scholarly journals Finding a Home: Stopping Theory and Its Application to Home Range Establishment in a Novel Environment

2021 ◽  
Vol 2 ◽  
Author(s):  
David Saltz ◽  
Wayne M. Getz
Keyword(s):  
Home Range ◽  
Cost Minimization ◽  
Stopping Time ◽  
Stopping Rules ◽  
Foraging Efficiency ◽  
Missed Opportunities ◽  
Novel Environment ◽  
Movement Data ◽  
Optimal Stopping Theory ◽  
Cost Minimization Problem

Familiarity with the landscape increases foraging efficiency and safety. Thus, when animals are confronted with a novel environment, either by natural dispersal or translocation, establishing a home range becomes a priority. While the search for a home range carries a cost of functioning in an unfamiliar environment, ceasing the search carries a cost of missed opportunities. Thus, when to establish a home range is essentially a weighted sum of a two-criteria cost-minimization problem. The process is predominantly heuristic, where the animal must decide how to study the environment and, consequently, when to stop searching and establish a home range in a manner that will reduce the cost and maximize or at least satisfice its fitness. These issues fall within the framework of optimal stopping theory. In this paper we review stopping theory and three stopping rules relevant to home range establishment: the best-of-n rule, the threshold rule, and the comparative Bayes rule. We then describe how these rules can be distinguished from movement data, hypothesize when each rule should be practiced, and speculate what and how environmental factors and animal attributes affect the stopping time. We provide a set of stopping-theory-related predictions that are testable within the context of translocation projects and discuss some management implications.

scholarly journals STEADY-STATE OPTIMIZATION OF AN EXHAUSTIVE LÉVY STORAGE PROCESS WITH INTERMITTENT OUTPUT AND RANDOM OUTPUT RATE

2020 ◽  
pp. 1-15
Author(s):  
Royi Jacobovic ◽  
Offer Kella
Keyword(s):  
Steady State ◽  
Cost Minimization ◽  
Stopping Time ◽  
Random Variable ◽  
Storage Process ◽  
Output Rate ◽  
Steady State Distribution ◽  
Optimal Output ◽  
Deterministic Function ◽  
Cost Minimization Problem

Consider a regenerative storage process with a nondecreasing Lévy input (subordinator) such that every cycle may be split into two periods. In the first (off), the output is shut off and the workload accumulates. This continues until some stopping time. In the second (on), the process evolves like a subordinator minus a positive drift (output rate) until it hits the origin. In addition, we assume that the output rate of every on period is a random variable, which is determined at the beginning of this period. For example, at each period, the output rate may depend on the workload level at the beginning of the corresponding busy period. We derive the Laplace–Stieltjes transform of the steady-state distribution of the workload process and then apply this result to solve a steady-state cost minimization problem with holding, setup and output capacity costs. It is shown that the optimal output rate is a nondecreasing deterministic function of the workload level at the beginning of the corresponding on period.

Prophet Inequalities for Independent and Identically Distributed Random Variables from an Unknown Distribution

2021 ◽  
Author(s):  
José Correa ◽  
Paul Dütting ◽  
Felix Fischer ◽  
Kevin Schewior
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Optimal Solution ◽  
Random Order ◽  
Secretary Problem ◽  
Maximum Value ◽  
Optimal Stopping Theory ◽  
Long Time ◽  
Object Of Study ◽  
Independent And Identically Distributed

A central object of study in optimal stopping theory is the single-choice prophet inequality for independent and identically distributed random variables: given a sequence of random variables [Formula: see text] drawn independently from the same distribution, the goal is to choose a stopping time τ such that for the maximum value of α and for all distributions, [Formula: see text]. What makes this problem challenging is that the decision whether [Formula: see text] may only depend on the values of the random variables [Formula: see text] and on the distribution F. For a long time, the best known bound for the problem had been [Formula: see text], but recently a tight bound of [Formula: see text] was obtained. The case where F is unknown, such that the decision whether [Formula: see text] may depend only on the values of the random variables [Formula: see text], is equally well motivated but has received much less attention. A straightforward guarantee for this case of [Formula: see text] can be derived from the well-known optimal solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F, and we show that, even with o(n) samples, [Formula: see text]. On the other hand, n samples allow for a significant improvement, whereas [Formula: see text] samples are equivalent to knowledge of the distribution: specifically, with n samples, [Formula: see text] and [Formula: see text], and with [Formula: see text] samples, [Formula: see text] for any [Formula: see text].

