Deterministic Multi-objective Optimization Research Articles

Multiobjective robust optimization method for drawbead design in sheet metal forming

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality.

Multiobjective optimization of an industrial grinding operation under uncertainty

Abstract Multiobjective optimization of an industrial grinding operation under various parameter uncertainties is carried out in this work. Two sources of uncertainties considered here are related to the (i) parameters that are used inside a model representing the process under consideration and subjected to experimental and regression errors and (ii) parameters that express operators’ choice for assigning bounds in the constraints and operators prefer them to be expressed around some value rather than certain crisp value. Uncertainty propagation of these parameters through nonlinear model equations is reflected in terms of system constraints and objectives that are treated here using chance constrained fuzzy simulation based approach. Such problems are treated in literature using the standard two stage stochastic programming methodology that has a drawback of leading to combinatorial explosion with an increase in the number of uncertain parameters. This problem is overcome here using a combination of fuzzy and chance constrained programming approach that tackles the problem by representing and treating the uncertain parameters in a different manner. Simultaneous maximization of grinding circuit throughput and percent passing mid size fraction are studied here with upper bound constraints for various performance metrics for the grinding circuit, e.g. percent passing of fine and coarse size classes, percent solids in the grinding circuit final outlet stream and circulation load of the grinding circuit. Uncertain parameters considered are grindability indices of rod mill and ball mill, sharpness indices of primary and secondary cyclones and the respective upper bounds for the constraints mentioned above. The deterministic multiobjective grinding optimization model of Mitra and Gopinath [2004. Multiobjective optimization of an industrial grinding operation using elitist nondominated sorting genetic algorithm. Chem. Eng. Sci. 59, 385–396.] forms the basis of this work on which various effects of uncertain parameters are shown and analyzed in a Pareto fashion. Nondominated sorting genetic algorithm, NSGA II, a popular elitist evolutionary multiobjective optimization approach, is used for this purpose.

UNCERTAINTY BASED ROBUST OPTIMIZATION IN AERODYNAMICS

The Taguchi robust design concept is combined with the multi-objective deterministic optimization method to overcome single point design problems in Aerodynamics. Starting from a statistical definition of stability, the method finds, Nash equilibrium solutions for performance and its stability simultaneously.

An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method

An optimization method is proposed to solve uncertain structural problems based on a nonlinear interval number programming method and an interval analysis method. A nonlinear interval number programming method is suggested to transform the uncertain optimization problem to a deterministic multi-objective optimization problem based on an order relation of interval. For each specific design vector, an interval analysis method is applied to calculate the interval of the objective function caused by uncertainty, and whereby the optimization nesting problem can be solved. A non-constraint and single-objective optimization problem is then formulated through the linear combination method of multi-objective optimization and the penalty function method. An intergeneration projection genetic algorithm is employed to seek for Pareto optimum of the uncertain problem. The presented method is applied to a benchmark test of ten-bar truss and a practical automobile frame, and the optimization results demonstrate its efficiency.

Battery-aware adaptive modulation with QoS constraints

We consider the problem of joint battery management and modulation optimization for maximizing the lifetime of a battery-powered autonomic wireless system while satisfying certain quality-of-service constraints. Our objective is to design the optimal transmission schemes adapting to the battery state, the delay constraints, and channel conditions. A delay-constrained data-transmission scenario is considered, where the battery state information is only available at the beginning of the entire transmission duration. The corresponding problem is formulated as a multiobjective stochastic optimization problem, which is hard to solve. We approximately transform the original problem to a multiobjective deterministic optimization problem by using a lower bound to replace the objective function of the original problem. The optimal, as well as efficient suboptimal solutions are developed. Simulation results are provided to demonstrate that the proposed algorithms can significantly increase the lifetime of the battery-powered autonomic wireless systems