#### DMCA

## RESEARCH ARTICLE Constraint Consensus Concentration for Identifying Disjoint Feasible Regions in Nonlinear Programs

### Citations

906 |
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code
- McKay, WJ, et al.
- 1979
(Show Context)
Citation Context ... defined by the variable bounds. This ensures that the points are distributed throughout the search space, and Latin Hypercube sampling is known to provide better coverage than simple random sampling =-=[15]-=-. Further, the number of samples required for Latin Hypercube sampling is independent of the number of dimensions of the model. This is important since our methods are intended for large-scale problem... |

616 |
Numerical Optimization of Computer Models
- SCHWEFEL
- 1981
(Show Context)
Citation Context ...he best solution value found by any of the local solver launches. 5. Illustrated Experiments This section illustrates the method using models that have constraints based on variations of the Schwefel =-=[18]-=- and Rastrigin [17, 24] functions. The Latin hypercube sampling, CC concentration, and clustering steps from Section 4 are performed on each model with results as shown in Fig. 4 and Fig. 5. To focus ... |

375 | Benchmarking optimization software with performance profiles
- Dolan, Moré
(Show Context)
Citation Context ...telligent exploration of the variable space prior to launching the local solver. The results are compared in terms of feasibility, optimality, and time, and are presented as performance profiles (see =-=[6]-=-). The success rate for the performance profiles in Fig. 6 and Fig. 7 is the percentage of models for which a particular algorithm found the best feasible solution, i.e., the feasible solution vector ... |

293 | On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
- Wächter, Biegler
- 2004
(Show Context)
Citation Context ...e interpreted using A Modeling Language for Mathematical Programming (AMPL) [8]. The local solver used in our implementation is Ipopt, an open source interiorpoint solver for large-scale optimization =-=[26]-=-. Parameter settings for Ipopt were: • honor original bounds = yes. Project final point back inside original bounds. • bound relax factor = 0. Set to 0 to disable bounds relaxation. • max iter = 99999... |

287 | Global Optimization
- Torn, Zilinskas
- 1989
(Show Context)
Citation Context ...lue found by any of the local solver launches. 5. Illustrated Experiments This section illustrates the method using models that have constraints based on variations of the Schwefel [18] and Rastrigin =-=[17, 24]-=- functions. The Latin hypercube sampling, CC concentration, and clustering steps from Section 4 are performed on each model with results as shown in Fig. 4 and Fig. 5. To focus on the performance of t... |

219 |
The parallel genetic algorithm as function opti-mizer,”
- Muhlenbein, Schomish, et al.
- 1991
(Show Context)
Citation Context ...lue found by any of the local solver launches. 5. Illustrated Experiments This section illustrates the method using models that have constraints based on variations of the Schwefel [18] and Rastrigin =-=[17, 24]-=- functions. The Latin hypercube sampling, CC concentration, and clustering steps from Section 4 are performed on each model with results as shown in Fig. 4 and Fig. 5. To focus on the performance of t... |

216 | Near neighbor search in large metric spaces.
- Brin
- 1995
(Show Context)
Citation Context ...i. We develop a new procedure for doing so automatically that depends on two parameters. We first reduce the high-dimensional clustering data to a simple distribution of distances between data points =-=[1]-=-. We exploit the fact that the frequency distribution of the inter-point distances between the concentrated CC end points tends to have peaks that correspond to the distances within and between cluste... |

178 |
SLINK: An optimally efficient algorithm for the single-link cluster method,”
- Sibson
- 1973
(Show Context)
Citation Context ...e regions. We use the Basic CC algorithm with augmented feasibility vectors, though other versions of CC could be substituted. 4.3. Choosing the Critical Distance The single-linkage clustering method =-=[21]-=- that we use depends heavily on the accurate identification of an appropriate critical distance. Points that are closer together than the critical distance are merged into the same cluster. Any point ... |

110 | KNITRO: An integrated package for nonlinear optimization
- Byrd, Nocedal, et al.
- 2006
(Show Context)
Citation Context ...y subdivided into zones with associated vote totals. Promising experiments in finding feasible regions in difficult NLPs were carried out using this method in conjunction with the Knitro local solver =-=[2]-=-. A drawback of the voting method used is that it tends to make the feasible regions appear larger than they actually are. For the purposes of this paper, the major drawback is that the method is orie... |

