Visualizing multi-dimensional pareto-optimal fronts with a 3D virtual reality system

In multiobjective optimization, there are several targets that are in conflict, and thus they all cannot reach their optimum simultaneously. Hence, the solutions of the problem form a set of compromised trade-off solutions (a Pareto-optimal front or Pareto-optimal solutions) from which the best solution for the particular problem can be chosen. However, finding that best compromise solution is not an easy task for the human mind. Pareto-optimal fronts are often visualized for this purpose because in this way a comparison between solutions according to their location on the Pareto-optimal front becomes somewhat easier. Visualizing a Pareto-optimal front is straightforward when there are only two targets (or objective functions), but visualizing a front for more than two objective functions becomes a difficult task. In this paper, we introduce a new and innovative method of using three-dimensional virtual reality (VR) facilities to present multi-dimensional Pareto-optimal fronts. Rotation, zooming and other navigation possibilities of VR facilities make easy to compare different trade-off solutions, and fewer solutions need to be explored in order to understand the interrelationships among conflicting objective functions. In addition, it can be used to highlight and characterize interesting features of specific Pareto-optimal solutions, such as whether a particular solution is close to a constraint boundary or whether a solution lies on a relatively steep trade-off region. Based on these additional visual aids for analyzing trade-off solutions, a preferred compromise solution may be easier to choose than by other means

Capso: A Multi-Objective Cultural Algorithm System To Predict Locations Of Ancient Sites

ABSTRACT CAPSO: A MULTI-OBJECTIVE CULTURAL ALGORITHM SYSTEM TO PREDICT LOCATIONS OF ANCIENT SITES by SAMUEL DUSTIN STANLEY August 2019 Advisor: Dr. Robert Reynolds Major: Computer Science Degree: Doctor of Philosophy The recent archaeological discovery by Dr. John O’Shea at University of Michigan of prehistoric caribou remains and Paleo-Indian structures underneath the Great Lakes has opened up an opportunity for Computer Scientists to develop dynamic systems modelling these ancient caribou routes and hunter-gatherer settlement systems as well as the prehistoric environments that they existed in. The Wayne State University Cultural Algorithm team has been interested assisting Dr. O’Shea’s archaeological team by predicting new structures in the Alpena-Amberley Ridge Region. To further this end, we developed a rule-based expert prediction system to work with our team’s dynamic model of the Paleolithic environment. In order to evolve the rules and thresholds within this expert system, we developed a Pareto-based multi-objective optimizer called CAPSO, which stands for Cultural Algorithm Particle Swarm Optimizer. CAPSO is fully parallelized and is able to work with modern multicore CPU architecture, which enables CAPSO to handle “big data” problems such as this one. The crux of our methodology is to set up a biobjective problem with the objectives being locations predicted by the expert system (minimize) vs. training set occupational structures within those predicted locations (maximize). The first of these quantities plays the role of “cost” while the second plays the role of “benefit”. Four separate such biobjective problems are created, one for each of the four relevant occupational structure types (hunting blinds, drive lines, caches, and logistical camps). For each of these problems, when CAPSO tunes the system’s rules and thresholds, it changes which locations are predicted and hence also which structures are flagged. By repeatedly tuning the rules and thresholds, CAPSO creates a Pareto Front of locations predicted vs. structures predicted for each of the four occupational structure types. Statistical analysis of these Pareto Fronts reveals that as the number of structures predicted (benefit) increases linearly, the number of locations predicted (cost) increases exponentially. This pattern is referred to in the dissertation as the Accelerating Cost Hypothesis (ACH). The ACH statistically holds for all four structure types, and is the result of imperfect information

Computational Tradespace Exploration, Analysis, and Decision-Making: A Proposed Framework for Organizational Self-Assessment

The ability to assess technical feasibility, project risk, technical readiness, and realistic performance expectations in early-phase conceptual design is a challenging mission-critical task for large procurement projects. At present, there is not a well-defined framework for evaluating current practices of organizations performing computational trade studies. One such organization is the US Army Ground Vehicle Systems Center (GVSC). When defining requirements and priorities for the next-generation autonomy-enabled ground vehicle system, GVSC is faced with the challenge of an increasingly complex programmatic tradespace due to emerging complexities of ground vehicle systems. This thesis aims to document and evaluate tradespace processes, methods, and tools within GVSC. A systematic review of the literature was conducted to investigate existing gaps, limitations, and potential growth opportunities related to tradespace activities reflecting the greater body of knowledge observed in the literature. Following this review, an interview-based study was developed through which a series of interviews with GVSC personnel was conducted and subsequently benchmarked against the baseline established in the literature. In addition to characterizing the current practices of tradespace exploration and analysis within GVSC, the analysis of the collected interview data revealed current capability gaps, areas of excellence, and potential avenues for improvement within GVSC. Through this thesis, other organizations can perform similar self-assessments to improve internal capabilities with respect to tradespace studies

Multiobjective optimization of classifiers by means of 3-D convex Hull based evolutionary algorithms

The receiver operating characteristic (ROC) and detection error tradeoff (DET) curves are frequently used in the machine learning community to analyze the performance of binary classifiers. Recently, the convex-hull-based multiobjective genetic programming algorithm was proposed and successfully applied to maximize the convex hull area for binary classification problems by minimizing false positive rate and maximizing true positive rate at the same time using indicator-based evolutionary algorithms. The area under the ROC curve was used for the performance assessment and to guide the search. Here we extend this research and propose two major advancements: Firstly we formulate the algorithm in detection error tradeoff space, minimizing false positives and false negatives, with the advantage that misclassification cost tradeoff can be assessed directly. Secondly, we add complexity as an objective function, which gives rise to a 3D objective space (as opposed to a 2D previous ROC space). A domain specific performance indicator for 3D Pareto front approximations, the volume above DET surface, is introduced, and used to guide the indicator -based evolutionary algorithm to find optimal approximation sets. We assess the performance of the new algorithm on designed theoretical problems with different geometries of Pareto fronts and DET surfaces, and two application-oriented benchmarks: (1) Designing spam filters with low numbers of false rejects, false accepts, and low computational cost using rule ensembles, and (2) finding sparse neural networks for binary classification of test data from the UCI machine learning benchmark. The results show a high performance of the new algorithm as compared to conventional methods for multicriteria optimization.info:eu-repo/semantics/submittedVersio

The Component Packaging Problem: A Vehicle for the Development of Multidisciplinary Design and Analysis Methodologies

This report summarizes academic research which has resulted in an increased appreciation for multidisciplinary efforts among our students, colleagues and administrators. It has also generated a number of research ideas that emerged from the interaction between disciplines. Overall, 17 undergraduate students and 16 graduate students benefited directly from the NASA grant: an additional 11 graduate students were impacted and participated without financial support from NASA. The work resulted in 16 theses (with 7 to be completed in the near future), 67 papers or reports mostly published in 8 journals and/or presented at various conferences (a total of 83 papers, presentations and reports published based on NASA inspired or supported work). In addition, the faculty and students presented related work at many meetings, and continuing work has been proposed to NSF, the Army, Industry and other state and federal institutions to continue efforts in the direction of multidisciplinary and recently multi-objective design and analysis. The specific problem addressed is component packing which was solved as a multi-objective problem using iterative genetic algorithms and decomposition. Further testing and refinement of the methodology developed is presently under investigation. Teaming issues research and classes resulted in the publication of a web site, (http://design.eng.clemson.edu/psych4991) which provides pointers and techniques to interested parties. Specific advantages of using iterative genetic algorithms, hurdles faced and resolved, and institutional difficulties associated with multi-discipline teaming are described in some detail