In this paper, a new method for optimum design of frame structures is presented. The method is based on a hierarchical decomposition of the structure into two-levels, namely, the bottom- and the top-level. The bottom-level consists of several subproblems each dealing with the cross-sectional sizing of a given frame-element. The top-level consists of one subproblem which is formulated for configuration design of the frame structure. Since there may be a large number of frame elements, a new shape multiplier method has been developed to simplify the formulation of the bottom-level subproblems. Furthermore, a two-level solution procedure has been developed which first solves the bottom-level subproblems based on their monotonicity analysis. It then solves the top-level subproblem as it coordinates, based on a linear approximation, the solutions to the bottom-level subproblems. Three examples with increasing degree of difficulty are presented to demonstrate the effectiveness of the method.

In this paper, a new approach for optimization-based design of non-linearly mixed discrete-continuous problems has been developed. The approach is based on a two-level decomposition strategy in which the entire domain of variables is partitioned into two levels, one involving the continuous variables and the other involving the discrete variables. Variables in one level are optimized for fixed values of the variable from the other level. A modified penalty function is formed, based on monotonicity analysis, to solve for the discrete variables, and a conventional optimization method was used to solve for the continuous variables. To improve the computational effectiveness of the approach, a constrained derivative relationship was also adopted. The performance of the entire algorithm is then demonstrated through an example involving printed circuit board assemblies. The objective in the example is to maximize assembly reliability by: (1) adding redundant components to the boards and (2) optimally distributing allocated mass flow to the individual channels of the circuit boards. Number of variables in the example is then varied to investigate the effectiveness and potential of the approach for large-scale problems.

In a previous article, a new and simple reduction method was presented for optimization-based design of nonhierarchically decomposed engineering systems. As a sequel to that work, in this paper we first examine some significant issues in relation to the reduction method: the optimality conditions when the method is applied, the reason why move limits are not required, and some of the factors that might affect the robustness of the cumulative constraints. For verification and validation, we then present some numerical test results in which the method is applied to twenty-one (21) test problems. Based on the test results reported, some guidelines for applying the method are suggested.

Nonhierarchical decomposition-based optimization, especially when compared to the hierarchical one, has the advantage that no restriction is imposed on how the decomposed subsystems should interact with one another. However, the difficulty inherent in nonhierarchically decomposed subsystems is how to coordinate their activities so that an overall optimum design can be achieved. In this paper, a new and simple method for optimization-based design of nonhierarchically decomposed systems is presented. The driving force behind the method is to formulate and iteratively solve a reduced-size problem so that the decomposed subsystems can be coordinated. Since the size reduction measures developed in the method does not include any problem-dependent assumptions, the procedure is applicable to a wide variety of optimization problems. To illustrate the application of the method, a simple numerical and a flywheel design example are presented.

In this paper, several new set quality metrics are introduced that can be used to evaluate the ‘goodness’ of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include coverage difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer either monitor the quality of an observed Pareto solution set as obtained by a multiobjective optimization method, or compare the quality of observed Pareto solution sets as reported by different multiobjective optimization methods. A vibrating platform example is used to demonstrate the calculation of these metrics for an observed Pareto solution set.

This paper presents an approach wherein product design is viewed as a selection process with two main stages: design alternative generation and design alternative evaluation. The focus of this paper is mainly on a design alternative evaluation model in that designer’s preferences, customers’ preferences, and market competition are accounted for in order to select the best possible design. In the model, uncertainties in the product design life, market size and its yearly change, cost and its yearly change, price, and discount rate are considered. Product design selection of a cordless screwdriver is used as a demonstration example. However, the emphasis in the example is on the approach, and not on the details per se .

An approach for product line design is presented in which a line of products is selected for launching into the market. In the approach, the product line design is viewed as a selection process with two main stages: design alternative generation and design alternative evaluation. The focus of this paper is on the design alternative evaluation stage. Issues considered include a large variety of customer preferences, market competitions, multiple business goals, uncertainty, and commonality among the alternatives in a product line. Because of the combinatorial nature of the problem, genetic algorithms are used in the design evaluation stage. Product line design selection of a cordless screwdriver is used as a demonstration example. However, the emphasis in the example is on the approach and not in the details per se .