Particle Swarm Optimization for Cost Reduction in Mobile Location Management Using Reporting Cell Planning Approach

2017 ◽  
pp. 171-189 ◽  
Author(s):  
Smita Parija ◽  
Sudhansu Sekhar Singh ◽  
Swati Swayamsiddha
Keyword(s):  
Particle Swarm Optimization ◽  
Cellular Network ◽  
Cost Minimization ◽  
Location Management ◽  
Particle Swarm ◽  
Location Update ◽  
Swarm Optimization ◽  
Cell Planning ◽  
Wireless Mobile Communication ◽  
Cost Minimization Problem

Location management is a very critical and intricate problem in wireless mobile communication which involves tracking the movement of the mobile users in the cellular network. Particle Swarm Optimization (PSO) is proposed for the optimal design of the cellular network using reporting cell planning (RCP) strategy. In this state-of-the-art approach, the proposed algorithm reduces the involved total cost such as location update and paging cost for the location management issue. The same technique is proved to be a competitive approach to different existing test network problems showing the efficacy of the proposed method through simulation results. The result obtained is also validated for real network data obtained from BSNL, Odisha. Particle Swarm Optimization is used to find the optimal set of reporting cells in a given cellular network by minimizing the location management cost. This RCP technique applied to this cost minimization problem has given improved result as compared to the results obtained in the previous literature.

Core-Based GRASP for Delay-Constrained Group Communications

2013 ◽  
Vol 4 (4) ◽  
pp. 1-22
Author(s):  
Zrinka Lukač ◽  
Manuel Laguna
Keyword(s):  
Data Stream ◽  
Cost Minimization ◽  
Multimedia Technology ◽  
Computational Results ◽  
Adaptive Search ◽  
End To End Delay ◽  
Efficient Delivery ◽  
Asymmetric Networks ◽  
Cost Minimization Problem

The recent development in network multimedia technology has created numerous real-time multimedia applications where the Quality-of-Service (QoS) requirements are quite rigorous. This has made multicasting under QoS constraints one of the most prominent routing problems. The authors consider the problem of the efficient delivery of data stream to receivers for multi-source communication groups. Efficiency in this context means to minimize cost while meeting bounds on the end-to-end delay of the application. The authors adopt the multi-core approach and utilize SPAN (Karaman and Hassane, 2007)—a core-based framework for multi-source group applications — as the basis to develop greedy randomized adaptive search procedures (GRASP) for the associated constrained cost minimization problem. The procedures are tested in asymmetric networks and computational results show that they consistently outperform their counterparts in the literature.

scholarly journals Genetic algorithm for network cost minimization using threshold based discounting

2003 ◽  
Vol 7 (4) ◽  
pp. 207-228 ◽  
Author(s):  
Hrvoje Podnar ◽  
Jadranka Skorin-Kapov
Keyword(s):  
Genetic Algorithm ◽  
Communication Networks ◽  
Branch And Bound ◽  
Cost Minimization ◽  
Total Flow ◽  
Cpu Time ◽  
Network Cost ◽  
Cost Minimization Problem ◽  
The Cost ◽  
Different Sources

We present a genetic algorithm for heuristically solving a cost minimization problem applied to communication networks with threshold based discounting. The network model assumes that every two nodes can communicate and offers incentives to combine flow from different sources. Namely, there is a prescribed threshold on every link, and if the total flow on a link is greater than the threshold, the cost of this flow is discounted by a factor α. A heuristic algorithm based on genetic strategy is developed and applied to a benchmark set of problems. The results are compared with former branch and bound results using the CPLEX® solver. For larger data instances we were able to obtain improved solutions using less CPU time, confirming the effectiveness of our heuristic approach.

scholarly journals PEMROGRAMAN LINEAR INTEGER DENGAN ENAM VARIABEL ORIENTASI KARGO UNTUK MASALAH MINIMISASI BIAYA PEMUATAN MULTI-KONTAINER