61 | An Interior Point Algorithm for Large-Scale Nonlinear Optimization with Applications in Process Engineering
- Wächter
- 2002
(Show Context)
Citation Context ... intention is not to compare the local solvers, but the multistart methods they use for global optimization (comparisons of Knitro and Ipopt as local solvers are found at [16] and in Section 5.1.3 of =-=[25]-=-). Initial results data (not included) indicate that Knitro outperforms MS over Problem Set IIB. Both algorithms found feasible solutions to 35 (59%) of theOptimization Methods and Software 21 Figure... |

30 | Benchmarking global optimization and constraint satisfaction nodes
- Shcherbina, Neumaier, et al.
- 2004
(Show Context)
Citation Context ...st feasible region. 6. Experimental Setup 6.1. Test Set The models used in the experiments are taken from libraries 1 and 2 of the COntinuous CONstraints - Updating the Technology (COCONUT) benchmark =-=[20]-=-. We have divided them into two sets based on the number of nonlinear constraints: Problem Set I contains the 148 models with 10 to 1000 nonlinear constraints, and Problem Set II contains the 75 model... |

27 |
A Global Minimization Method: The Multi-dimensional case
- Jansson, Knüppel
- 1992
(Show Context)
Citation Context ...n (regions in which a CC run will lead to the same feasible region) as shown in Fig. 1. Consider the Branin1 model illustrated in Fig. 1, in which g1(x) is a variant of the well-known Branin function =-=[11]-=- used as a constraint: find x = {x1, x2} ( s.t. g1(x) = x2 − 5.1x2 1 4π 2 (7a) ) 2 ( 5x1 + − 6 + 10 − π 10 ) cos(x1) + 9 ≤ 0 (7b) 8π g2(x) = x2 + x1 − 12 ≤ 0 1.2 (7c) −5 ≤ x1 ≤ 10 (7d) 0 ≤ x2 ≤ 15 (7e... |

17 |
Constraint handling in genetic algorithms using a gradientbased repair method
- Chootinan, Chen
(Show Context)
Citation Context ...region. 2.2. Constraint Consensus Methods for Constraint Satisfaction A variety of iterative procedures move points towards locations where they satisfy the constraints. Variations on Newton’s method =-=[5, 7, 9, 12]-=- are popular, but require the calculation of an inverse matrix. For example, the method of Chootinan and Chen [5] requires the calculation of a pseudo-inverse matrix at every iteration. The inverse ca... |

16 |
Recent benchmarks of optimization software
- Mittelmann
- 2007
(Show Context)
Citation Context ...r comparison can be made. Our intention is not to compare the local solvers, but the multistart methods they use for global optimization (comparisons of Knitro and Ipopt as local solvers are found at =-=[16]-=- and in Section 5.1.3 of [25]). Initial results data (not included) indicate that Knitro outperforms MS over Problem Set IIB. Both algorithms found feasible solutions to 35 (59%) of theOptimization M... |

11 | The constraint consensus method for finding approximately feasible points in nonlinear programs,”
- Chinneck
- 2004
(Show Context)
Citation Context ...Consensus (CC) algorithm rapidly and inexpensively moves an infeasible initial point that may be very far away from feasibility to a final point that is close to feasibility in large nonlinear models =-=[3]-=-. Running the CC algorithm prior to launching an NLP solver greatly reduces the total solution time in most cases, and improves the probability that a nonlinear solver will find a feasible point [10].... |

10 | Globsol: History, composition, and advice on use
- Kearfott
- 2003
(Show Context)
Citation Context ...region. 2.2. Constraint Consensus Methods for Constraint Satisfaction A variety of iterative procedures move points towards locations where they satisfy the constraints. Variations on Newton’s method =-=[5, 7, 9, 12]-=- are popular, but require the calculation of an inverse matrix. For example, the method of Chootinan and Chen [5] requires the calculation of a pseudo-inverse matrix at every iteration. The inverse ca... |

4 |
Feasibility and Infeasibility in Optimization: Algorithms and
- Chinneck
- 2007
(Show Context)
Citation Context ...lly end if x ← x + t Reset x to respect any violated variable bounds k ← k + 1 end while the local solver can be launched exactly once near each one, thereby reducing the number of redundant launches =-=[4]-=-. Two of the main concepts are concentration and acceptance/rejection. Multistart-NLP (MSNLP) is a heuristic multistart algorithm composed of two phases [13]. The first phase generates a set of random... |

