1002/nme.1620240207 10.1007/978-1-4899-3734-6 10.1007/BF01743804 |
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| References | Yu PL, Leitmann G. Compromise solutions, dominations structures, and Salukvadze's solution. Journal of Optimization Theory and Applications 1974; 13:362-378. Svanberg K. Method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering 1987; 24(2):359-373. Athan TW, Papalambros Y. A note on weighted criteria methods for compromise solutions in multi-objective optimization. Engineering Optimization 1996; 27:155-176. Zhang WH, Yang HC. A study of the weighting method for a certain type of multicriteria structural optimization problems. Computers and Structures 2001; 79:2741-2749. Gearhart WB. Compromise solutions and estimation of the non-inferior set. Journal of Optimization Theory and Applications 1979; 28:29-47. Chen W, Wiecek MM, Zhang J. Quality utility-a compromise programming approach to robust design. Journal of Mechanical Design (ASME) 1999; 121:179-187. Fleury C. First and second order convex approximation strategies in structural optimization. Structural Optimization 1989; 1:3-10. Koski J. Defectiveness of weighting method in multicriterion optimization of structures. Communications in Applied Numerical Methods 1985; 1:333-337. Zhang WH, Domaszewski M, Fleury C. An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization. International Journal for Numerical Methods in Engineering 2001; 52(9):889-902. Zhang WH, Yang HC. Efficient gradient calculation of the Pareto optimal curve in multicriteria optimization. Structural and Multidisciplinary Optimization 2002; 23(4):311-319. Stadler W. Multicriteria Optimization in Engineering and in the Sciences. Plenum Press: New York, 1988. 1979; 28 1987; 24 1999; 121 1973 1974; 13 1985; 1 1989; 1 1996; 27 2001; 79 2002; 23 2001; 52 1988 e_1_2_1_6_2 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_11_2 e_1_2_1_3_2 e_1_2_1_12_2 e_1_2_1_10_2 e_1_2_1_13_2 Zeleny M (e_1_2_1_2_2) 1973 e_1_2_1_8_2 e_1_2_1_9_2 |
| References_xml | – reference: Zhang WH, Yang HC. Efficient gradient calculation of the Pareto optimal curve in multicriteria optimization. Structural and Multidisciplinary Optimization 2002; 23(4):311-319. – reference: Chen W, Wiecek MM, Zhang J. Quality utility-a compromise programming approach to robust design. Journal of Mechanical Design (ASME) 1999; 121:179-187. – reference: Fleury C. First and second order convex approximation strategies in structural optimization. Structural Optimization 1989; 1:3-10. – reference: Gearhart WB. Compromise solutions and estimation of the non-inferior set. Journal of Optimization Theory and Applications 1979; 28:29-47. – reference: Koski J. Defectiveness of weighting method in multicriterion optimization of structures. Communications in Applied Numerical Methods 1985; 1:333-337. – reference: Yu PL, Leitmann G. Compromise solutions, dominations structures, and Salukvadze's solution. Journal of Optimization Theory and Applications 1974; 13:362-378. – reference: Stadler W. Multicriteria Optimization in Engineering and in the Sciences. Plenum Press: New York, 1988. – reference: Zhang WH, Domaszewski M, Fleury C. An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization. International Journal for Numerical Methods in Engineering 2001; 52(9):889-902. – reference: Svanberg K. Method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering 1987; 24(2):359-373. – reference: Zhang WH, Yang HC. A study of the weighting method for a certain type of multicriteria structural optimization problems. Computers and Structures 2001; 79:2741-2749. – reference: Athan TW, Papalambros Y. A note on weighted criteria methods for compromise solutions in multi-objective optimization. Engineering Optimization 1996; 27:155-176. – start-page: 262 year: 1973 end-page: 301 – volume: 52 start-page: 889 issue: 9 year: 2001 end-page: 902 article-title: An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization publication-title: International Journal for Numerical Methods in Engineering – volume: 23 start-page: 311 issue: 4 year: 2002 end-page: 319 article-title: Efficient gradient calculation of the Pareto optimal curve in multicriteria optimization publication-title: Structural and Multidisciplinary Optimization – volume: 13 start-page: 362 year: 1974 end-page: 378 article-title: Compromise solutions, dominations structures, and Salukvadze's solution publication-title: Journal of Optimization Theory and Applications – volume: 27 start-page: 155 year: 1996 end-page: 176 article-title: A note on weighted criteria methods for compromise solutions in multi‐objective optimization publication-title: Engineering Optimization – volume: 121 start-page: 179 year: 1999 end-page: 187 article-title: Quality utility—a compromise programming approach to robust design publication-title: Journal of Mechanical Design – volume: 1 start-page: 3 year: 1989 end-page: 10 article-title: First and second order convex approximation strategies in structural optimization publication-title: Structural Optimization – volume: 1 start-page: 333 year: 1985 end-page: 337 article-title: Defectiveness of weighting method in multicriterion optimization of structures publication-title: Communications in Applied Numerical Methods – volume: 24 start-page: 359 issue: 2 year: 1987 end-page: 373 article-title: Method of moving asymptotes—a new method for structural optimization publication-title: International Journal for Numerical Methods in Engineering – year: 1988 – volume: 28 start-page: 29 year: 1979 end-page: 47 article-title: Compromise solutions and estimation of the non‐inferior set publication-title: Journal of Optimization Theory and Applications – volume: 79 start-page: 2741 year: 2001 end-page: 2749 article-title: A study of the weighting method for a certain type of multicriteria structural optimization problems publication-title: Computers and Structures – ident: e_1_2_1_4_2 doi: 10.1007/BF00934871 – ident: e_1_2_1_5_2 doi: 10.1115/1.2829440 – start-page: 262 volume-title: Multiple Criteria Decision Making year: 1973 ident: e_1_2_1_2_2 – ident: e_1_2_1_13_2 doi: 10.1007/s00158-002-0185-3 – ident: e_1_2_1_6_2 doi: 10.1080/03052159608941404 – ident: e_1_2_1_12_2 doi: 10.1016/S0045-7949(01)00142-0 – ident: e_1_2_1_8_2 doi: 10.1002/cnm.1630010613 – ident: e_1_2_1_3_2 doi: 10.1007/BF00933599 – ident: e_1_2_1_7_2 doi: 10.1002/nme.229 – ident: e_1_2_1_11_2 doi: 10.1002/nme.1620240207 – ident: e_1_2_1_9_2 doi: 10.1007/978-1-4899-3734-6 – ident: e_1_2_1_10_2 doi: 10.1007/BF01743804 |
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| Title | A compromise programming method using multibounds formulation and dual approach for multicriteria structural optimization |
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