2020 ◽  
Vol 15 (3) ◽  
pp. 162-168
Author(s):  
Dian Pratiwi Sahar ◽  
Mohammad Thezar Afifudin
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Cost Minimization ◽  
Mathematic Model ◽  
Transport Cost ◽  
Container Loading ◽  
Volume Load ◽  
Cost Minimization Problem ◽  
The Given

Penelitian ini bertujuan untuk mengembangkan model matematika untuk masalah minimisasi biaya pemuatan multi-kontainer dengan enam variabel orientasi kargo. Masalah ini dirumuskan sebagai model pemrograman linier biner integer untuk meminimalkan biaya. Faktor-faktor yang dipertimbangkan dalam formulasi termasuk alokasi kargo, lokasi kargo, hubungan kargo, dan orientasi kargo. Sedangkan, biaya yang dipertimbangkan termasuk biaya muatan volume kontainer ke kargo dan biaya transportasi kargo ke kontainer. Validasi model dilakukan melalui percobaan numerik pada ukuran kecil kargo dan kontainer. Hasil penelitian menunjukkan bahwa model dengan konsep orientasi kargo yang dikembangkan dapat menyelesaikan masalah sesuai dengan parameter numerik yang diberikan. Abstract[Integer Linear Programming with Six Cargo Orientation Variables for Multi-Container Loading Cost Minimization Problem] This research aims to develop the mathematic model for multi-container loading cost minimization problems with six cargo orientation variables. The problem is formulated as a binary integer linear programming model to minimize costs. The factors considered in the formulation include cargo allocation, cargo location, cargo relations, and cargo orientation. Whereas, the costs considered include the container volume load cost to cargo and the cargo transport cost to the container. Model validation is performed through numerical experiments on the small size of cargo and containers. The results show that the model with developed cargo orientation concept can solve the problem according to the given numerical parameters.Keywords: integer programming; cargo orientation; container loading; cost minimization

scholarly journals Membrane-Based Processes: Optimization of Hydrogen Separation by Minimization of Power, Membrane Area, and Cost

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 221 ◽  
Author(s):  
Patricia Mores ◽  
Ana Arias ◽  
Nicolás Scenna ◽  
José Caballero ◽  
Sergio Mussati ◽  
...  
Keyword(s):  
Cost Minimization ◽  
Initial Guess ◽  
Total Power ◽  
Total Annual Cost ◽  
Membrane Area ◽  
Trade Offs ◽  
Processing Plants ◽  
Cost Minimization Problem ◽  
H2 Recovery ◽  
Total Membrane

This work deals with the optimization of two-stage membrane systems for H2 separation from off-gases in hydrocarbons processing plants to simultaneously attain high values of both H2 recovery and H2 product purity. First, for a given H2 recovery level of 90%, optimizations of the total annual cost (TAC) are performed for desired H2 product purity values ranging between 0.90 and 0.95 mole fraction. One of the results showed that the contribution of the operating expenditures is more significant than the contribution of the annualized capital expenditures (approximately 62% and 38%, respectively). In addition, it was found that the optimal trade-offs existing between process variables (such as total membrane area and total electric power) depend on the specified H2 product purity level. Second, the minimization of the total power demand and the minimization of the total membrane area were performed for H2 recovery of 90% and H2 product purity of 0.90. The TAC values obtained in the first and second cases increased by 19.9% and 4.9%, respectively, with respect to that obtained by cost minimization. Finally, by analyzing and comparing the three optimal solutions, a strategy to systematically and rationally provide ‘good’ lower and upper bounds for model variables and initial guess values to solve the cost minimization problem by means of global optimization algorithms is proposed, which can be straightforward applied to other processes.

scholarly journals Optimal Day-Ahead Scheduling of a Smart Micro-Grid via a Probabilistic Model for Considering the Uncertainty of Electric Vehicles’ Load

