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Combinatorial optimization under uncertainty with applications to engineering synthesis and design reliability models.

机译：不确定性下的组合优化，应用于工程综合和设计可靠性模型。

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This dissertation approaches decision making using combinatorial optimization. Decisions are both stochastic and combinatorial problems, because they involve uncertainty and a large number of choices about individual units or subcomponents of a problem. Instead of using conventional approaches to decision making such as decision trees, which often require complete enumeration of the state space, this work extends the combinatorial optimization methods of simulated annealing and genetic algorithms to incorporate uncertainties in the decision space. The definition of an objective function in a stochastic problem is addressed. These optimization techniques are applied to a particular class of problems, those of optimizing the design of reliable, complex engineered systems. The case studies examined are in chemical process synthesis and reliability engineering: the design of a Brayton cycle power plant and a multi-stage compression/expansion cycle, and the design of a highly reliable personal computer and laser debridement system. The fundamental contribution of this dissertation is in providing an improved methodology for decision making under uncertainty. General findings and conclusions are as follows: (1) The techniques of simulated annealing and genetic algorithms work well and are useful in arriving at an optimal set of solutions in a "jittery," stochastic solution space. (2) The performance of heuristic techniques such as simulated annealing and genetic algorithms are dependent upon problem representation, objective function formulation, and method of implementation. Incorporation of constraints can be extremely important in determining the shape of the solution space. (3) The approaches presented may be applied to synthesis problems involving simultaneous structural and parameter optimization. (4) Uncertainties in the input parameters change the nature of the output space and the optimal solution. The optimal solution also varies depending upon the objective function used. (5) Most of the literature on optimization of stochastic problems has dealt with optimization of the expected value of the objective function. This implies a risk neutral decision maker. Risk averse preferences can easily change the optimal decision and should be explicitly incorporated into the objective function through the use of utility functions.
机译：本文采用组​​合优化方法进行决策。决策既是随机问题又是组合问题，因为决策涉及不确定性以及对问题的单个单元或子组件的大量选择。代替使用通常需要状态空间完整枚举的常规决策方法（例如决策树），这项工作扩展了模拟退火和遗传算法的组合优化方法，以将不确定性纳入决策空间。讨论了随机问题中目标函数的定义。这些优化技术适用于一类特定的问题，即对可靠，复杂的工程系统的设计进行优化的技术。研究的案例研究涉及化学过程合成和可靠性工程：布雷顿循环发电厂和多级压缩/膨胀循环的设计，以及高度可靠的个人计算机和激光清创系统的设计。本论文的基本贡献在于提供了一种改进的不确定性决策方法。总体发现和结论如下：（1）模拟退火和遗传算法的技术运行良好，可用于在“不稳定的”随机解空间中获得最优解集。 （2）启发式技术（如模拟退火和遗传算法）的性能取决于问题表示，目标函数公式和实现方法。约束的合并对于确定解空间的形状非常重要。 （3）提出的方法可应用于涉及同时结构和参数优化的综合问题。 （4）输入参数的不确定性改变了输出空间的性质和最优解。最佳解决方案还取决于所使用的目标函数。 （5）关于随机问题优化的大多数文献都涉及目标函数期望值的优化。这意味着风险中立的决策者。规避风险的偏好很容易改变最佳决策，应通过使用效用函数将其明确地纳入目标函数。

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