2 |
DMM, Kernighan BW, AMPL: A Modeling Language for
- Fourer, Gay
- 2002
(Show Context)
Citation Context ...d was gcc 4.1.2. The C++ source code is available online at https://github.com/LSmith4/ LaunchPointGenerator. All models were interpreted using A Modeling Language for Mathematical Programming (AMPL) =-=[8]-=-. The local solver used in our implementation is Ipopt, an open source interiorpoint solver for large-scale optimization [26]. Parameter settings for Ipopt were: • honor original bounds = yes. Project... |

2 |
A Starting-Point Strategy for Nonlinear Interior Methods
- Gertz, Nocedal, et al.
(Show Context)
Citation Context ...region. 2.2. Constraint Consensus Methods for Constraint Satisfaction A variety of iterative procedures move points towards locations where they satisfy the constraints. Variations on Newton’s method =-=[5, 7, 9, 12]-=- are popular, but require the calculation of an inverse matrix. For example, the method of Chootinan and Chen [5] requires the calculation of a pseudo-inverse matrix at every iteration. The inverse ca... |

2 |
Multistart Algorithms for Seeking Feasibility
- Lasdon, Plummer
- 2008
(Show Context)
Citation Context ...y reducing the number of redundant launches [4]. Two of the main concepts are concentration and acceptance/rejection. Multistart-NLP (MSNLP) is a heuristic multistart algorithm composed of two phases =-=[13]-=-. The first phase generates a set of random candidate points, which are stored along with their calculated measure of merit. The second phase applies a distance filter and a merit filter that reject p... |

2 |
Multistart Constraint Consensus for Seeking Feasibility in Nonlinear Programs, MASc Thesis
- MacLeod
- 2006
(Show Context)
Citation Context ... the critical distance (Eqn. 10 in [19]). This approach may not be dependable since problems and their respective characteristics vary greatly, regardless of the number of variables involved. MacLeod =-=[14]-=- was the first to use Constraint Consensus to explore the variable space in an effort to identify good launch points for a local solver. His Multistart Constraint Consensus method uses the information... |

2 |
Extensions of a Multistart Clustering Algorithm for Constrained Global Optimization Problems
- Sendin, Banga, et al.
- 2009
(Show Context)
Citation Context ... as the global optimum point. An issue is that the hypersphere approximations of basins of attraction are not always accurate, as can be seen in Fig. 1. GLOBALm is another two-phase multistart method =-=[19]-=-. It takes a uniform sample of points from the variable space in the first phase. These candidate points areOptimization Methods and Software 5 (a) 50 points. (b) 1500 points. Figure 1. Basin visuali... |

2 |
Improved Placement of Local Solver Launch Points for Large-scale Global Optimization
- Smith
- 2011
(Show Context)
Citation Context ...ble improvements in both the effectiveness and efficiency of multistart methods for global optimization. A variety of additional experiments further supporting these conclusions are reported by Smith =-=[23]-=-. 8. Conclusions and Future Research This paper presents a method for efficiently and effectively computing local solver launch points that are typically near all of the feasible regions in a constrai... |

1 |
Methods for Finding Feasible Points in
- Elwakeil, Arora
- 1995
(Show Context)
Citation Context |

1 |
Improving Solver Success in Reaching Feasibility for Sets of Nonlinear Constraints
- Ibrahim, Chinneck
- 2008
(Show Context)
Citation Context ...s [3]. Running the CC algorithm prior to launching an NLP solver greatly reduces the total solution time in most cases, and improves the probability that a nonlinear solver will find a feasible point =-=[10]-=-. CC calculates a feasibility vector for each constraint that is violated at the current point; this vector estimates the smallest update needed to satisfy the ∗ Corresponding author. Email: chinneck@... |

1 |
Augmented and Quadratic Feasibility Vectors for Constraint Consensus
- Smith, Chinneck, et al.
- 2010
(Show Context)
Citation Context ...iable in the i th constraint. In the algorithms developed here, CC is used for concentrating points near regions of attraction. We use the Basic consensus [3] and the new Augmented feasibility vector =-=[22]-=- variants of CC in this paper. The augmented version is a predictorcorrector style algorithm that adjusts the length of the feasibility vectors. 2.3. Multistart Heuristics for Global Optimization The ... |