FINDING MULTIPLE LOCAL MINIMA USING CHAOTIC JUMP

1998 ◽  
Vol 07 (01) ◽  
pp. 105-115 ◽  
Author(s):  
CHANGKYU CHOI ◽  
JU-JANG LEE
Keyword(s):  
Search Algorithm ◽  
Gaussian Function ◽  
Search Space ◽  
Planning Problem ◽  
Local Minima ◽  
Chaotic Motions ◽  
Quality Function ◽  
Unstructured Search ◽  
Free Search ◽  
Minimum Points

In this paper, the local minima free search algorithm using chaos is proposed for an unstructured search space. The problem is that given the quality function, find the value of a configuration that minimizes the quality function. The proposed algorithm started basically from the gradient search technique but at the prescribed points, that is, local minimum points, which are to be automatically detected the chaotic jump is introduced by the dynamics of a chaotic neuron. Chaotic motions are mainly because of the Gaussian function having a hysteresis as a refractoriness. In order to enhance the probability of finding the global minimum, a parallel search strategy is also given. The validity of the proposed method wil be verified in simulation examples of the function minimization problem and the motion planning problem of a mobile robot.

Nelder-Mead Evolutionary Hybrid Algorithms

2011 ◽  
pp. 1191-1196 ◽  
Author(s):  
Sanjoy Das
Keyword(s):  
Evolutionary Algorithms ◽  
Local Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Simplex Algorithm ◽  
Stochastic Methods ◽  
Great Success ◽  
Local Minima ◽  
Swarm Optimization

Real world optimization problems are often too complex to be solved through analytic means. Evolutionary algorithms are a class of algorithms that borrow paradigms from nature to address them. These are stochastic methods of optimization that maintain a population of individual solutions, which correspond to points in the search space of the problem. These algorithms have been immensely popular as they are derivativefree techniques, are not as prone to getting trapped in local minima, and can be tailored specifically to suit any given problem. The performance of evolutionary algorithms can be improved further by adding a local search component to them. The Nelder-Mead simplex algorithm (Nelder & Mead, 1965) is a simple local search algorithm that has been routinely applied to improve the search process in evolutionary algorithms, and such a strategy has met with great success. In this article, we provide an overview of the various strategies that have been adopted to hybridize two wellknown evolutionary algorithms - genetic algorithms (GA) and particle swarm optimization (PSO).

scholarly journals A Streamlined Search Algorithm for Path Modifications of a Safe Robot Manipulator*

2010 ◽  
Vol 1 (2) ◽  
Author(s):  
Nima Najmaei ◽  
Mehrdad R. Kermani
Keyword(s):  
Robot Manipulator ◽  
Search Algorithm ◽  
Search Space ◽  
Planning Problem ◽  
Minimum Number ◽  
Gradient Based ◽  
On Line ◽  
Line Path ◽  
Path Modification ◽  
Path Planning Problem

AbstractIn recent years, the interest in human-robot interactions has added a new dimension to the on-line path planning problem by requiring a method that guarantees a risk-free path. This paper presents a streamlined search algorithm for fast path modification. The algorithm is formulated as an optimization problem that evaluates alternative paths nearby each obstacle. Each path is evaluated based on the value of the danger assigned to that path. To reduce the size of the search space, the minimum number of via points necessary to alter the path is initially obtained using a geometrical method. Given the number of via points, the algorithm proceeds to locate the via points around the obstacle such that the resulting path through these via points satisfies all problem constraints. Obtaining a solution in this way renders a fast algorithm for path modification, while it better avoids problems often encountered in other gradient-based search algorithms. Case studies for two planar robots are provided to highlight some of the advantages of the proposed algorithm. Experimental results using a CRS-F3 robot manipulator validate the effectiveness of the algorithm for applications involving human-robot interactions.

Localization of WSN using Distributed Particle Swarm Optimization algorithm with precise references

2016 ◽  
Vol 7 ◽  
pp. 1
Author(s):  
Ravichander Janapati ◽  
Ch. Balaswamy ◽  
K. Soundararajan
Keyword(s):  
Particle Swarm Optimization ◽  
Search Algorithm ◽  
Particle Swarm ◽  
Search Space ◽  
Research Area ◽  
Population Based ◽  
Wireless Sensor ◽  
Cooperative Localization ◽  
Localization Algorithm ◽  
Swarm Optimization

Localization is the key research area in wireless sensor networks. Finding the exact position of the node is known as localization. Different algorithms have been proposed. Here we consider a cooperative localization algorithm with censoring schemes using Crammer Rao bound (CRB). This censoring scheme  can improve the positioning accuracy and reduces computation complexity, traffic and latency. Particle swarm optimization (PSO) is a population based search algorithm based on the swarm intelligence like social behavior of birds, bees or a school of fishes. To improve the algorithm efficiency and localization precision, this paper presents an objective function based on the normal distribution of ranging error and a method of obtaining the search space of particles. In this paper  Distributed localization of wireless sensor networksis proposed using PSO with best censoring technique using CRB. Proposed method shows better results in terms of position accuracy, latency and complexity.  

