On Maximum Discounted Effort Reward Search Problem

2016 ◽  
Vol 33 (03) ◽  
pp. 1650019 ◽  
Author(s):  
Mohamed Abd Allah El-Hadidy
Keyword(s):  
Optimization Problem ◽  
Random Variable ◽  
Fixed Number ◽  
Search Model ◽  
Search Problem ◽  
Time Intervals ◽  
Search Effort ◽  
Stochastic Optimization Problem ◽  
Finite Set ◽  
Fuzzy Parameter

In this paper, we formulate a new search model for detecting two related targets that randomly located in a finite set of different cells or randomly moved through those cells. We assume that the search effort at each fixed number of time intervals is a random variable with a normal distribution. Rather than minimizing the expected effort of detecting two related targets, the proposed mathematical model allows us to include the search effort as a function with fuzzy parameter (discounted parameter). Another feature of this paper is considering a fuzzy extension of a stochastic optimization problem, which is interesting. We present an algorithm that gives the optimal distribution of an effort which makes the discounted effort reward of finding the targets is maximum. Two numerical examples are illustrated to show the effectiveness of this model by setting some parameters to represent some situations, such as detecting the enemy ships, fighters and the landmines in the war.

scholarly journals A Hybrid Metaheuristic Algorithm for the Efficient Placement of UAVs

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 323
Author(s):  
Stephanie Alvarez Fernandez ◽  
Marcelo M. Carvalho ◽  
Daniel G. Silva
Keyword(s):  
Optimization Problem ◽  
Data Transfer ◽  
Fixed Number ◽  
Metaheuristic Algorithm ◽  
Network Coverage ◽  
Time Intervals ◽  
Hybrid Metaheuristic ◽  
Relay Communications ◽  
Real World Application ◽  
Short Time

This work addresses the problem of using Unmanned Aerial Vehicles (UAV) to deploy a wireless aerial relay communications infrastructure for stations scattered on the ground. In our problem, every station in the network must be assigned to a single UAV, which is responsible for handling all data transfer on behalf of the stations that are assigned to it. Consequently, the placement of UAVs is key to achieving both network coverage and the maximization of the aggregate link capacities between UAVs and stations, and among the UAVs themselves. Because the complexity of this problem increases significantly with the number of stations to cover, for a given fixed number p of available UAVs, we model it as a single allocation p-hub median optimization problem, and we propose a hybrid metaheuristic algorithm to solve it. A series of numerical experiments illustrate the efficiency of the proposed algorithm against traditional optimization tools, which achieves high-quality results in very short time intervals, thus making it an attractive solution for real-world application scenarios.

scholarly journals Optimal Multi Zones Search Technique to Detect a Lost Target by Using K Sensors

2021 ◽  
Vol 9 (4) ◽  
pp. 871-885
Author(s):  
Mohamed El-Hadidy ◽  
Hamdy Abou-Gabal ◽  
Aya Gabr
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Random Variable ◽  
Time Interval ◽  
Search Technique ◽  
Detection Function ◽  
Numerical Application ◽  
Reward Function ◽  
Stochastic Optimization Problem ◽  
Discrete Search

This paper presents the discrete search technique on multi zones to detect a lost target by using  sensors. The search region is divided into  zones. These zones contain an equal number of states (cells) not necessarily identical. Each zone has a one sensor to detect the target. The target moves over the cells according to a random process. We consider the searching effort as a random variable with a known probability distribution. The detection function with the discounted reward function in a certain state  and time interval  are given. The optimal effort distribution that minimizes the probability of undetection is obtained after solving a discrete stochastic optimization problem. An algorithm is constructed to obtain the optimal solution as in the numerical application.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

scholarly journals On Exact Sampling of Nonnegative Infinitely Divisible Random Variables

2012 ◽  
Vol 44 (3) ◽  
pp. 842-873 ◽  
Author(s):  
Zhiyi Chi
Keyword(s):  
Basic Result ◽  
Random Variables ◽  
Random Variable ◽  
Fixed Number ◽  
Rejection Sampling ◽  
Infinitely Divisible ◽  
Exact Sampling ◽  
Special Cases ◽  
Wide Range ◽  
Lévy Density

Nonnegative infinitely divisible (i.d.) random variables form an important class of random variables. However, when this type of random variable is specified via Lévy densities that have infinite integrals on (0, ∞), except for some special cases, exact sampling is unknown. We present a method that can sample a rather wide range of such i.d. random variables. A basic result is that, for any nonnegative i.d. random variable X with its Lévy density explicitly specified, if its distribution conditional on X ≤ r can be sampled exactly, where r > 0 is any fixed number, then X can be sampled exactly using rejection sampling, without knowing the explicit expression of the density of X. We show that variations of the result can be used to sample various nonnegative i.d. random variables.

