Search Techniques for Multi-Objective Optimization of Mixed-Variable Systems Having Stochastic Responses

A method is proposed for solving stochastic multi-objective optimization problems. Such problems are typically encountered when one desires to optimize systems with multiple, often competing, objectives that do not have a closed form representation and must be estimated via simulation. A two-stage method is proposed that combines generalized pattern search/ranking and selection (GPS/R&S) and and Mesh Adaptive Direct Search (MADS) developed for single-objective stochastic problems with three multi-objective methods: interactive techniques for the specification of aspiration/reservation levels, scalarization functions, and multi-objective ranking and selection. This combination is devised specifically so as to keep the desirable convergence properties of GPS/R&S and MADS while extending application to the multi-objective case

On the Use of Surrogate Functions for Mixed Variable Optimization of Simulated Systems

This research considers the efficient numerical solution of linearly constrained mixed variable programming (MVP) problems, in which the objective function is a black-box stochastic simulation, function evaluations may be computationally expensive, and derivative information is typically not available. MVP problems are those with a mixture of continuous, integer, and categorical variables, the latter of which may take on values only from a predefined list and may even be non-numeric. Mixed Variable Generalized Pattern Search with Ranking and Selection (MGPS-RS) is the only existing, provably convergent algorithm that can be applied to this class of problems. Present in this algorithm is an optional framework for constructing and managing less expensive surrogate functions as a means to reduce the number of true function evaluations that are required to find approximate solutions. In this research, the NOMADm software package, an implementation of pattern search for deterministic MVP problems, is modified to incorporate a sequential selection with memory (SSM) ranking and selection procedure for handling stochastic problems. In doing so, the underlying algorithm is modified to make the application of surrogates more efficient. A second class of surrogates based on the Nadaraya-Watson kernel regression estimator is also added to the software. Preliminary computational testing of the modified software is performed to characterize the relative efficiency of selected surrogate functions for mixed variable optimization in simulated systems

Comparison of Direct Multiobjective Optimization Methods for the Design of Electric Vehicles

"System design oriented methodologies" are discussed in this paper through the comparison of multiobjective optimization methods applied to heterogeneous devices in electrical engineering. Avoiding criteria function derivatives, direct optimization algorithms are used. In particular, deterministic geometric methods such as the Hooke & Jeeves heuristic approach are compared with stochastic evolutionary algorithms (Pareto genetic algorithms). Different issues relative to convergence rapidity and robustness on mixed (continuous/discrete), constrained and multiobjective problems are discussed. A typical electrical engineering heterogeneous and multidisciplinary system is considered as a case study: the motor drive of an electric vehicle. Some results emphasize the capacity of each approach to facilitate system analysis and particularly to display couplings between optimization parameters, constraints, objectives and the driving mission

Pattern Search Ranking and Selection Algorithms for Mixed-Variable Optimization of Stochastic Systems

A new class of algorithms is introduced and analyzed for bound and linearly constrained optimization problems with stochastic objective functions and a mixture of design variable types. The generalized pattern search (GPS) class of algorithms is extended to a new problem setting in which objective function evaluations require sampling from a model of a stochastic system. The approach combines GPS with ranking and selection (R&S) statistical procedures to select new iterates. The derivative-free algorithms require only black-box simulation responses and are applicable over domains with mixed variables (continuous, discrete numeric, and discrete categorical) to include bound and linear constraints on the continuous variables. A convergence analysis for the general class of algorithms establishes almost sure convergence of an iteration subsequence to stationary points appropriately defined in the mixed-variable domain. Additionally, specific algorithm instances are implemented that provide computational enhancements to the basic algorithm. Implementation alternatives include the use modern R&S procedures designed to provide efficient sampling strategies and the use of surrogate functions that augment the search by approximating the unknown objective function with nonparametric response surfaces. In a computational evaluation, six variants of the algorithm are tested along with four competing methods on 26 standardized test problems. The numerical results validate the use of advanced implementations as a means to improve algorithm performance

Improved branch and bound method for control structure screening

The main aim of this paper is to present an improved algorithm of “Branch and Bound” method for control structure screening. The new algorithm uses a best- first search approach, which is more efficient than other algorithms based on depth-first search approaches. Detailed explanation of the algorithms is provided in this paper along with a case study on Tennessee–Eastman process to justify the theory of branch and bound method. The case study uses the Hankel singular value to screen control structure for stabilization. The branch and bound method provides a global ranking to all possible input and output combinations. Based on this ranking an efficient control structure with least complexity for stabilizing control is detected which leads to a decentralized proportional cont

Optimization of Stochastic Discrete Event Simulation Models

Many systems in logistics can be adequately modeled using stochastic discrete event simulation models. Often these models are used to find a good or optimal configuration of the system. This implies that optimization algorithms have to be coupled with the models. Optimization of stochastic simulation models is a challenging research topic since the approaches should be efficient, reliable and should provide some guarantee to find at least in the limiting case with a runtime going to infinite the optimal solution with a probability converging to 1. The talk gives an overview on the state of the art in simulation optimization. It shows that hybrid algorithms combining global and local optimization methods are currently the best class of optimization approaches in the area and it outlines the need for the development of software tools including available algorithms