scholarly journals Graph-Based Upper Bounds for the Probability of the Union of Events

10.37236/752 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Pierangela Veneziani
Keyword(s):  
Objective Function ◽  
Upper Bounds ◽  
Linear Program ◽  
Graph Structures ◽  
Basic Feasible Solutions ◽  
Objective Function Values ◽  
Feasible Solutions ◽  
The Individual

We consider the problem of generating upper bounds for the probability of the union of events when the individual probabilities of the events as well as the probabilities of pairs of these events are known. By formulating the problem as a Linear Program, we can obtain bounds as objective function values corresponding to dual basic feasible solutions. The new upper bounds are based on underlying bipartite and threshold type graph structures.

An Evolutionary Algorithm for Black-Box Chance-Constrained Function Optimization

2013 ◽  
Vol 17 (2) ◽  
pp. 272-282
Author(s):  
Kazuyuki Masutomi ◽  
◽  
Yuichi Nagata ◽  
Isao Ono ◽  
◽  
...  
Keyword(s):  
Objective Function ◽  
Evolutionary Algorithm ◽  
Black Box ◽  
Function Optimization ◽  
Benchmark Problems ◽  
Objective Functions ◽  
Neural Network Controller ◽  
Objective Function Values ◽  
The Individual ◽  
Constrained Function

This paper presents an evolutionary algorithm for Black-Box Chance-Constrained Function Optimization (BBCCFO). BBCCFO is to minimize the expectation of the objective function under the constraints that the feasibility probability is higher than a userdefined constant in uncertain environments not given the mathematical expressions of objective functions and constraints explicitly. In BBCCFO, only objective function values of solutions and their feasibilities are available because the algebra expressions of objective functions and constraints cannot be used. In approaches to BBCCFO, a method based on an evolutionary algorithm proposed by Loughlin and Ranjithan shows relatively good performance in a realworld application, but this conventional method has a problem in that it requires many samples to obtain a good solution because it estimates the expectation of the objective function and the feasibility probability of an individual by sampling the individual plural times. In this paper, we propose a new evolutionary algorithm that estimates the expectation of the objective function and the feasibility probability of an individual by using the other individuals in the neighborhood of the individual. We show the effectiveness of the proposed method through experiments both in benchmark problems and in the problem of a inverted pendulum balancing with a neural network controller.

NEW SIMULATED ANNEALING ALGORITHMS FOR CONSTRAINED OPTIMIZATION

2010 ◽  
Vol 27 (03) ◽  
pp. 347-367 ◽  
Author(s):  
LINET ÖZDAMAR ◽  
CHANDRA SEKHAR PEDAMALLU
Keyword(s):  
Simulated Annealing ◽  
Constrained Optimization ◽  
Objective Function ◽  
Population Based ◽  
Performance Criteria ◽  
Local Optimum ◽  
Starting Solution ◽  
Objective Function Values ◽  
Feasible Solutions ◽  
Dual Sequence

We propose a Population based dual-sequence Non-Penalty Annealing algorithm (PNPA) for solving the general nonlinear constrained optimization problem. The PNPA maintains a population of solutions that are intermixed by crossover to supply a new starting solution for simulated annealing throughout the search. Every time the search gets stuck at a local optimum, this crossover procedure is triggered and simulated annealing search re-starts from a new subspace. In both the crossover and simulated annealing procedures, the objective function value and the total solution infeasibility degrees are treated as separate performance criteria. Feasible solutions are assessed according to their objective function values and infeasible solutions are assessed with regard to their absolute degree of constraint infeasibility. In other words, in the proposed approach, there exist two sequences of solutions: the feasible sequence and the infeasible sequence. We compare the population based dual sequence PNPA with the standard single sequence Penalty Annealing (the PA), and with the random seed dual sequence Non-Penalty Annealing (NPA). Numerical experiments show that PNPA is more effective than its counterparts.

