1,391 research outputs found
Challenges of continuous global optimization in molecular structure prediction
The molecular geometry, the three dimensional arrangement of atoms in space, is a major factor determining the properties and reactivity of molecules, biomolecules and macromolecules. Computation of stable molecular conformations can be done by locating minima on the potential energy surface (PES). This is a very challenging global optimization problem because of extremely large numbers of shallow local minima and complicated landscape of PES. This paper illustrates the mathematical and computational challenges on one important instance of the problem, computation of molecular geometry of oligopeptides, and proposes the use of the Extended Cutting Angle Method (ECAM) to solve this problem.ECAM is a deterministic global optimization technique, which computes tight lower bounds on the values of the objective function and fathoms those part of the domain where the global minimum cannot reside. As with any domain partitioning scheme, its challenge is an extremely large partition of the domain required for accurate lower bounds. We address this challenge by providing an efficient combinatorial algorithm for calculating the lower bounds, and by combining ECAM with a local optimization method, while preserving the deterministic character of ECAM.<br /
Barrier Frank-Wolfe for Marginal Inference
We introduce a globally-convergent algorithm for optimizing the
tree-reweighted (TRW) variational objective over the marginal polytope. The
algorithm is based on the conditional gradient method (Frank-Wolfe) and moves
pseudomarginals within the marginal polytope through repeated maximum a
posteriori (MAP) calls. This modular structure enables us to leverage black-box
MAP solvers (both exact and approximate) for variational inference, and obtains
more accurate results than tree-reweighted algorithms that optimize over the
local consistency relaxation. Theoretically, we bound the sub-optimality for
the proposed algorithm despite the TRW objective having unbounded gradients at
the boundary of the marginal polytope. Empirically, we demonstrate the
increased quality of results found by tightening the relaxation over the
marginal polytope as well as the spanning tree polytope on synthetic and
real-world instances.Comment: 25 pages, 12 figures, To appear in Neural Information Processing
Systems (NIPS) 2015, Corrected reference and cleaned up bibliograph
Extended cutting angle method of global optimization
Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach.<br /
On parallel Branch and Bound frameworks for Global Optimization
Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity
A GPU-accelerated Branch-and-Bound Algorithm for the Flow-Shop Scheduling Problem
Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration
methods for solving to optimality combinatorial optimization problems. In this
paper, we investigate the use of GPU computing as a major complementary way to
speed up those methods. The focus is put on the bounding mechanism of B&B
algorithms, which is the most time consuming part of their exploration process.
We propose a parallel B&B algorithm based on a GPU-accelerated bounding model.
The proposed approach concentrate on optimizing data access management to
further improve the performance of the bounding mechanism which uses large and
intermediate data sets that do not completely fit in GPU memory. Extensive
experiments of the contribution have been carried out on well known FSP
benchmarks using an Nvidia Tesla C2050 GPU card. We compared the obtained
performances to a single and a multithreaded CPU-based execution. Accelerations
up to x100 are achieved for large problem instances
Bounds on the Objective Value of Feasible Roundings
For mixed-integer linear and nonlinear optimization problems we study the objective value of feasible points which are constructed by the feasible rounding approaches from Neumann et al. (Comput. Optim. Appl. 72, 309–337, 2019; J. Optim. Theory Appl. 184, 433–465, 2020). We provide a-priori bounds on the deviation of such objective values from the optimal value and apply them to explain and quantify the positive effect of finer grids of integer feasible points on the performance of the feasible rounding approaches. Computational results for large scale knapsack problems illustrate our theoretical findings
The Hybridization of Branch and Bound with Metaheuristics for Nonconvex Multiobjective Optimization
A hybrid framework combining the branch and bound method with multiobjective
evolutionary algorithms is proposed for nonconvex multiobjective optimization.
The hybridization exploits the complementary character of the two optimization
strategies. A multiobjective evolutionary algorithm is intended for inducing
tight lower and upper bounds during the branch and bound procedure. Tight
bounds such as the ones derived in this way can reduce the number of
subproblems that have to be solved. The branch and bound method guarantees the
global convergence of the framework and improves the search capability of the
multiobjective evolutionary algorithm. An implementation of the hybrid
framework considering NSGA-II and MOEA/D-DE as multiobjective evolutionary
algorithms is presented. Numerical experiments verify the hybrid algorithms
benefit from synergy of the branch and bound method and multiobjective
evolutionary algorithms
- …