Finding all global optima of engineering design problems with discrete signomial terms

References

• Balas, E., and R. Jeroslow. 1972. “Canonical Cuts on the Unit Hypercube.” SIAM Journal on Applied Mathematics 23 (1): 61–69.
   Web of Science ®Google Scholar
• Björk, K. M., P. O. Lindberg, and T. Westerlund. 2003. “Some Convexifications in Global Optimization of Problems Containing Signomial Terms.” Computers and Chemical Engineering 27: 669–679.
   Web of Science ®Google Scholar
• Boussaid, I., J. Lepagnot, and P. Siarry. 2013. “A Survey on Optimization Metaheuristics.” Information Sciences 237: 82–117.
   Web of Science ®Google Scholar
• Cagnina, L. C., S. C. Esquivel, and C. A. C. Coello. 2008. “Solving Engineering Optimization Problems with the Simple Constrained Particle Swarm Optimizer.” Informatica 32: 319–326.
   Google Scholar
• Cao, Y. J., and Q. H. Wu. 1997. “Mechanical Design Optimization by Mixed-Variable Evolutionary Programming.” Presented at the IEEE Conference on Evolutionary Computation, ICEC, Indianapolis, IN, April 13–16.
   Google Scholar
• Chelouah, R., and P. Siarry. 2000. “Tabu Search Applied to Global Optimization.” European Journal of Operational Research 123: 256–270.
   Web of Science ®Google Scholar
• Chun, S., Y. T. Kim, and T. H. Kim. 2013. “A Diversity-Enhanced Constrained Particle Swarm Optimizer for Mixed Integer-Discrete-Continuous Engineering Design Problems.” Advances in Mechanical Engineering 2013: 1–11. doi:10.1155/2013/130750
   Google Scholar
• Floudas, C. A. 1999. “Global Optimization in Design and Control of Chemical Process Systems.” Journal of Process Control 10: 125–134.
   Web of Science ®Google Scholar
• Floudas, C. A. 2000. “Generalized Geometric Programming. Deterministic Global Optimization: Theory.” In Methods and Applications, 257–306. Boston: Kluwer Academic Publishers.
   Google Scholar
• Floudas, C. A., P. M. Pardalos, C. S. Adjiman, W. R. Esposito, Z. Gumus, S. T. Harding, J. L. Klepeis, C. A. Meyer, and C. A. Schweiger. 1999. Handbook of Test Problems for Local and Global Optimization. Dordrecht: Kluwer Academic Publishers.
   Google Scholar
• Fu, J. F., R. G. Fenton, and W. L. Cleghorn. 1991. “A Mixed Integer Discrete-Continuous Programming Method and its Application to Engineering Design Optimization.” Engineering Optimization 17 (3): 263–280.
   Google Scholar
• Gao, X. Z., X. Wang, S. J. Ovaska, and K. Zenger. 2012. “A Hybrid Optimization Method of Harmony Search and Opposition-Based Learning.” Engineering Optimization 44 (8): 895–914.
   Web of Science ®Google Scholar
• Gounaris, C. E., and C. A. Floudas. 2008. “Convexity of Products of Univariate Functions and Convexification Transformations for Geometric Programming.” Journal of Optimization Theory and Applications 138 (3): 407–427.
   Web of Science ®Google Scholar
• Huang, M. W., and J. S. Arora. 1997. “Optimal Design of Steel Structures Using Standard Sections.” Structural Optimization 14 (1): 24–35.
   Google Scholar
• Kalivarapu, J., S. Jain, and S. Bag. 2016. “An Improved Harmony Search Algorithm with Dynamically Varying Bandwidth.” Engineering Optimization 48 (7): 1091–1108.
   Web of Science ®Google Scholar
• Kanagaraj, G., S. G. Ponnambalam, N. Jawahar, and J. Mukund Nilakantan. 2014. “An Effective Hybrid Cuckoo Search and Genetic Algorithm for Constrained Engineering Design Optimization.” Engineering Optimization 46 (10): 1331–1351.
   Web of Science ®Google Scholar
• Kotinis, M. 2010. “A Particle Swarm Optimizer for Constrained Multiobjective Engineering Design Problems.” Engineering Optimization 42 (10): 907–926.
   Web of Science ®Google Scholar
• Kuang, J. K., S. S. Rao, and L. Chen. 1998. “Taguchi-Aided Search Method for Design Optimization of Engineering Systems.” Engineering Optimization 30 (1): 1–23.