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

2020 ◽  
Vol 5 (1) ◽  
pp. 456
Author(s):  
Tolulope Latunde ◽  
Joseph Oluwaseun Richard ◽  
Opeyemi Odunayo Esan ◽  
Damilola Deborah Dare
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Transportation Cost ◽  
North West ◽  
Life Problems ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Road Freight Transportation ◽  
The Cost ◽  
Cost Of Transportation

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

scholarly journals Cable Tension Analysis Oriented the Enhanced Stiffness of a 3-DOF Joint Module of a Modular Cable-Driven Human-Like Robotic Arm

2020 ◽  
Vol 10 (24) ◽  
pp. 8871
Author(s):  
Kaisheng Yang ◽  
Guilin Yang ◽  
Chi Zhang ◽  
Chinyin Chen ◽  
Tianjiang Zheng ◽  
...  
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Human Robot Interaction ◽  
Robotic Arm ◽  
Robot Interaction ◽  
Cable Tension ◽  
Tension Distribution ◽  
Stiffness Model ◽  
Redundantly Actuated ◽  
Objective Function Values

Inspired by the structure of human arms, a modular cable-driven human-like robotic arm (CHRA) is developed for safe human–robot interaction. Due to the unilateral driving properties of the cables, the CHRA is redundantly actuated and its stiffness can be adjusted by regulating the cable tensions. Since the trajectory of the 3-DOF joint module (3DJM) of the CHRA is a curve on Lie group SO(3), an enhanced stiffness model of the 3DJM is established by the covariant derivative of the load to the displacement on SO(3). In this paper, we focus on analyzing the how cable tension distribution problem oriented the enhanced stiffness of the 3DJM of the CHRA for stiffness adjustment. Due to the complexity of the enhanced stiffness model, it is difficult to solve the cable tensions from the desired stiffness analytically. The problem of stiffness-oriented cable tension distribution (SCTD) is formulated as a nonlinear optimization model. The optimization model is simplified using the symmetry of the enhanced stiffness model, the rank of the Jacobian matrix and the equilibrium equation of the 3DJM. Since the objective function is too complicated to compute the gradient, a method based on the genetic algorithm is proposed for solving this optimization problem, which only utilizes the objective function values. A comprehensive simulation is carried out to validate the effectiveness of the proposed method.

scholarly journals Self-adaptive potential-based stopping criteria for Particle Swarm Optimization with forced moves

2020 ◽  
Vol 14 (4) ◽  
pp. 285-311
Author(s):  
Bernd Bassimir ◽  
Manuel Schmitt ◽  
Rolf Wanka
Keyword(s):  
Particle Swarm Optimization ◽  
Objective Function ◽  
Particle Swarm ◽  
Upper Bounds ◽  
Local Optimum ◽  
Adaptive Potential ◽  
Stopping Criteria ◽  
Swarm Optimization ◽  
Self Adaptive

Abstract We study the variant of Particle Swarm Optimization that applies random velocities in a dimension instead of the regular velocity update equations as soon as the so-called potential of the swarm falls below a certain small bound in this dimension, arbitrarily set by the user. In this case, the swarm performs a forced move. In this paper, we are interested in how, by counting the forced moves, the swarm can decide for itself to stop its movement because it is improbable to find better candidate solutions than the already-found best solution. We formally prove that when the swarm is close to a (local) optimum, it behaves like a blind-searching cloud and that the frequency of forced moves exceeds a certain, objective function-independent value. Based on this observation, we define stopping criteria and evaluate them experimentally showing that good candidate solutions can be found much faster than setting upper bounds on the iterations and better solutions compared to applying other solutions from the literature.

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

scholarly journals Locomotor Development Prediction Based on Statistical Model Parameters Identification

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
A. V. Wildemann ◽  
A. A. Tashkinov ◽  
V. A. Bronnikov
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Parameters Identification ◽  
Model Parameters ◽  
Large Set ◽  
Constrained Optimization Problem ◽  
Unknown Parameters ◽  
Locomotor Development ◽  
Feasible Solutions ◽  
The Individual

This paper introduces an approach for parameters identification of a statistical predicting model with the use of the available individual data. Unknown parameters are separated into two groups: the ones specifying the average trend over large set of individuals and the ones describing the details of a concrete person. In order to calculate the vector of unknown parameters, a multidimensional constrained optimization problem is solved minimizing the discrepancy between real data and the model prediction over the set of feasible solutions. Both the individual retrospective data and factors influencing the individual dynamics are taken into account. The application of the method for predicting the movement of a patient with congenital motility disorders is considered.

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