Showing papers on "Multi-objective optimization published in 1997"

A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems

Abstract: A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the weights. However, it is well-known that this method succeeds in getting points from all parts of the Pareto set only when the Pareto curve is convex. This article provides a geometrical argument as to why this is the case.

Two basic problems in reliability-based structural optimization

Abstract: Optimization of structures with respect to performance, weight or cost is a well-known application of mathematical optimization theory. However optimization of structures with respect to weight or cost under probabilistic reliability constraints or optimization with respect to reliability under cost/weight constraints has been subject of only very few studies. The difficulty in using probabilistic constraints or reliability targets lies in the fact that modern reliability methods themselves are formulated as a problem of optimization. In this paper two special formulations based on the so-called first-order reliability method (FORM) are presented. It is demonstrated that both problems can be solved by a one-level optimization problem, at least for problems in which structural failure is characterized by a single failure criterion. Three examples demonstrate the algorithm indicating that the proposed formulations are comparable in numerical effort with an approach based on semi-infinite programming but are definitely superior to a two-level formulation.

Inverse Optimization: Functional and Physiological Considerations Related to the Force-Sharing Problem

Abstract: This paper is a review of the optimization techniques used for the solution of the force-sharing problem in biomechanics; that is, the distribution of the net joint moment to the force generating structures such as muscles and ligaments. The solution to this problem is achieved by the minimization (or maximization) of an objective function that includes the design variable (usually muscle forces) that are subject to certain constraints, and it is generally related to physiological or mechanical properties such as muscle stress, maximum force or moment, activation level, etc. The usual constraints require the sum of the exerted moments to be equal to the net joint moment and certain boundary conditions restrict the force solutions within physiologically acceptable limits. Linear optimization (objective and constraint functions are both linear relationships) has limited capabilities for the solution of the force sharing problem, although the use of appropriate constraints and physiologically realistic boundary conditions can improve the solution and lead to reasonable and functionally acceptable muscle force predictions. Nonlinear optimization provides more physiologically acceptable results, especially when the criteria used are related to the dynamics of the movement (e.g., instantaneous maximum force derived from muscle modeling based on length and velocity histories). The evaluation of predicted forces can be performed using direct measurements of forces (usually in animals), relationship with EMG patterns, comparisons with forces obtained from optimized forward dynamics, and by evaluating the results using analytical solutions of the optimal problem to highlight muscle synergism for example. Global objective functions are more restricting compared to local ones that are related to the specific objective of the movement at its different phases (e.g., maximize speed or minimize pain). In complex dynamic activities multiobjective optimization is likely to produce more realistic results.

Multiobjective Optimization Design with Pareto Genetic Algorithm

Abstract: This paper presents a constrained multiobjective (multicriterion, vector) optimization methodology by integrating a Pareto genetic algorithm (GA) and a fuzzy penalty function method. A Pareto GA ge...

A multi-sexual genetic algorithm for multiobjective optimization

Abstract: In this paper a new method for solving multicriteria optimization problems by Genetic Algorithms is proposed. Standard Genetic Algorithms use a population, where each individual has the same sex (or has no sex) and any two individuals can be crossed over. In the proposed Multisexual Genetic Algorithm (MSGA), individuals have an additional feature, their sex or gender and one individual from each sex is used in the recombination process. In our multicriteria optimization application there are as many sexes as optimization criteria and each individual is evaluated according to the optimization criterion related to its sex. Furthermore, a multi-parent crossover is applied to generate offspring of parents belonging to all different sexes, so the offspring represents intermediate solutions not totally optimal with respect to any single criterion. During the execution of the algorithm the set of nondominated solutions is updated and this set is presented as the output of MSGA at the end.

A Non-Generational Genetic Algorithm for Multiobjective Optimization.

Abstract: This paper describes a non-generational genetic algorithm for multiobjective optimization. The tness of each individual in the population is calculated incrementally based on the degree in which it is dominated in the Pareto sense, or close to other individuals. The closeness of individuals is measured using a sharing function. The performance of the algorithm presented is compared to previous eeorts on three multiobjec-tive optimization problems of growing dii-culty. The behavior of each algorithm is analyzed with regard to the visited search space, the quality of the nal population attained, and the percentage of non-dominated individuals in the population through time. According to all these performance measures, the algorithm presented clearly outperforms previous eeorts based on generational genetic algorithms.

Applying Family Competition to Evolution Strategies for Constrained Optimization

Abstract: This paper applies family competition to evolution strategies to solve constrained optimization problems. The family competition of Family Competition Evolution Strategy (FCES) can be viewed as a local competition involving the children generated from the same parent, while the selection is a global competition among all of the members in the population. According to our experimental results, the self-adaptation of strategy parameters with deterministic elitist selection may trap ESs into local optima when they are applied to heavy constrained optimization problems. By controlling strategy parameters with non-self adaptive rule, FCES can reduce the computation time of self-adaptive Gaussian mutation, diminish the complexity of selection from (m+1) to (m+m), and avoid to be premature. Therefore, FCES is capable of obtaining better performance and saving the computation time. In this paper, FCES is compared with other evolutionary algorithms on various benchmark problems and the results indicate that FCES is a powerful optimization technique.

