Quantifying the Shape of Pareto Fronts During Multi-Objective Trade Space Exploration

Recent advances in simulation and computation capabilities have enabled designers to model increasingly complex engineering problems, taking into account many dimensions, or objectives, in the problem formulation. Increasing the dimensionality often results in a large trade space, where decision-makers (DM) must identify and negotiate conflicting objectives to select the best designs. Trade space exploration often involves the projection of nondominated solutions, that is, the Pareto front, onto two-objective trade spaces to help identify and negotiate tradeoffs between conflicting objectives. However, as the number of objectives increases, an exhaustive exploration of all of the two-dimensional (2D) Pareto fronts can be inefficient due to a combinatorial increase in objective pairs. Recently, an index was introduced to quantify the shape of a Pareto front without having to visualize the solution set. In this paper, a formal derivation of the Pareto Shape Index is presented and used to support multi-objective trade space exploration. Two approaches for trade space exploration are presented and their advantages are discussed, specifically: (1) using the Pareto shape index for weighting objectives and (2) using the Pareto shape index to rank objective pairs for visualization. By applying the two approaches to two multi-objective problems, the efficiency of using the Pareto shape index for weighting objectives to identify solutions is demonstrated. We also show that using the index to rank objective pairs provides DM with the flexibility to form preferences throughout the process without closely investigating all objective pairs. The limitations and future work are also discussed.

Exploring the science trade space with the JPL Innovation Foundry A-Team

The Jet Propulsion Laboratory Innovation Foundry has established a new approach for exploring, developing, and evaluating early concepts with a group called the Architecture Team. The Architecture Team combines innovative collaborative methods and facilitated sessions with subject matter experts and analysis tools to help mature mission concepts. Science, implementation, and programmatic elements are all considered during an A-Team study. In these studies, Concept Maturity Levels are used to group methods. These levels include idea generation and capture (Concept Maturity Level 1), initial feasibility assessment (Concept Maturity Level 2), and trade space exploration (Concept Maturity Level 3). Methods used for exploring the science objectives, feasibility, and scope will be described including the use of a new technique for understanding the most compelling science, called a Science Return Diagram. In the process of developing the Science Return Diagram, gradients in the science trade space are uncovered along with their implications for implementation and mission architecture. Special attention is paid toward developing complete investigations, establishing a series of logical claims that lead to the natural selection of a measurement approach. Over 20 science-focused A-Team studies have used these techniques to help science teams refine their mission objectives, make implementation decisions, and reveal the mission concept’s most compelling science. This article will describe the A-Team process for exploring the mission concept’s science trade space and the Science Return Diagram technique.

Trade Space Exploration of a Magnetically Actuated Miura-Ori Structure

Origami folding patterns are finding use in novel applications where actual device response depends on current, possibly intermediate, shapes on the path toward the final target shape. This works investigates one origami pattern, developing metrics for performance that incorporate traditional shape approximation and actuator efficiency, while adding proxy measures of adherence to the target folding path. Magnetically actuated Miura-Ori structures were develop using an initially heuristic strategy involving experiment, observation, and computation before being studied using trade space optimization/visualization. Constructed from PDMS substrates, notched to promote the crease pattern, and neodymium magnets, four initial configurations were chosen based on heuristic arguments that (1) maximized the amount of magnetic torque applied to the creases and (2) reduced the number of magnets needed to affect all creases in the pattern. Experiments were conducted, and calculations performed, on prototypes from each configuration to determine their degree of closure for a fixed maximum field strength, their ability to follow the ideal Miura-Ori folding pattern, and the amount of work theoretically performed by each magnet on each crease. Each configuration was further optimized theoretically using the Army Trade Space Visualization (ATSV) software. A final prototype was constructed following the weighted sum scoring of the four now optimized configurations. Somewhat surprisingly, trade space optimization showed that the configuration with the highest number of actuators was theoretically the least effective per magnet at delivering torque to each crease. Unsurprisingly, optimization was successful at increasing the amount of work theoretically apportioned to each crease. Overall, though the winning configuration experimentally outperformed its initial, non-optimal counterparts, results showed that the choice of optimum configuration was heavily dependent on the weighting factors within the objective function. These results highlight the ability of the Miura-Ori to be actuated with external magnetic stimuli, the effectiveness of a hybrid heuristic - trade space design approach that focuses on the actuation mechanism, and the need to address path-dependent metrics in assessing performance in origami folding structures.