Showing papers on "Multi-objective optimization published in 1994"

Muiltiobjective optimization using nondominated sorting in genetic algorithms

Abstract: In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands that the user have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms (GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias toward some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaffer and others suggest that the proposed method can be extended to higher dimensional and more difficult multiobjective problems. A number of suggestions for extension and application of the algorithm are also discussed.

A niched Pareto genetic algorithm for multiobjective optimization

Abstract: Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic algorithm (GA), however, is readily modified to deal with multiple objectives by incorporating the concept of Pareto domination in its selection operator, and applying a niching pressure to spread its population out along the Pareto optimal tradeoff surface. We introduce the Niched Pareto GA as an algorithm for finding the Pareto optimal set. We demonstrate its ability to find and maintain a diverse "Pareto optimal population" on two artificial problems and an open problem in hydrosystems. >

Simulated Annealing for Multi Objective Optimization Problems

Abstract: In the last decade some large scale combinatorial optimization problems have been tackled by way of a stochastic technique called ‘simulated annealing’ first proposed by Kirkpatrick et al. (1983). This technique has proved to be a valid tool to find acceptable solutions for problems whose size makes impossible any exact solution method.

Multicriteria Optimization in Engineering Design

Abstract: An engineering design optimization problem can be formulated as a search of the solution space for which the relationships among various groups of attributes are given. The search can be also conducted for a multicriteria optimization. The paper discusses three classes of problems associated with multicriteria optimization in engineering design. First, multicriteria optimization methods with a single domination relationship are reviewed. Next, such methods with many domination functions are discussed. The last part of the paper focuses on the search when the ideal solution, or solutions, are known, but they are infeasible and the solutions sought should come as close as possible.

Multiobjective optimization of a plastic injection molding process

Abstract: It is well known that the PID regulator has been very successful and widely accepted for controlling industrial systems where one objective function is the performance criterion. The question is whether the same success can be achieved for more than one objective function using the basic PID controller, while preserving its simplicity for use by an operator. Here the authors explore the use of multiobjective optimization for the purpose of extending PID controllers to applications that require the optimization of multiple objectives. An algorithm is implemented that runs in real-time and provides immediate feedback to a process operator about the current operating point. It was applied to the tuning of a PID controller to meet multiple objectives for the plastication phase of an injection molding process. The algorithm was implemented on an injection molding machine and allowed to tune the controller on-line. Simulation and experimental results are presented and compared. >

Lagrange multipliers and saddle points in multiobjective programming

Abstract: In this paper, we present several conditions for the existence of a Lagrange multiplier or a weak saddle point in multiobjective optimization. Relations between a Lagrange multiplier and a weak saddle point are established. A sufficient condition is also given for the equivalence of the Benson proper efficiency and the Borwein proper efficiency.

On the use of optimization models for portfolio selection: a review and some computational results

Abstract: Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different portfolio models with emphasis on the corresponding optimization problems. For the classical Markowitz mean-variance model we present computational results, applying a dual algorithm for constrained optimization.

On lagrange-kuhn-tucker multipliers for pareto optimization problems

Abstract: We give a simple proof of the existence of Lagrange-Kuhn-Tucker multipliers for Pareto Multiobjective programming problems.

A simulated annealing technique for multiobjective optimization of intelligent structures

Abstract: A multiobjective optimization procedure is developed to address the combined problems of the synthesis of structures/controls and the actuator-location problem for the design of intelligent structures Continuous and discrete variables are treated equally in the formulation Multiple and conflicting design objectives such as vibration reduction, dissipated energy, power and a performance index are included by utilizing an efficient multiobjective optimization formulation Piezoelectric materials are used as actuators in the control system A simulated annealing algorithm is used for optimization and an approximation technique is used to reduce computational effort A numerical example using a cantilever box beam demonstrates the utility of the optimization procedure when compared with a previous nonlinear programming technique

Optimal design of structural concrete bridge systems

Abstract: Superstructure design of short‐ and medium‐span highway bridge systems may be conceived as a process of multilevel and multiobjective optimization. Three optimization levels are identified: (1) Level 1—component optimization; (2) level 2—structural configuration optimization; and (3) level 3—overall system optimization. Designs may be optimized by separately or simultaneously considering one, two, or more of the following objectives: cost, prestressing steel or concrete consumption, and superstructure depth. The optimal solution may be found by a sequence of nonlinear programming and sieve‐search techniques. Levels 1 and 2 optimizations identify the best solutions for specific components (precast I‐girders, voided and solid slabs, single‐ and two‐cell box girders) and layouts (for precast I‐girder: one, two, and three; simple or continuous spans). Level 3 optimization selects the overall best system for given bridge lengths, widths, and traffic loadings. The present study results in: (1) A systematic proc...

