A new method for decision making in multi-objective optimization problems

Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.

Multiobjective engineering design optimization problems: a sensitivity analysis approach

This paper proposes two new approaches for the sensitivity analysis of multiobjective design optimization problems whose performance functions are highly susceptible to small variations in the design variables and/or design environment parameters. In both methods, the less sensitive design alternatives are preferred over others during the multiobjective optimization process. While taking the first approach, the designer chooses the design variable and/or parameter that causes uncertainties. The designer then associates a robustness index with each design alternative and adds each index as an objective function in the optimization problem. For the second approach, the designer must know, a priori, the interval of variation in the design variables or in the design environment parameters, because the designer will be accepting the interval of variation in the objective functions. The second method does not require any law of probability distribution of uncontrollable variations. Finally, the authors give two illustrative examples to highlight the contributions of the paper.

Reliability-based design optimization strategies based on FORM: a review

In deterministic optimization, the uncertainties of the structural system (i.e. dimension, model, material, loads, etc) are not explicitly taken into account. Hence, resulting optimal solutions may lead to reduced reliability levels. The objective of reliability based design optimization (RBDO) is to optimize structures guaranteeing that a minimum level of reliability, chosen a priori by the designer, is maintained. Since reliability analysis using the First Order Reliability Method (FORM) is an optimization procedure itself, RBDO (in its classical version) is a double-loop strategy: the reliability analysis (inner loop) and the structural optimization (outer loop). The coupling of these two loops leads to very high computational costs. To reduce the computational burden of RBDO based on FORM, several authors propose decoupling the structural optimization and the reliability analysis. These procedures may be divided in two groups: (i) serial single loop methods and (ii) unilevel methods. The basic idea of serial single loop methods is to decouple the two loops and solve them sequentially, until some convergence criterion is achieved. On the other hand, uni-level methods employ different strategies to obtain a single loop of optimization to solve the RBDO problem. This paper presents a review of such RBDO strategies. A comparison of the performance (computational cost) of the main strategies is presented for several variants of two benchmark problems from the literature and for a structure modeled using the finite element method.