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Pareto Front (pareto + front)
Selected AbstractsMultiobjective Optimization of Concrete Frames by Simulated AnnealingCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 8 2008Ignacio Paya The evaluation of solutions follows the Spanish Code for structural concrete. The methodology was applied to a symmetrical building frame with two bays and four floors. This example has 77 design variables. Pareto results of the MOSA algorithm indicate that more practical, more constructable, more sustainable, and safer solutions than the lowest cost solution are available at a cost increment acceptable in practice. Results Ns -SMOSA1 and Ns -SMOSA2 of the cost versus constructability Pareto front are finally recommended because they are especially good in terms of cost, constructability, and environmental impact. Further, the methodology proposed will help structural engineers to enhance their designs of building frames. [source] Seismic design of RC structures: A critical assessment in the framework of multi-objective optimizationEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 12 2007Nikos D. Lagaros Abstract The assessment of seismic design codes has been the subject of intensive research work in an effort to reveal weak points that originated from the limitations in predicting with acceptable precision the response of the structures under moderate or severe earthquakes. The objective of this work is to evaluate the European seismic design code, i.e. the Eurocode 8 (EC8), when used for the design of 3D reinforced concrete buildings, versus a performance-based design (PBD) procedure, in the framework of a multi-objective optimization concept. The initial construction cost and the maximum interstorey drift for the 10/50 hazard level are the two objectives considered for the formulation of the multi-objective optimization problem. The solution of such optimization problems is represented by the Pareto front curve which is the geometric locus of all Pareto optimum solutions. Limit-state fragility curves for selected designs, taken from the Pareto front curves of the EC8 and PBD formulations, are developed for assessing the two seismic design procedures. Through this comparison it was found that a linear analysis in conjunction with the behaviour factor q of EC8 cannot capture the nonlinear behaviour of an RC structure. Consequently the corrected EC8 Pareto front curve, using the nonlinear static procedure, differs significantly with regard to the corresponding Pareto front obtained according to EC8. Furthermore, similar designs, with respect to the initial construction cost, obtained through the EC8 and PBD formulations were found to exhibit different maximum interstorey drift and limit-state fragility curves. Copyright © 2007 John Wiley & Sons, Ltd. [source] Kinetic Analysis and Optimization for the Catalytic Esterification Step of PPT PolymerizationMACROMOLECULAR THEORY AND SIMULATIONS, Issue 1 2005Saptarshi Majumdar Abstract Summary: A well-validated kinetic scheme has been studied for PPT, poly(propylene terephthalate) polymerization process in batch and semi-batch mode with tetrabutoxytitanium (TBOT), a proven catalyst. Optimization study and analysis for PPT are rare, as the industrial relevance of PPT just became vibrant due to the commercial availability of one of its monomers in industrial scale in the recent past. Correctness of the analysis is checked by a new approach and parameters for the model are estimated from available experimental data. Solubility of terephthalic acid (TPA) is less in reaction medium and this effect is also considered along with the reaction scheme. Several simulations have been performed to see various process dynamics and this ultimately helps in formulating optimization problems. Using recently developed and well tested real-coded non-dominated sorting genetic algorithm-II, a state-of-the art evolutionary optimization algorithm, a couple of three objective optimization problems have been solved and corresponding Pareto sets are presented. Results show remarkably promising aspects of productivity enhancement with an improvement in product quality. Sensitivity analysis for relatively uncertain solubility parameter is also performed to estimate its effect over the proposed optimal solutions. Multiobjective Pareto front for 3 objectives: degree of polymerization, time and (bTPA,+,bPG). [source] Dielectric filter optimal design suitable for microwave communications by using multiobjective evolutionary algorithmsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 10 2007S. K. Goudos Abstract A multiobjective evolutionary technique is applied to design dielectric filters useful in microwave communications technology. The optimal geometry of the filters is derived by utilizing two different multiobjective optimization algorithms. The first one is the Nondominated Sorting Genetic Algorithm-II (NSGA-II), which is a popular multiobjective genetic algorithm. The second algorithm is based on multiobjective Particle Swarm Optimization with fitness sharing (MOPSO-fs). MOPSO-fs algorithm is a novel Pareto PSO algorithm that produces the Pareto front in a fast and efficient way. In the present work, MOPSO-fs is compared with NSGA-II to optimize the geometry of the filters under specific requirements concerning the frequency response of the filters. Several examples are studied to exhibit the efficiency of the multiobjective evolutionary optimizers and also the ability of the technique to derive optimal structures that can be used in practice. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2324,2329, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22755 [source] Efficient optimization strategies with constraint programming,AICHE JOURNAL, Issue 2 2010Prakash R. Kotecha Abstract In this article, we propose novel strategies for the efficient determination of multiple solutions for a single objective, as well as globally optimal pareto fronts for multiobjective, optimization problems using Constraint Programming (CP). In particular, we propose strategies to determine, (i) all the multiple (globally) optimal solutions of a single objective optimization problem, (ii) K -best feasible solutions of a single objective optimization problem, and (iii) globally optimal pareto fronts (including nonconvex pareto fronts) along with their multiple realizations for multiobjective optimization problems. It is shown here that the proposed strategy for determining K -best feasible solutions can be tuned as per the requirement of the user to determine either K -best distinct or nondistinct solutions. Similarly, the strategy for determining globally optimal pareto fronts can also be modified as per the requirement of the user to determine either only the distinct set of pareto points or determine the pareto points along with all their multiple realizations. All the proposed techniques involve appropriately modifying the search techniques and are shown to be computationally efficient in terms of not requiring successive re-solving of the problem to obtain the required solutions. This work therefore convincingly addresses the issue of efficiently determining globally optimal pareto fronts; in addition, it also guarantees the determination of all the possible realizations associated with each pareto point. The uncovering of such solutions can greatly aid the designer in making informed decisions. The proposed approaches are demonstrated via two case studies, which are nonlinear, combinatorial optimization problems, taken from the area of sensor network design. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] | ||||||||||