Reliability-Based Optimization as an Information Tool*

Abstract: Reliability-based optimization is presented as an information tool in the process of achieving knowledge about the nature of a problem. Sensitivity analysis in pre- and post-evaluation of reliability-based optimization models is introduced for the purpose of identification of important problem parameters. A reliability-based optimization problem is formulated and a solution procedure is suggested. Various techniques for achievement of the sensitivities both with respect to model parameters and optimization variables are described. Finally, the way in which the sensitivities used in pre- and post-evaluations and the optimal design give additional insight into the nature of the problem is discussed and illustrated.

A Goal Programming model of the reference point method

Abstract: Real-life decision problems are usually so complex they cannot be modeled with a single objective function, thus creating a need for clear and efficient techniques of handling multiple criteria to support the decision process. The most commonly used technique is Goal Programming. It is clear and appealing, but in the case of multiobjective optimization problems strongly criticized due to its noncompliance with the efficiency (Pareto-optimality) principle. On the other hand, the reference point method, although using similar control parameters as Goal Programming, always generates efficient solutions. In this paper, we show how the reference point method can be modeled within the Goal Programming methodology. It allows us to simplify implementations of the reference point method as well as shows how Goal Programming with relaxation of some traditional assumptions can be extended to a multiobjective optimization technique meeting the efficiency principle.

Multiobjective trajectory optimization by goal programming with fuzzy decisions

Abstract: A sequential goal programming approach is considered for not only well-defined flight trajectory problems but also ill-defined problems that have no feasible solutions satisfying all design requirements due to strict boundary conditions or tight path constraints. By using a time integration algorithm, trajectory optimization problems are transformed into numerical optimization problems that seek optimal control variables at discrete time points to minimize an objective function and satisfy various design constraints. By defining the target goal values of both the constraints and the objective functions and by prioritizing each goal according to its significance, the GP formulation modifies ill-defined problems as multiobjective design problems. Additionally, a fuzzy decision making method is applied for those goals that are prioritized, not precisely, but in a fuzzy manner. Numerical applications for simple ascent trajectory problems show that this method can efficiently find the trajectories when various kinds of design requirements are imposed for the ill-defined problem.

Parallel global optimization: numerical methods, dynamic scheduling methods, and application to molecular configuration

Abstract: : Global optimization problems are computationally extensive problems that arise in many important applications. The solution of very large practical global optimization problems, which may have thousands of variables and huge numbers of local minimizers, is not yet possible. It will require efficient numerical algorithms that take advantage of the properties of the particular application, as well as efficient utilization of the fastest available computers, which will almost certainly be highly parallel machines. This paper summarizes our research efforts in this direction. First, we describe general purpose adaptive, asynchronous parallel stochastic global optimization methods that we have developed, our computational experience with them. Second, we describe several alternative dynamic scheduling algorithms that are required to control such dynamic parallel algorithms on distributed memory multiprocessors, and compare their performance in the context of our parallel in the context of our parallel global optimization methods. Third, we discuss the application and refinement of these methods to global optimization problems arising from the structural optimization of chemical molecules, and present preliminary computational results on some problems with between 15 and 100 variables. This work includes the development of new algorithmic features that are motivated by the molecular configuration problem but are applicable to a wider class of large scale, partially separable global optimization problems.

Algorithms for bilevel optimization

Abstract: General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multicriteria optimization problems. Here for clarity in displaying our ideas, we restrict ourselves to general bilevel optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bilevel problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.

Optimization in industry 2: Mathematical programming and modeling techniques in practice

Abstract: Modelling Techniques for Automated Production Planning in the Semiconductor Industry Crew Pairing Optimization at American Airlines Decision Technology Optimization in Microelectronics Manufacturing Combinatorial Models for Manufacturing: Optimizing Flow Management in Flexible Manufacturing Systems Optimal Planning and Control of Consumer Products Packaging Lines Optimization in Refinery Scheduling: Modelling and Solution Nonlinear Optimization Algorithm for Mixed Integer Programming Problems Mixed Integer Programming in Production Scheduling: A Case Study Large Recursion Models: Practical Aspects of Recursion Techniques The Job Sequencing Ordering Problems on a Card Assembly Line Model Structures and Optimization Strategies.

Case-based acquisition of user preferences for solution improvement in ill-structured domains

Abstract: We have developed an approach to acquire complicated user optimization criteria and use them to guide iterative solution improvement. The effectiveness of the approach was tested on job shop scheduling problems. The ill-structuredness of the domain and the desired optimization objectives in real-life problems, such as factory scheduling, makes the problems difficult to formalize and costly to solve. Current optimization technology requires explicit global optimization criteria in order to control its search for the optimal solution. But often, a user's optimization preferences are state-dependent and cannot be expressed in terms of a single global optimization criterion. In our approach, the optimization preferences are represented implicitly and extensionally in a case base. Experimental results in job shop scheduling problems support the hypotheses that our approach (1) is capable of capturing diverse user optimization preferences and re-using them to guide solution quality improvement, (2) is robust in the sense that it improves solution quality independent of the method of initial solution generation, and (3) produces high quality solutions, which are comparable with solutions generated by traditional iterative optimization techniques, such as simulated annealing, at much lower computational cost.