This paper presents the results of a comparison study of three solution strategies for integrating a routing and a control model for a fleet of vehicles planned to visit a number of customer locations. The three strategies considered are: (i) shortest route followed by a constant speed model, (ii) shortest route followed by an optimal control model, and (iii) optimal control-based route. The objective is to compare and contrast optimized costs, a combination of vehicles’ travel time and control cost (or energy consumption), following these different strategies. The routing problem considers a capacitated multi-vehicle routing without time windows but with capacity and customer demand requirements. The control problem considers a continuous-time optimal control problem. Using the data from a benchmark multi-vehicle routing problem, as an example, it is shown that when compared with using a commonly used constant speed model for all vehicles, the optimized cost can be reduced by incorporating optimal control strategies. To the best of our knowledge, this is the first study in the literature that compares solution strategies for control-based vehicle routing, and in particular, formulates and explores continuous time optimal control combined with capacitated multi-vehicle routing. Furthermore, the effect of existence of wind on the vehicle dynamic equations is considered, and optimal results of the routing problem with different wind directions are compared.

Online prediction of dynamical system behavior based on a combination of simulation data and sensor measurement data has numerous applications. Examples include predicting safe flight configurations, forecasting storms and wildfire spread, estimating railway track and pipeline health conditions. In such applications, high-fidelity simulations may be used to accurately predict a system’s dynamical behavior offline (“non-real time”). However, due to the computational expense, these simulations have limited usage for online (“real-time”) prediction of a system’s behavior. To remedy this, one possible approach is to allocate a significant portion of the computational effort to obtain data through offline simulations. The obtained offline data can then be combined with online sensor measurements for online estimation of the system’s behavior with comparable accuracy as the off-line, high-fidelity simulation. The main contribution of this paper is in the construction of a fast data-driven spatiotemporal prediction framework that can be used to estimate general parametric dynamical system behavior. This is achieved through three steps. First, high-order singular value decomposition is applied to map high-dimensional offline simulation datasets into a subspace. Second, Gaussian processes are constructed to approximate model parameters in the subspace. Finally, reduced-order particle filtering is used to assimilate sparsely located sensor data to further improve the prediction. The effectiveness of the proposed approach is demonstrated through a case study. In this case study, aeroelastic response data obtained for an aircraft through simulations is integrated with measurement data obtained from a few sparsely located sensors. Through this case study, the authors show that along with dynamic enhancement of the state estimates, one can also realize a reduction in uncertainty of the estimates.

Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

Multi-subsystem co-design refers to the simultaneous optimization of physical plant and controller of a system decomposed into multiple interconnected co-design subsystems. In this paper, a new decentralized approach based on the direct collocation and decomposition-based optimization methods is formulated to solve multi-subsystem co-design problems. First, the problem is decomposed into physical plant and control parts. In the control part, the entire time horizon is discretized into subintervals and grid points. In this way, a continuous optimal control problem is converted into a finite dimensional nonlinear programming (NLP) problem. The optimality condition decomposition (OCD) method is employed to decompose and solve the converted NLP problem in a decentralized manner. Next, the dual decomposition method is used to optimize the plant part. Finally, the plant and control parts are connected by the gradients of Hamiltonian with respect to the plant variables. The proposed approach is applied to two examples. First, a numerical example is presented to illustrate the approach step-by-step. Then in the second example, a spring-mass-damper system is solved. For both examples, the solutions obtained by the proposed decentralized approach are compared against a centralized (all-in-one) approach.

Traditional robust optimization formulations can be considered to be “passive” in the sense that they can obtain optimized design and operational solutions for a system for all realizations of uncertainty. However, flexibility in the system’s operation can be used to devise formulations that obtain solutions that are optimum for all realizations of uncertainty while operational variables are used to mitigate or eliminate the effects of uncertainty. The objective of this paper is to extend existing formulations in single-objective robust optimization to multi-objective robust optimization with or without operational flexibility under discretized uncertainty. The formulations with operational flexibility are referred to as flexible optimization. The flexible optimization formulations and corresponding solutions are demonstrated and compared with those from robust and deterministic optimization formulations using numerical examples, and an engineering example with black-box objective and constraint functions.

Co-design refers to the process of integrating the optimization of the physical design as well as the controller for a system. In this paper, a new class of co-design problems with a multi-subsystem architecture is formulated and solved, which extends earlier works on models and solution approaches from single-system to multi-subsystem co-design. In this class, the design part in each subsystem has a strictly convex objective function with linear equality constraints. The control part of each subsystem belongs to a class of finite time-horizon Linear Quadratic Regulator (LQR) feedback control. A new multi-level decentralized model and method is proposed to obtain optimal or near-optimal solutions for this class of co-design problems. Details of the model and approach are demonstrated by a numerical as well as a more complex spring-mass-damper system example. Comparison of optimal results from both centralized and decentralized methods are presented and discussed.