   Web of Science ®Google Scholar
• Lee, K. M., J. T. Tsai, T. K. Liu, and J. H. Chou. 2010. “Improved Genetic Algorithm for Mixed-Discrete-Continuous Design Optimization Problems.” Engineering Optimization 42 (10): 927–941.
   Web of Science ®Google Scholar
• Lejeune, M. A. 2003. “Heuristic Optimization of Experimental Designs.” European Journal of Operational Research 147: 484–498.
   Web of Science ®Google Scholar
• Li, W. C., and S. Azarm. 1990. “Optimality and Constrained Derivatives in Two-Level Design Optimization.” ASME Journal of Mechanical Design 112 (4): 563–568.
   Web of Science ®Google Scholar
• Li, H. L., S. C. Fang, Y. H. Huang, and T. Nie. 2016. “An Enhanced Logarithmic Method for Signomial Programming with Discrete Variables.” European Journal of Operational Research 255: 922–934.
   Web of Science ®Google Scholar
• Li, H. L., Y. H. Huang, and S. C. Fang. 2013. “A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems.” INFORMS Journal on Computing 25: 643–653.
   Web of Science ®Google Scholar
• Li, H. L., and H. C. Lu. 2009. “Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables.” Operations Research 57 (3): 701–713.
   Web of Science ®Google Scholar
• Li, H. L., and P. Papalambros. 1985. “A Production System for Use of Global Optimization Knowledge.” Journal of Mechanisms, Transmissions, and Automation in Design 107: 277–284.
   Web of Science ®Google Scholar
• Lin, B., and D. C. Miller. 2004. “Solving Heat Exchanger Network Synthesis Problems with Tabu Search.” Computers & Chemical Engineering 28: 1451–1464.
   Web of Science ®Google Scholar
• Lin, M. H., and J. F. Tsai. 2011. “Finding Multiple Optimal Solutions of Signomial Discrete Programming Problems with Free Variables.” Optimization and Engineering 12: 425–443.
   Web of Science ®Google Scholar
• Lin, M. H., J. F. Tsai, and S. C. Chang. 2017. “A Superior Linearization Method for Signomial Discrete Functions in Solving Three-Dimensional Open-Dimension Rectangular Packing Problems.” Engineering Optimization 49 (5): 746–761.
   Web of Science ®Google Scholar
• Lin, M. H., J. F. Tsai, and P. C. Wang. 2012. “Solving Engineering Optimization Problems by a Deterministic Global Optimization Approach.” Applied Mathematics & Information Sciences 6 (3): 1101–1107.
   Google Scholar
• Lin, Y. C., F. S. Wang, and K. Hwang. 1999. “A Hybrid Method of Evolutionary Algorithms for Mixed-Integer Nonlinear Optimization Problems.” In Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), 2159–2166. Piscataway, NJ: IEEE.
   Google Scholar
• Lu, H. C. 2012. “An Efficient Convexification Method for Solving Generalized Geometric Problems.” Journal of Industrial and Management Optimization 8 (2): 429–455.
   Web of Science ®Google Scholar
• Lu, H. C. 2013. “A Logarithmic Method for Eliminating Binary Variables and Constraints for the Product of Free-Sign Discrete Functions.” Discrete Optimization 10: 11–24.
   Web of Science ®Google Scholar
• Lundell, A., J. Westerlund, and T. Westerlund. 2009. “Some Transformation Techniques with Applications in Global Optimization.” Journal of Global Optimization 43: 391–405.
   Web of Science ®Google Scholar
• Luo, Y., X. Yuan, and Y. Liu. 2007. “An Improved PSO Algorithm for Solving Non-Convex NLP/MINLP Problems with Equality Constraints.” Computers & Chemical Engineering 31: 153–162.
   Web of Science ®Google Scholar
• Maranas, C. D., and C. A. Floudas. 1997. “Global Optimization in Generalized Geometric Programming.” Computers & Chemical Engineering 21 (4): 351–369.
   Web of Science ®Google Scholar
• Mareli, M., and B. Twala. 2018. “An Adaptive Cuckoo Search Algorithm for Optimization.” Applied Computing and Informatics 14 (2): 107–115.
   Google Scholar
• Nahas, N., and D. Thien-My. 2010. “Harmony Search Algorithm: Application to the Redundancy Optimization Problem.” Engineering Optimization 42 (9): 845–861.
   Web of Science ®Google Scholar
• Pedamallu, C. S., and L. Ozdamar. 2008. “Investigating a Hybrid Simulated Annealing and Local Search Algorithm for Constrained Optimization.” European Journal of Operational Research 185: 1230–1245.
