Data Driven Surrogate Based Optimization in the Problem Solving Environment WBCSim

Large scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming due to the complexity of the underlying simulation codes. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations, that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate based optimization algorithm that uses a trust region based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from two packages—SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques—full factorial (FF), Latin hypercube sampling (LHS), and central composite design (CCD)—are used to train the surrogates. The results are compared with the optimization results obtained by directly coupling an optimizer with the simulation code. The biggest concern in using the SAO framework based on statistical sampling is the generation of the required database. As the number of design variables grows, the computational cost of generating the required database grows rapidly. A data driven approach is proposed to tackle this situation, where the trick is to run the expensive simulation if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the proposed methodology dramatically reduces the total number of calls to the expensive simulation runs during the optimization process

A test problem for visual investigation of high-dimensional multi-objective search

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions

An Extensible Benchmarking Infrastructure for Motion Planning Algorithms

Sampling-based planning algorithms are the most common probabilistically complete algorithms and are widely used on many robot platforms. Within this class of algorithms, many variants have been proposed over the last 20 years, yet there is still no characterization of which algorithms are well-suited for which classes of problems. This has motivated us to develop a benchmarking infrastructure for motion planning algorithms. It consists of three main components. First, we have created an extensive benchmarking software framework that is included with the Open Motion Planning Library (OMPL), a C++ library that contains implementations of many sampling-based algorithms. Second, we have defined extensible formats for storing benchmark results. The formats are fairly straightforward so that other planning libraries could easily produce compatible output. Finally, we have created an interactive, versatile visualization tool for compact presentation of collected benchmark data. The tool and underlying database facilitate the analysis of performance across benchmark problems and planners.Comment: Submitted to IEEE Robotics & Automation Magazine (Special Issue on Replicable and Measurable Robotics Research), 201

Open source environment to define constraints in route planning for GIS-T

Route planning for transportation systems is strongly related to shortest path algorithms, an optimization problem extensively studied in the literature. To find the shortest path in a network one usually assigns weights to each branch to represent the difficulty of taking such branch. The weights construct a linear preference function ordering the variety of alternatives from the most to the least attractive.Postprint (published version