Automatic Mining of Quantitative Association Rules with Gravitational Search Algorithm

2017 ◽  
Vol 27 (03) ◽  
pp. 343-372 ◽  
Author(s):  
Umit Can ◽  
Bilal Alatas
Keyword(s):  
Association Rules ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Fitness Function ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Search Space ◽  
Search Method ◽  
Quantitative Association Rules ◽  
Gravitational Search

The classical optimization algorithms are not efficient in solving complex search and optimization problems. Thus, some heuristic optimization algorithms have been proposed. In this paper, exploration of association rules within numerical databases with Gravitational Search Algorithm (GSA) has been firstly performed. GSA has been designed as search method for quantitative association rules from the databases which can be regarded as search space. Furthermore, determining the minimum values of confidence and support for every database which is a hard job has been eliminated by GSA. Apart from this, the fitness function used for GSA is very flexible. According to the interested problem, some parameters can be removed from or added to the fitness function. The range values of the attributes have been automatically adjusted during the time of mining of the rules. That is why there is not any requirements for the pre-processing of the data. Attributes interaction problem has also been eliminated with the designed GSA. GSA has been tested with four real databases and promising results have been obtained. GSA seems an effective search method for complex numerical sequential patterns mining, numerical classification rules mining, and clustering rules mining tasks of data mining.

scholarly journals Incorporation of Potential Fields and Motion Primitives for the Collision Avoidance of Unmanned Aircraft

2021 ◽  
Vol 11 (7) ◽  
pp. 3103
Author(s):  
Kyuman Lee ◽  
Daegyun Choi ◽  
Donghoon Kim
Keyword(s):  
Collision Avoidance ◽  
Search Algorithm ◽  
Unmanned Aircraft ◽  
Artificial Potential Field ◽  
Tree Search ◽  
Local Minima ◽  
Collision Risk ◽  
Motion Primitives ◽  
Multiple Uavs ◽  
Tree Search Algorithm

Collision avoidance (CA) using the artificial potential field (APF) usually faces several known issues such as local minima and dynamically infeasible problems, so unmanned aerial vehicles’ (UAVs) paths planned based on the APF are safe only in a certain environment. This research proposes a CA approach that combines the APF and motion primitives (MPs) to tackle the known problems associated with the APF. Since MPs solve for a locally optimal trajectory with respect to allocated time, the trajectory obtained by the MPs is verified as dynamically feasible. When a collision checker based on the k-d tree search algorithm detects collision risk on extracted sample points from the planned trajectory, generating re-planned path candidates to avoid obstacles is performed. After rejecting unsafe route candidates, one applies the APF to select the best route among the remaining safe-path candidates. To validate the proposed approach, we simulated two meaningful scenario cases—the presence of static obstacles situation with local minima and dynamic environments with multiple UAVs present. The simulation results show that the proposed approach provides smooth, efficient, and dynamically feasible pathing compared to the APF.

scholarly journals Binary Spring Search Algorithm for Solving Various Optimization Problems

2021 ◽  
Vol 11 (3) ◽  
pp. 1286 ◽  
Author(s):  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Ali Dehghani ◽  
Om P. Malik ◽  
Ruben Morales-Menendez ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
High Performance ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Bat Algorithm ◽  
Search Space ◽  
Binary Particle Swarm Optimization ◽  
Dragonfly Algorithm ◽  
Grasshopper Optimization Algorithm

One of the most powerful tools for solving optimization problems is optimization algorithms (inspired by nature) based on populations. These algorithms provide a solution to a problem by randomly searching in the search space. The design’s central idea is derived from various natural phenomena, the behavior and living conditions of living organisms, laws of physics, etc. A new population-based optimization algorithm called the Binary Spring Search Algorithm (BSSA) is introduced to solve optimization problems. BSSA is an algorithm based on a simulation of the famous Hooke’s law (physics) for the traditional weights and springs system. In this proposal, the population comprises weights that are connected by unique springs. The mathematical modeling of the proposed algorithm is presented to be used to achieve solutions to optimization problems. The results were thoroughly validated in different unimodal and multimodal functions; additionally, the BSSA was compared with high-performance algorithms: binary grasshopper optimization algorithm, binary dragonfly algorithm, binary bat algorithm, binary gravitational search algorithm, binary particle swarm optimization, and binary genetic algorithm. The results show the superiority of the BSSA. The results of the Friedman test corroborate that the BSSA is more competitive.