scholarly journals Some Remarks on a Recent Paper by Borch

1961 ◽  
Vol 1 (5) ◽  
pp. 265-272 ◽  
Author(s):  
Paul Markham Kahn
Keyword(s):  
Distribution Function ◽  
Random Variable ◽  
Fixed Number ◽  
Point Of View ◽  
Optimum Amount ◽  
Measurable Transformation ◽  
The Difference ◽  
Image Position ◽  
Stop Loss ◽  
Condition B

In his recent paper, “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, presented to the XVIth International Congress of Actuaries, Dr. Karl Borch considers the problem of minimizing the variance of the total claims borne by the ceding insurer. Adopting this variance as a measure of risk, he considers as the most efficient reinsurance scheme that one which serves to minimize this variance. If x represents the amount of total claims with distribution function F (x), he considers a reinsurance scheme as a transformation of F (x). Attacking his problem from a different point of view, we restate and prove it for a set of transformations apparently wider than that which he allows.The process of reinsurance substitutes for the amount of total claims x a transformed value Tx as the liability of the ceding insurer, and hence a reinsurance scheme may be described by the associated transformation T of the random variable x representing the amount of total claims, rather than by a transformation of its distribution as discussed by Borch. Let us define an admissible transformation as a Lebesgue-measurable transformation T such thatwhere c is a fixed number between o and m = E (x). Condition (a) implies that the insurer will never bear an amount greater than the actual total claims. In condition (b), c represents the reinsurance premium, assumed fixed, and is equal to the expected value of the difference between the total amount of claims x and the total retained amount of claims Tx borne by the insurer.

scholarly journals Knee Point Search Using Cascading Top-kSorting with Minimized Time Complexity

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zheng Wang ◽  
Shian-Shyong Tseng
Keyword(s):  
Time Complexity ◽  
Optimization Problem ◽  
Search Algorithm ◽  
A Priori ◽  
Search Problem ◽  
Time Cost ◽  
Point Distribution ◽  
Expected Time ◽  
Knee Point ◽  
Point Search

Anomaly detection systems and many other applications are frequently confronted with the problem of finding the largest knee point in the sorted curve for a set of unsorted points. This paper proposes an efficient knee point search algorithm with minimized time complexity using the cascading top-ksorting when a priori probability distribution of the knee point is known. First, a top-ksort algorithm is proposed based on a quicksort variation. We divide the knee point search problem into multiple steps. And in each step an optimization problem of the selection numberkis solved, where the objective function is defined as the expected time cost. Because the expected time cost in one step is dependent on that of the afterwards steps, we simplify the optimization problem by minimizing the maximum expected time cost. The posterior probability of the largest knee point distribution and the other parameters are updated before solving the optimization problem in each step. An example of source detection of DNS DoS flooding attacks is provided to illustrate the applications of the proposed algorithm.

scholarly journals Caputo Fractional Differential Equations with Non-Instantaneous Random Erlang Distributed Impulses

2019 ◽  
Vol 3 (2) ◽  
pp. 28 ◽  
Author(s):  
Snezhana Hristova ◽  
Krasimira Ivanova
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Random Variable ◽  
Time Intervals ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Dini Derivatives ◽  
Moment Exponential Stability

The p-moment exponential stability of non-instantaneous impulsive Caputo fractional differential equations is studied. The impulses occur at random moments and their action continues on finite time intervals with initially given lengths. The time between two consecutive moments of impulses is the Erlang distributed random variable. The study is based on Lyapunov functions. The fractional Dini derivatives are applied.

scholarly journals On optimal stopping of risk processes with regime switching

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Elżbieta Ferenstein ◽  
Adam Pasternak-Winiarski
Keyword(s):  
Optimal Stopping ◽  
Regime Switching ◽  
Random Variable ◽  
Risk Process ◽  
Stopping Rules ◽  
Process Change ◽  
Programming Methodology ◽  
Finite Set ◽  
Alternative Settings ◽  
Risk Processes

AbstractIn the paper we solve a problem of optimal stopping of a risk process in two alternative settings. We assume that the main characteristics of the risk process change according to unobservable random variable. In the first model we assume that the post-disorder distributions are not known a’priori and are randomly chosen from a finite set of admissible distributions. The second model concentrates on a situation when more than one disorder is possible. For both models optimal stopping rules with respect to given utility function are constructed using dynamic programming methodology.

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