   Web of Science ®Google Scholar
• Pörn, R., K. M. Bjork, and T. Westerlund. 2008. “Global Solution of Optimization Problems with Signomial Parts.” Discrete Optimization 5: 108–120.
   Web of Science ®Google Scholar
• Pörn, R., I. Harjunkoski, and T. Westerlund. 1999. “Convexification of Different Classes of Non-Convex MINLP Problems.” Computers & Chemical Engineering 23: 439–448.
   Web of Science ®Google Scholar
• Rao, S. S., and Y. Xiong. 2005. “A Hybrid Genetic Algorithm for Mixed-Discrete Design Optimization.” ASME Journal of Mechanical Design 127 (6): 1100–1112.
   Web of Science ®Google Scholar
• Sandgren, E. 1990. “Nonlinear Integer and Discrete Programming in Mechanical Design Optimization.” ASME Journal of Mechanical Design 112: 223–229.
   Web of Science ®Google Scholar
• Schlüter, M., J. A. Egea, and J. R. Banga. 2009. “Extended Ant Colony Optimization for Non-Convex Mixed Integer Nonlinear Programming.” Computers & Operations Research 36: 2217–2229.
   Web of Science ®Google Scholar
• Serban, A. T., and G. Sandou. 2007. “Mixed Ant Colony Optimization for the Unit Commitment Problem.” Lecture Notes in Computer Science 4431: 332–340.
   Google Scholar
• Sharif, B., G. G. Wang, and T. EIMekkawy. 2008. “Mode Pursuing Sampling Method for Discrete Variable Optimization on Expensive Black-Box Functions.” ASME Journal of Mechanical Design 130 (2): 021402-1–021402-11. doi:10.1115/1.2803251
   Web of Science ®Google Scholar
• Shopova, E. G., and N. G. Vaklieva-Bancheva. 2006. “BASIC—A Genetic Algorithm for Engineering Problems Solution.” Computers & Chemical Engineering 30: 1293–1309.
   Web of Science ®Google Scholar
• Socha, K. 2004. “ACO for Continuous and Mixed-Variable Optimization.” In Proceedings of 4th International Workshop on Ant Colony Optimization and Swarm, edited by M. Dorigo, M. Birattari, C. Blum, L. M. Gambardella, F. Mondada, and T. Stützle, 25–36. Berlin: Springer.
   Google Scholar
• Sun, C., J. Zeng, and J. S. Pan. 2011. “A Modified Particle Swarm Optimization with Feasibility-Based Rules for Mixed-Variable Optimization Problems.” International Journal of Innovative Computing, Information and Control 7 (6): 3081–3096.
   Web of Science ®Google Scholar
• Tsai, J. F., and M. H. Lin. 2008. “Global Optimization of Signomial Mixed-Integer Nonlinear Programming Problems with Free Variables.” Journal of Global Optimization 42: 39–49.
   Web of Science ®Google Scholar
• Tsai, J. F., and M. H. Lin. 2011. “An Efficient Global Approach for Posynomial Geometric Programming Problems.” INFORMS Journal on Computing 23 (3): 483–492.
   Web of Science ®Google Scholar
• Tsai, J. F., and M. H. Lin. 2013. “An Improved Framework for Solving NLIPs with Signomial Terms in the Objective or Constraints to Global Optimality.” Computers and Chemical Engineering 53: 44–54.
   Web of Science ®Google Scholar
• Tsai, H. C., Y. Y. Tyan, Y. W. Wu, and Y. H. Lin. 2012. “Isolated Particle Swarm Optimization with Particle Migration and Global Best Adoption.” Engineering Optimization 44 (12): 1405–1424.
   Web of Science ®Google Scholar
• Vielma, J. P., and G. L. Nemhauser. 2011. “Modeling Disjunctive Constraints with a Logarithmic Number of Binary Variables and Constraints.” Mathematical Programming 128: 49–72.
   Web of Science ®Google Scholar
• Yang, X. S., and F. S. Deb. 2010. “Engineering Optimisation by Cuckoo Search.” International Journal of Mathematical Modelling and Numerical Optimisation 1 (4): 330–343.
   Google Scholar
• Young, C. T., Y. Zheng, C. W. Yeh, and S. S. Jang. 2007. “Information-Guided Genetic Algorithm Approach to the Solution of MINLP Problems.” Industrial & Engineering Chemistry Research 46 (5): 1527–1537.
   Web of Science ®Google Scholar
• Zhang, C., and H. P. Wang. 1993. “Mixed-Discrete Nonlinear Optimization with Simulated Annealing.” Engineering Optimization 21 (44): 277–291.
   Google Scholar