Deterministic and probabilistic occupancy detection with a novel heuristic optimization and Back-Propagation (BP) based algorithm

2021 ◽  
pp. 1-13
Author(s):  
Nuzhat Fatema ◽  
Saeid Gholami Farkoush ◽  
Mashhood Hasan ◽  
H Malik
Keyword(s):  
Convergence Rate ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Hybrid Approach ◽  
Experimental Studies ◽  
Back Propagation ◽  
Heuristic Optimization ◽  
Local Minima ◽  
Occupancy Detection ◽  
Trapping Problem

In this paper, a novel hybrid approach for deterministic and probabilistic occupancy detection is proposed with a novel heuristic optimization and Back-Propagation (BP) based algorithms. Generally, PB based neural network (BPNN) suffers with the optimal value of weight, bias, trapping problem in local minima and sluggish convergence rate. In this paper, the GSA (Gravitational Search Algorithm) is implemented as a new training technique for BPNN is order to enhance the performance of the BPNN algorithm by decreasing the problem of trapping in local minima, enhance the convergence rate and optimize the weight and bias value to reduce the overall error. The experimental results of BPNN with and without GSA are demonstrated and presented for fair comparison and adoptability. The demonstrated results show that BPNNGSA has outperformance for training and testing phase in form of enhancement of processing speed, convergence rate and avoiding the trapping problem of standard BPNN. The whole study is analyzed and demonstrated by using R language open access platform. The proposed approach is validated with different hidden-layer neurons for both experimental studies based on BPNN and BPNNGSA.

scholarly journals Optimum Distribution System Expansion Planning Incorporating DG Based on N-1 Criterion for Sustainable System

2021 ◽  
Vol 13 (12) ◽  
pp. 6708
Author(s):  
Hamza Mubarak ◽  
Nurulafiqah Nadzirah Mansor ◽  
Hazlie Mokhlis ◽  
Mahazani Mohamad ◽  
Hasmaini Mohamad ◽  
...  
Keyword(s):  
Power Systems ◽  
Distribution System ◽  
Industrial Revolution ◽  
Optimal Solution ◽  
Search Space ◽  
Planning Problem ◽  
System Expansion ◽  
Optimum Distribution ◽  
Optimal Sizing ◽  
Expansion Planning

Demand for continuous and reliable power supply has significantly increased, especially in this Industrial Revolution 4.0 era. In this regard, adequate planning of electrical power systems considering persistent load growth, increased integration of distributed generators (DGs), optimal system operation during N-1 contingencies, and compliance to the existing system constraints are paramount. However, these issues need to be parallelly addressed for optimum distribution system planning. Consequently, the planning optimization problem would become more complex due to the various technical and operational constraints as well as the enormous search space. To address these considerations, this paper proposes a strategy to obtain one optimal solution for the distribution system expansion planning by considering N-1 system contingencies for all branches and DG optimal sizing and placement as well as fluctuations in the load profiles. In this work, a hybrid firefly algorithm and particle swarm optimization (FA-PSO) was proposed to determine the optimal solution for the expansion planning problem. The validity of the proposed method was tested on IEEE 33- and 69-bus systems. The results show that incorporating DGs with optimal sizing and location minimizes the investment and power loss cost for the 33-bus system by 42.18% and 14.63%, respectively, and for the 69-system by 31.53% and 12%, respectively. In addition, comparative studies were done with a different model from the literature to verify the robustness of the proposed method.

Optimal Policy for Dynamic Assortment Planning Under Multinomial Logit Models

2021 ◽  
Author(s):  
Xi Chen ◽  
Yining Wang ◽  
Yuan Zhou
Keyword(s):  
Choice Model ◽  
Current Knowledge ◽  
Search Algorithm ◽  
Multinomial Logit ◽  
Planning Problem ◽  
Assortment Planning ◽  
Substitutable Products ◽  
Dynamic Decisions ◽  
Mnl Model ◽  
Regret Bound

We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and the customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Because all the utility parameters of the MNL model are unknown, the seller needs to simultaneously learn customers’ choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or, equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products [Formula: see text]. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model—the MNL model—is still open. By carefully analyzing a revenue potential function, we develop a trisection-based policy combined with adaptive confidence bound construction, which achieves an item-independent regret bound of [Formula: see text], where [Formula: see text] is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There are two major advantages of the proposed policy. First, the regret of all our policies has no dependence on [Formula: see text]. Second, our policies are almost assumption-free: there is no assumption on mean utility nor any “separability” condition on the expected revenues for different assortments. We also extend our trisection search algorithm to capacitated MNL models and obtain the optimal regret [Formula: see text] (up to logrithmic factors) without any assumption on the mean utility parameters of items.

How significant are the known collision and element distinctness quantum algorithms?

2004 ◽  
Vol 4 (3) ◽  
pp. 201-206
Author(s):  
L. Grover ◽  
T. Rudolph
Keyword(s):  
Search Algorithm ◽  
Quantum Algorithms ◽  
Search Space ◽  
Space Complexity ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Space ◽  
Simple Quantum ◽  
Structured Problems ◽  
Better Than

Quantum search is a technique for searching $N$ possibilities for a desired target in $O(\sqrt{N})$ steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum hardware. In this paper we propose the criterion that an algorithm which requires $O(S)$ hardware should be considered significant if it produces a speedup of better than $O\left(\sqrt{S}\right)$ over a simple quantum search algorithm. This is because a speedup of $O\left(\sqrt{S}\right)$ can be trivially obtained by dividing the search space into $S$ separate parts and handing the problem to $S$ independent processors that do a quantum search (in this paper we drop all logarithmic factors when discussing time/space complexity). Known algorithms for collision and element distinctness exactly saturate the criterion.

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