A one-step worst-case optimal algorithm for bi-objective univariate optimization

2013 ◽  
Vol 8 (7) ◽  
pp. 1945-1960 ◽  
Author(s):  
Antanas Z̆ilinskas
Keyword(s):  
Optimal Algorithm ◽  
Worst Case ◽  
One Step ◽  
Univariate Optimization

scholarly journals Parallel One-Step Control of Parametrised Boolean Networks

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 560 ◽  
Author(s):  
Luboš Brim ◽  
Samuel Pastva ◽  
David Šafránek ◽  
Eva Šmijáková
Keyword(s):  
Control Problem ◽  
Boolean Networks ◽  
Actual State ◽  
Worst Case ◽  
Symbolic Data ◽  
One Step ◽  
The One ◽  
Step Control ◽  
Symbolic Algorithm ◽  
Naive Approach

Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as this model allows leaving some update functions unspecified. In our work, we attack the control problem for ParBNs with asynchronous semantics. While there is an extensive work on controlling BNs without parameters, the problem of control for ParBNs has not been in fact addressed yet. The goal of control is to ensure the stabilisation of a system in a given state using as few interventions as possible. There are many ways to control BN dynamics. Here, we consider the one-step approach in which the system is instantaneously perturbed out of its actual state. A naïve approach to handle control of ParBNs is using parameter scan and solve the control problem for each parameter valuation separately using known techniques for non-parametrised BNs. This approach is however highly inefficient as the parameter space of ParBNs grows doubly exponentially in the worst case. We propose a novel semi-symbolic algorithm for the one-step control problem of ParBNs, that builds on symbolic data structures to avoid scanning individual parameters. We evaluate the performance of our approach on real biological models.

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 130 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džunić–Petković–Petković; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

scholarly journals Efficiency Through Procrastination: Approximately Optimal Algorithm Configuration with Runtime Guarantees

2017 ◽  
Author(s):  
Robert Kleinberg ◽  
Kevin Leyton-Brown ◽  
Brendan Lucier
Keyword(s):  
High Probability ◽  
Optimal Algorithm ◽  
Optimal Performance ◽  
Worst Case ◽  
Running Time ◽  
Performance Guarantees ◽  
Algorithm Configuration ◽  
Time Requirements

Algorithm configuration methods have achieved much practical success, but to date have not been backed by meaningful performance guarantees. We address this gap with a new algorithm configuration framework, Structured Procrastination. With high probability and nearly as quickly as possible in the worst case, our framework finds an algorithm configuration that provably achieves near optimal performance. Moreover, its running time requirements asymptotically dominate those of existing methods.

Filling Patterning with a Replicate Color: Maximum Increase in Minimax Magazine Movement

1992 ◽  
Vol 62 (9) ◽  
pp. 522-530 ◽  
Author(s):  
R. M. Dawson
Keyword(s):  
Color Change ◽  
Initial Number ◽  
Maximum Increase ◽  
Worst Case ◽  
One Step

Spare filling patterning capacity on a loom can be utilized by replicating one or more filling colors, which can increase the filling replenishment interval. However, with the magazine-type mechanisms used on shuttle and Sulzer-type projectile machines, larger minimax magazine movements, and hence lower machine speeds, could result. The effects on minimax movement of replicating one of up to five colors are investigated for the worst case. Each combination of an initial number of colors, degree of replicate-color vertex in the color-change diagram, and sizes of minimax magazine movements with and without replication is considered. Even in this worst case, about 53% of all forms of replication do not affect the minimax movement; the others increase it by only one step. The forms of replication that increase the minimax movement are specified. The greater the number of colors adjacent to the replicate in the filling repeat, the more likely replication will increase minimax movement, other things being equal.

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