Clustering a 2d Pareto Front: P-center Problems Are Solvable in Polynomial Time

2020 ◽  
pp. 179-191
Author(s):  
Nicolas Dupin ◽  
Frank Nielsen ◽  
El-Ghazali Talbi
Keyword(s):  
Polynomial Time ◽  
Pareto Front

scholarly journals Representative Solutions for Bi-Objective Optimisation

2020 ◽  
Vol 34 (02) ◽  
pp. 1436-1443
Author(s):  
Emir Demirovi? ◽  
Nicolas Schwind
Keyword(s):  
Polynomial Time ◽  
Pareto Front ◽  
Mixed Integer ◽  
Linear Programs ◽  
Objective Functions ◽  
Nondominated Solutions ◽  
Integer Linear Programs ◽  
Trade Offs ◽  
Continuous Problems ◽  
Discrete Problems

Bi-objective optimisation aims to optimise two generally competing objective functions. Typically, it consists in computing the set of nondominated solutions, called the Pareto front. This raises two issues: 1) time complexity, as the Pareto front in general can be infinite for continuous problems and exponentially large for discrete problems, and 2) lack of decisiveness. This paper focusses on the computation of a small, “relevant” subset of the Pareto front called the representative set, which provides meaningful trade-offs between the two objectives. We introduce a procedure which, given a pre-computed Pareto front, computes a representative set in polynomial time, and then we show how to adapt it to the case where the Pareto front is not provided. This has three important consequences for computing the representative set: 1) does not require the whole Pareto front to be provided explicitly, 2) can be done in polynomial time for bi-objective mixed-integer linear programs, and 3) only requires a polynomial number of solver calls for bi-objective problems, as opposed to the case where a higher number of objectives is involved. We implement our algorithm and empirically illustrate the efficiency on two families of benchmarks.

The 2-closure of a 32-transitive group in polynomial time

2018 ◽  
Vol 60 (2) ◽  
pp. 360-375
Author(s):  
A. V. Vasil'ev ◽  
D. V. Churikov
Keyword(s):  
Polynomial Time ◽  
Transitive Group

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

scholarly journals Learn your opponent's strategy (in polynomial time)!

1996 ◽  
pp. 164-176 ◽  
Author(s):  
Yishay Mor ◽  
Claudia V. Goldman ◽  
Jeffrey S. Rosenschein
Keyword(s):  
Polynomial Time

A First Step Toward On-Chip Memory Mapping for Parallel Turbo and LDPC Decoders: A Polynomial Time Mapping Algorithm

2013 ◽  
Vol 61 (16) ◽  
pp. 4127-4140 ◽  
Author(s):  
Awais Hussain Sani ◽  
Philippe Coussy ◽  
Cyrille Chavet
Keyword(s):  
Polynomial Time ◽  
Mapping Algorithm ◽  
Memory Mapping ◽  
On Chip

scholarly journals Sensitivity Based Selection of an Optimal Cable-Driven Parallel Robot Design for Rehabilitation Purposes

Robotics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 7
Author(s):  
Ferdaws Ennaiem ◽  
Abdelbadiâ Chaker ◽  
Juan Sebastián Sandoval Arévalo ◽  
Med Amine Laribi ◽  
Sami Bennour ◽  
...  
Keyword(s):  
Pareto Front ◽  
Parallel Robot ◽  
Elastic Stiffness ◽  
Upper Limb Rehabilitation ◽  
Daily Life Activities ◽  
System A ◽  
The Monte Carlo Method ◽  
Genetic Algorithm Method ◽  
Limb Rehabilitation ◽  
Selection Of

This paper deals with the design of an optimal cable-driven parallel robot (CDPR) for upper limb rehabilitation. The robot’s prescribed workspace is identified with the help of an occupational therapist based on three selected daily life activities, which are tracked using a Qualisys motion capture system. A preliminary architecture of the robot is proposed based on the analysis of the tracked trajectories of all the activities. A multi-objective optimization process using the genetic algorithm method is then performed, where the cable tensions and the robot size are selected as the objective functions to be minimized. The cables tensions are bounded between two limits, where the lower limit ensures a positive tension in the cables at all times and the upper limit represents the maximum torque of the motor. A sensitivity analysis is then performed using the Monte Carlo method to yield the optimal design selected out of the non-dominated solutions, forming the obtained Pareto front. The robot with the highest robustness toward the disturbances is identified, and its dexterity and elastic stiffness are calculated to investigate its performance.

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