Inverse and Direct Airfoil Design Using a Multiobjective Genetic Algorithm

Abstract: Some of the advantages and drawbacks of genetic algorithms applications to aerodynamic design are demonstrated. A numerical procedure for the aerodynamic design of transonic airfoils by means of genetic algorithms, with single-point, multipoint, and multiobjective optimization capabilities, is presented. In the ® rst part, an investigation on the relative ef® ciency of different genetic operators combinations is carried out on an aerodynamic inverse design problem. It is shown how an appropriate tuning of the algorithm can provide improved performances, better adaption to design space size and topology, and variables cross correlation. In the second part, the multiobjective approach to design is introduced. The problem of the optimization of the drag rise characteristics of a transonic airfoil is addressed and dealt with using a single point, a multipoint, and a multiobjective approach. A comparison between the results obtained using the three different strategies is ® nally established, showing the advantages of multiobjective optimization.

MOGAC: a multiobjective genetic algorithm for the co-synthesis of hardware-software embedded systems

Abstract: In this paper, we present a hardware-software co-synthesis system, called MOGAC, that partitions and schedules embedded system specifications consisting of multiple periodic task graphs. MOGAC synthesizes real-time heterogeneous distributed architectures using an adaptive multiobjective genetic algorithm that can escape local minima. Price and power consumption are optimized while hard real-time constraints are met. MOGAC places no limit on the number of hardware or software processing elements in the architectures it synthesizes. Our general model for bus and point-to-point communication links allows a number of link types to be used in an architecture. Application-specific integrated circuits consisting of multiple processing elements are modeled. Heuristics are used to tackle multi-rate systems, as well as systems containing task graphs whose hyperperiods are large relative to their periods. The application of a multiobjective optimization strategy allows a single co-synthesis run to produce multiple designs which trade off different architectural features. Experimental results indicate that MOGAC has advantages over previous work in terms of solution quality and running time.

Application of stochastic global optimization algorithms to practical problems

Abstract: We describe global optimization problems from three different fields representing many-body potentials in physical chemistry, optimal control of a chemical reactor, and fitting a statistical model to empirical data. Historical background for each of the problems as well as the practical significance of the first two are given. The problems are solved by using eight recently developed stochastic global optimization algorithms representing controlled random search (4 algorithms), simulated annealing (2 algorithms), and clustering (2 algorithms). The results are discussed, and the importance of global optimization in each respective field is focused.

Optimization and Persistence

Abstract: Most optimization-based decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a well-deserved reputation for amplifying small input changes into drastically different solutions. A previously optimal solution, or a slight variation of one, may still be nearly optimal in a new scenario and managerially preferable to a dramatically different solution that is mathematically optimal. Mathematical programming models can be stated and solved so that they exhibit varying degrees of persistence with respect to previous values of variables, constraints, or even exogenous considerations. We use case studies to highlight how modeling with persistence has improved managerial acceptance and describe how to incorporate persistence as an intrinsic feature of any optimization model.

Multiobjective Optimization of Bridge Deck Rehabilitation Using a Genetic Algorithm

Abstract: The solution methods of multiobjective optimization have undergone constant development over the past three decades However, the methods available to date are not particularly robust Because of the complicated relationship between the rehabilitation cost and deterioration degree of infrastructure systems, it is difficult to find a near-optimal solution using common optimization methods Since genetic algorithms work with a population of points, they can capture a number of solutions simultaneously and easily incorporate the concept of Pareto optimality In this paper a simple genetic algorithm with two additional techniques, Pareto optimality ranking and fitness sharing, is implemented for the deck rehabilitation plan of network-level bridges, aiming to minimize the total rehabilitation cost and deterioration degree This approach is illustrated by a simple example and then applied to a practical bridge system with a large number of bridges

Optimizing the Fiber-to-Yarn Production Process with a Combined Neural Network/Genetic Algorithm Approach

Abstract: An important aspect of the fiber-to-yam production process is the quality of the resulting yarn. The yarn should have optimal product characteristics (and minimal faults). In theory, this objective can be realized using an optimization algorithm. The complexity of a fiber-to-yarn process is very high, however, and no mathematical function is known to exist that represents the whole process. This paper presents a method to simulate and optimize the fiber-to-yam production process using a neural network combined with a genetic algorithm. The neural network is used to model the process, with the machine settings and fiber quality parameters as input and the yarn tenacity and elongation as output. The genetic algorithm is used afterward to optimize the input parameters for obtaining the best yarns. Since this is a multi-objective optimization, the genetic algorithm is enforced with a sharing function and a Pareto optimization. The paper shows that simultaneous optimization of yarn qualities is easily achieved...