2019 ◽  
Vol 9 (22) ◽  
pp. 4872 ◽  
Author(s):  
Behnam Rasouli ◽  
Mohammad Javad Salehpour ◽  
Jin Wang ◽  
Gwang-jun Kim
Keyword(s):  
Electric Vehicles ◽  
Cost Minimization ◽  
Power Level ◽  
Market Price ◽  
Simulation Method ◽  
Mixed Integer ◽  
Proposed Model ◽  
Battery Capacity ◽  
Micro Grid ◽  
Cost Minimization Problem

This paper presents a new model based on the Monte Carlo simulation method for considering the uncertainty of electric vehicles’ charging station’s load in a day-ahead operation optimization of a smart micro-grid. In the proposed model, some uncertain effective factors on the electric vehicles’ charging station’s load including battery capacity, type of electric vehicles, state of charge, charging power level and response to energy price changes are considered. In addition, other uncertainties of operating parameters such as market price, photovoltaic generation and loads are also considered. Therefore, various stochastic scenarios are generated and involved in a cost minimization problem, which is formulated in the form of mixed-integer linear programming. Finally, the proposed model is simulated on a typical micro-grid with two 60 kW micro-turbines, a 60 kW photovoltaic unit and some loads. The results showed that by applying the proposed model for estimation of charging station load, the total operation cost decreased.

scholarly journals Stopping at the maximum of geometric Brownian motion when signals are received

2005 ◽  
Vol 42 (03) ◽  
pp. 826-838 ◽  
Author(s):  
X. Guo ◽  
J. Liu
Keyword(s):  
Brownian Motion ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Geometric Brownian Motion ◽  
Stopping Rules ◽  
Optimal Stopping Problem ◽  
Signal Process ◽  
Optimal Stopping Time ◽  
A Free Boundary Problem ◽  
Random Times

Consider a geometric Brownian motion X t (ω) with drift. Suppose that there is an independent source that sends signals at random times τ 1 < τ 2 < ⋯. Upon receiving each signal, a decision has to be made as to whether to stop or to continue. Stopping at time τ will bring a reward S τ , where S t = max(max0≤u≤t X u , s) for some constant s ≥ X 0. The objective is to choose an optimal stopping time to maximize the discounted expected reward E[e−r τ i S τ i | X 0 = x, S 0 = s], where r is a discount factor. This problem can be viewed as a randomized version of the Bermudan look-back option pricing problem. In this paper, we derive explicit solutions to this optimal stopping problem, assuming that signal arrival is a Poisson process with parameter λ. Optimal stopping rules are differentiated by the frequency of the signal process. Specifically, there exists a threshold λ* such that if λ>λ*, the optimal stopping problem is solved via the standard formulation of a ‘free boundary’ problem and the optimal stopping time τ * is governed by a threshold a * such that τ * = inf{τ n : X τ n ≤a * S τ n }. If λ≤λ* then it is optimal to stop immediately a signal is received, i.e. at τ * = τ 1. Mathematically, it is intriguing that a smooth fit is critical in the former case while irrelevant in the latter.

scholarly journals Energy Cost Minimization in Heterogeneous Cellular Networks with Hybrid Energy Supplies

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Bang Wang ◽  
Qiao Kong ◽  
Qiang Yang
Keyword(s):  
Energy Consumption ◽  
Cellular Networks ◽  
Minimization Problem ◽  
Energy Cost ◽  
Cost Minimization ◽  
Energy Allocation ◽  
Green Energy ◽  
User Association ◽  
Heterogeneous Cellular Networks ◽  
Cost Minimization Problem

The ever increasing data demand has led to the significant increase of energy consumption in cellular mobile networks. Recent advancements in heterogeneous cellular networks and green energy supplied base stations provide promising solutions for cellular communications industry. In this article, we first review the motivations and challenges as well as approaches to address the energy cost minimization problem for such green heterogeneous networks. Owing to the diversities of mobile traffic and renewable energy, the energy cost minimization problem involves both temporal and spatial optimization of resource allocation. We next present a new solution to illustrate how to combine the optimization of the temporal green energy allocation and spatial mobile traffic distribution. The whole optimization problem is decomposed into four subproblems, and correspondingly our proposed solution is divided into four parts: energy consumption estimation, green energy allocation, user association, and green energy reallocation. Simulation results demonstrate that our proposed algorithm can significantly reduce the total energy cost.

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