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Objective Optimization Problems (objective + optimization_problem)
Selected AbstractsMultiple Objective Optimization Problems in StatisticsINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 4 2002Subhash C. Narula Many statistical problems can be viewed as optimization problems. A careful and detailed analysis of these procedures reveals that many of these problems are essentially multiple objective optimization problems. Furthermore, most of the standard statistical procedures aim at finding an efficient (non-dominated) solution. Our objective in this paper is to introduce some of the single sample statistical problems that can be formulated and solved as multiple objective optimization problems. [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] Quantitative Comparison of Approximate Solution Sets for Bi-criteria Optimization Problems,DECISION SCIENCES, Issue 1 2003W. Matthew Carlyle ABSTRACT We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near-pareto-optimal solutions to bi-criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives. [source] Crack identification of a planar frame structure based on a synthetic artificial intelligence techniqueINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Mun-Bo Shim Abstract It has been established that a crack has an important effect on the dynamic behaviour of a structure. This effect depends mainly on the location and depth of the crack. To identify the location and depth of a crack in a planar frame structure, a method is presented in this paper which uses a synthetic artificial intelligence technique, i.e. adaptive-network-based fuzzy inference system (ANFIS) solved via a hybrid learning algorithm (the backpropagation gradient descent and the least-squares method) and continuous evolutionary algorithms (CEAs) solving single objective optimization problems with a continuous function and continuous search space efficiently are unified. With ANFIS and CEAs it is possible to formulate the inverse problem. ANFIS is used to obtain the input (the location and depth of a crack),output (the structural eigenfrequencies) relation of the structural system. CEAs are used to identify the crack location and depth by minimizing the difference from the measured frequencies. We have tried this idea on 2D beam structures and the results are promising. Copyright © 2003 John Wiley & Sons, Ltd. [source] Multiple Objective Optimization Problems in StatisticsINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 4 2002Subhash C. Narula Many statistical problems can be viewed as optimization problems. A careful and detailed analysis of these procedures reveals that many of these problems are essentially multiple objective optimization problems. Furthermore, most of the standard statistical procedures aim at finding an efficient (non-dominated) solution. Our objective in this paper is to introduce some of the single sample statistical problems that can be formulated and solved as multiple objective optimization problems. [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] | ||||||||||