scholarly journals Sampling Scenario Set Partition Dual Bounds for Multistage Stochastic Programs

2020 ◽  
Vol 32 (1) ◽  
pp. 145-163 ◽  
Author(s):  
Ilke Bakir ◽  
Natashia Boland ◽  
Brian Dandurand ◽  
Alan Erera
Keyword(s):  
Optimization Problem ◽  
Computational Effort ◽  
Scenario Tree ◽  
Benchmark Problems ◽  
Set Partition ◽  
Random Parameters ◽  
Stochastic Programs ◽  
Require Solution ◽  
Multistage Stochastic Programs ◽  
Dual Bounds

We consider multistage stochastic programming problems in which the random parameters have finite support, leading to optimization over a finite scenario set. There has been recent interest in dual bounds for such problems, of two types. One, known as expected group subproblem objective (EGSO) bounds, require solution of a group subproblem, which optimizes over a subset of the scenarios, for all subsets of the scenario set that have a given cardinality. Increasing the subset cardinality in the group subproblem improves bound quality, (EGSO bounds form a hierarchy), but the number of group subproblems required to compute the bound increases very rapidly. Another is based on partitions of the scenario set into subsets. Combining the values of the group subproblems for all subsets in a partition yields a partition bound. In this paper, we consider partitions into subsets of (nearly) equal cardinality. We show that the expected value of the partition bound over all such partitions also forms a hierarchy. To make use of these bounds in practice, we propose random sampling of partitions and suggest two enhancements to the approach: sampling partitions that align with the multistage scenario tree structure and use of an auxiliary optimization problem to discover new best bounds based on the values of group subproblems already computed. We establish the effectiveness of these ideas with computational experiments on benchmark problems. Finally, we give a heuristic to save computational effort by ceasing computation of a partition partway through if it appears unpromising.

The Reduced Tolerance Allocation Problem

2016 ◽  
Author(s):  
David Sh. L. Shoukr ◽  
Mohamed H. Gadallah ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problem ◽  
Computational Effort ◽  
Allocation Problem ◽  
Tolerance Allocation ◽  
Benchmark Problems ◽  
Manufacturing Processes ◽  
Manufacturing Cost ◽  
Functional Requirements ◽  
Different Dimensions

Tolerance allocation is a necessary and important step in product design and development. It involves the assignment of tolerances to different dimensions such that the manufacturing cost is minimum, while maintaining the tolerance stack-up conditions satisfied. Considering the design functional requirements, manufacturing processes, and dimensional and/or geometrical tolerances, the tolerance allocation problem requires intensive computational effort and time. An approach is proposed to reduce the size of the tolerance allocation problem using design of experiments (DOE). Instead of solving the optimization problem for all dimensional tolerances, it is solved for the significant dimensions only and the insignificant dimensional tolerances are set at lower control levels. A Genetic Algorithm is developed and employed to optimize the synthesis problem. A set of benchmark problems are used to test the proposed approach, and results are compared with some standard problems in literature.

Scenario tree modeling for multistage stochastic programs

2007 ◽  
Vol 118 (2) ◽  
pp. 371-406 ◽  
Author(s):  
Holger Heitsch ◽  
Werner Römisch
Keyword(s):  
Scenario Tree ◽  
Stochastic Programs ◽  
Tree Modeling ◽  
Multistage Stochastic Programs

scholarly journals Scenario tree reduction for multistage stochastic programs

2008 ◽  
Vol 6 (2) ◽  
pp. 117-133 ◽  
Author(s):  
Holger Heitsch ◽  
Werner Römisch
Keyword(s):  
Scenario Tree ◽  
Stochastic Programs ◽  
Multistage Stochastic Programs

A Scalable Bounding Method for Multistage Stochastic Programs

2017 ◽  
Vol 27 (3) ◽  
pp. 1772-1800 ◽  
Author(s):  
Burhaneddi̇n Sandikçi ◽  
Osman Y. Özaltin
Keyword(s):  
Stochastic Programs ◽  
Multistage Stochastic Programs

scholarly journals Uncertainty-Aware Search Framework for Multi-Objective Bayesian Optimization

2020 ◽  
Vol 34 (06) ◽  
pp. 10044-10052 ◽  
Author(s):  
Syrine Belakaria ◽  
Aryan Deshwal ◽  
Nitthilan Kannappan Jayakodi ◽  
Janardhan Rao Doppa
Keyword(s):  
Optimization Problem ◽  
State Of The Art ◽  
Selection Method ◽  
Bayesian Optimization ◽  
Benchmark Problems ◽  
Multi Objective ◽  
Blackbox Optimization ◽  
Expensive Function ◽  
Area Overhead ◽  
Measure Of Uncertainty

We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions while minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel uncertainty-aware search framework referred to as USeMO to efficiently select the sequence of inputs for evaluation to solve this problem. The selection method of USeMO consists of solving a cheap MO optimization problem via surrogate models of the true functions to identify the most promising candidates and picking the best candidate based on a measure of uncertainty. We also provide theoretical analysis to characterize the efficacy of our approach. Our experiments on several synthetic and six diverse real-world benchmark problems show that USeMO consistently outperforms the state-of-the-art algorithms.

Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
W. Hu ◽  
M. Li ◽  
S. Azarm ◽  
A. Almansoori
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Effort ◽  
Interval Uncertainty ◽  
Test Results ◽  
Robust Solution ◽  
Multi Objective ◽  
Function Calls ◽  
Level Problem ◽  
Upper Level

Many engineering optimization problems are multi-objective, constrained and have uncertainty in their inputs. For such problems it is desirable to obtain solutions that are multi-objectively optimum and robust. A robust solution is one that as a result of input uncertainty has variations in its objective and constraint functions which are within an acceptable range. This paper presents a new approximation-assisted MORO (AA-MORO) technique with interval uncertainty. The technique is a significant improvement, in terms of computational effort, over previously reported MORO techniques. AA-MORO includes an upper-level problem that solves a multi-objective optimization problem whose feasible domain is iteratively restricted by constraint cuts determined by a lower-level optimization problem. AA-MORO also includes an online approximation wherein optimal solutions from the upper- and lower-level optimization problems are used to iteratively improve an approximation to the objective and constraint functions. Several examples are used to test the proposed technique. The test results show that the proposed AA-MORO reasonably approximates solutions obtained from previous MORO approaches while its computational effort, in terms of the number of function calls, is significantly reduced compared to the previous approaches.

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