On Lagrance-Kuhn-Tucker Mulitipliers for Muliobjective Optimization Problems

Abstract: Optimallty conditions are established in terms of Lagrange-Fritz-John and Lagrange-Kuhn-Tucker multipliers for multiobjective optimization problems by scalarization technique

A mathematical programming approach for generating alternatives in discrete structural optimization

Abstract: Structural design, like other complex decision problems, involves many tradeoffs among competing criteria. While mathematical programming models are increasingly realistic, there are often relevant issues that cannot be easily captured, if at all, in a formal system. This paper describes an approach to modelling that recognizes these limitations and allows a designer to explore unmodelled issues in a joint human-computer cognitive system. A prototype based on this approach is presented for topological truss optimization, and three modelling techniques are contrasted for their effectiveness in producing “different” alternatives. The results show that alternatives produced using these techniques are good with respect to modelled objectives, and yet are different, and often better, with respect to interesting objectives not present in the model.

Automating the process of optimization in spacecraft design

Abstract: Spacecraft design optimization is a difficult problem, due to the complexity of optimization cost surfaces and the human expertise in optimization that is necessary in order to achieve good results. In this paper, we propose the use of a set of generic, metaheuristic optimization algorithms (e.g., genetic algorithms, simulated annealing), which is configured for a particular optimization problem by an adaptive problem solver based on artificial intelligence and machine learning techniques. We describe work in progress on OASIS, a system for adaptive problem solving based on these principles.

Machine set up procedure using multivariate modeling and multiobjective optimization

Abstract: A method of setting up an electrostatographic printing machine having image quality attributes and parameters that control the attributes using multivariate modeling and multiobjective optimization. The method includes providing a discrete number of parameter settings and printing test patterns based upon the parameter settings. The test patterns are scanned to produce a set of image quality values. Using a multivariate adaptive regression splines technique, a model of the printing machine image quality is provided in response to the parameter settings and the image quality values. Optimum parameter settings for the printing machine are then determined from the discrete number of parameter settings to produce consistent image quality.

MOGAC: a multiobjective genetic algorithm for the co-synthesis of hardware-software embedded systems

Abstract: We present a hardware-software co-synthesis system, called MOGAC, that partitions and schedules embedded system specifications consisting of multiple periodic task graphs. MOGAC synthesizes real-time heterogeneous distributed architectures using an adaptive multiobjective genetic algorithm that can escape local minima. Price and power consumption are optimized while hard real-time constraints are met. MOGAC places no limit on the number of hardware or software processing elements in the architectures it synthesizes. Our general model for bus and point-to-point communication links allows a number of link types to be used in an architecture. Application-specific integrated circuits consisting of multiple processing elements are modeled. Heuristics are used to tackle multi-rate systems, as well as systems containing task graphs whose hyperperiods are large relative to their periods. The application of a multiobjective optimization strategy allows a single co-synthesis run to produce multiple designs which trade off different architectural features. Experimental results indicate that MOGAC has advantages over previous work in terms of solution quality and running time.

Multiobjective optimal design of interior permanent magnet synchronous motors considering improved core loss formula

Abstract: This paper describes the optimal design of interior permanent magnet synchronous motors for which two objective functions regarding motor efficiency and weight are used. Multiobjective optimization technique is applied to finding the optimal solution in this case. An optimal design method that determines both the noninferior solution set and the best compromise solution employing a modified genetic algorithm is proposed. The proposed algorithm adopts the structure of the conventional genetic algorithm, but fitness value and convergence criterion are redefined and some major parameters of the algorithm are adjusted to the multiobjective optimization. In order to predict the motor performance more accurately, a core loss formula is derived considering the flux variation due to the stator currents as well as that due to the magnet.

Pareto analysis vis-à-vis balance space approach in multiobjective global optimization

Abstract: There is much controversy about the balance space approach, introduced first in Ref. 1, pp. 138–140, with the consideration of the balance number and balance vectors, and then further developed in Ref. 2, with the consideration of balance points and balance sets. There were attempts to identify the balance space approach with some other methods of multiobjective optimization, notably the method proposed in Ref. 3 and most recently Pareto analysis, as presented in Ref. 4. In this paper, we compare Pareto analysis with the balance space approach on several examples to demonstrate the interrelation and the differences of the two methods. As a byproduct, it is shown that, in some cases, the entire Pareto sets, proper and adjoint, can be determined very simply, without any special investigation of the (nonscalarized, nonconvex) multiobjective global optimization problem. The method of parameter introduction is presented in application to determining the Pareto sets and balance set. The use of computer graphics software complemented with the Gauss–Jordan matrix reduction algorithm is proposed for a class of otherwise intractable problems with nonconvex constraint sets.