From weak Allee effect to no Allee effect in Richards’ growth models

Population dynamics have been attracting interest since many years. Among the considered models, the Richards’ equations remain one of the most popular to describe biological growth processes. On the other hand, Allee effect is currently a major focus of ecological research, which occurs when positive density dependence dominates at low densities. In this chapter, we propose the dynamical study of classes of functions based on Richards’ models describing the existence or not of Allee effect. We investigate bifurcation structures in generalized Richards’ functions and we look for the conditions in the (β, r) parameter plane for the existence of a weak Allee effect region. We show that the existence of this region is related with the existence of a dovetail structure. When the Allee limit varies, the weak Allee effect region disappears when the dovetail structure also disappears. Consequently, we deduce the transition from the weak Allee effect to no Allee effect to this family of functions. To support our analysis, we present fold and flip bifurcation curves and numerical simulations of several bifurcation diagrams.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.

Optimal scheduling of aircrafts’ engines repair process

We address a real world scheduling problem concerning the repair process of aircrafts’ engines by TAP - Maintenance & Engineering (TAP-ME). TAP-ME is the maintenance, repair and overhaul organization of TAP Portugal, Portugal’s leading airline, which employs about 4000 persons to provide maintenance and engineering services in aircraft, engines and components. TAP-ME is aiming to optimize its maintenance services, focusing on the reduction of the engines repair turnaround time.

Scheduling aircraft’s engines repair process: a mathematical model

In this talk, we discuss a scheduling problem that originated at TAP - Maintenance & Engineering - the maintenance, repair and overhaul organization of Portugal’s leading airline. In the repair process of aircrafts’ engines, the operations to be scheduled may be executed on a certain workstation by any processor of a given set, and the objective is to minimize the total weighted tardiness. A mixed integer linear programming formulation, based on the flexible job shop scheduling, is presented here, along with computational experiment on a real instance, provided by TAP-ME, from a regular working week. The model was also tested using benchmarking instances available in literature.

Multi-objective Parallel Particle Swarm Optimization for Day-ahead Vehicle-To-Grid Scheduling

This paper presents a methodology for multi-objective day-ahead energy resource scheduling for smart grids considering intensive use of distributed generation and Vehicle- To-Grid (V2G). The main focus is the application of weighted Pareto to a multi-objective parallel particle swarm approach aiming to solve the dual-objective V2G scheduling: minimizing total operation costs and maximizing V2G income. A realistic mathematical formulation, considering the network constraints and V2G charging and discharging efficiencies is presented and parallel computing is applied to the Pareto weights. AC power flow calculation is included in the metaheuristics approach to allow taking into account the network constraints. A case study with a 33-bus distribution network and 1800 V2G resources is used to illustrate the performance of the proposed method.

Dispatch of distributed Energy Resources to Provide Energy and Reserve in Smart Grids using a Particle Swarm Optimization Approach

The smart grid concept is a key issue in the future power systems, namely at the distribution level, with deep concerns in the operation and planning of these systems. Several advantages and benefits for both technical and economic operation of the power system and of the electricity markets are recognized. The increasing integration of demand response and distributed generation resources, all of them mostly with small scale distributed characteristics, leads to the need of aggregating entities such as Virtual Power Players. The operation business models become more complex in the context of smart grid operation. Computational intelligence methods can be used to give a suitable solution for the resources scheduling problem considering the time constraints. This paper proposes a methodology for a joint dispatch of demand response and distributed generation to provide energy and reserve by a virtual power player that operates a distribution network. The optimal schedule minimizes the operation costs and it is obtained using a particle swarm optimization approach, which is compared with a deterministic approach used as reference methodology. The proposed method is applied to a 33-bus distribution network with 32 medium voltage consumers and 66 distributed generation units.

Decision support tool for Virtual Power Players: Hybrid Particle Swarm Optimization applied to Day-ahead Vehicle-To-Grid Scheduling

This paper presents a decision support tool methodology to help virtual power players (VPPs) in the Smart Grid (SGs) context to solve the day-ahead energy resource scheduling considering the intensive use of Distributed Generation (DG) and Vehicle-To-Grid (V2G). The main focus is the application of a new hybrid method combing a particle swarm approach and a deterministic technique based on mixedinteger linear programming (MILP) to solve the day-ahead scheduling minimizing total operation costs from the aggregator point of view. A realistic mathematical formulation, considering the electric network constraints and V2G charging and discharging efficiencies is presented. Full AC power flow calculation is included in the hybrid method to allow taking into account the network constraints. A case study with a 33-bus distribution network and 1800 V2G resources is used to illustrate the performance of the proposed method.

Stochastic Short-term Incentive-based Demand Response Scheduling of Load-serving Entities

In competitive electricity markets it is necessary for a profit-seeking load-serving entity (LSE) to optimally adjust the financial incentives offering the end users that buy electricity at regulated rates to reduce the consumption during high market prices. The LSE in this model manages the demand response (DR) by offering financial incentives to retail customers, in order to maximize its expected profit and reduce the risk of market power experience. The stochastic formulation is implemented into a test system where a number of loads are supplied through LSEs.

Application-Specific Modified Particle Swarm Optimization for energy resource scheduling considering vehicle-to-grid

This paper presents a modified Particle Swarm Optimization (PSO) methodology to solve the problem of energy resources management with high penetration of distributed generation and Electric Vehicles (EVs) with gridable capability (V2G). The objective of the day-ahead scheduling problem in this work is to minimize operation costs, namely energy costs, regarding the management of these resources in the smart grid context. The modifications applied to the PSO aimed to improve its adequacy to solve the mentioned problem. The proposed Application Specific Modified Particle Swarm Optimization (ASMPSO) includes an intelligent mechanism to adjust velocity limits during the search process, as well as self-parameterization of PSO parameters making it more user-independent. It presents better robustness and convergence characteristics compared with the tested PSO variants as well as better constraint handling. This enables its use for addressing real world large-scale problems in much shorter times than the deterministic methods, providing system operators with adequate decision support and achieving efficient resource scheduling, even when a significant number of alternative scenarios should be considered. The paper includes two realistic case studies with different penetration of gridable vehicles (1000 and 2000). The proposed methodology is about 2600 times faster than Mixed-Integer Non-Linear Programming (MINLP) reference technique, reducing the time required from 25 h to 36 s for the scenario with 2000 vehicles, with about one percent of difference in the objective function cost value.

Polyglutamine diseases (PolyQ): construction and characterization of yeast models

Dissertação apresentada para a obtenção do Grau de Mestre em Genética Molecular e Biomedicina, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

A framework to operate transformations between distinct models differing in modelling concepts

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

Distributed energy resources scheduling considering real-time resources forecast

Energy resource scheduling is becoming increasingly important, such as the use of more distributed generators and electric vehicles connected to the distribution network. This paper proposes a methodology to be used by Virtual Power Players (VPPs), regarding the energy resource scheduling in smart grids and considering day-ahead, hour-ahead and realtime time horizons. This method considers that energy resources are managed by a VPP which establishes contracts with their owners. The full AC power flow calculation included in the model takes into account network constraints. In this paper, distribution function errors are used to simulate variations between time horizons, and to measure the performance of the proposed methodology. A 33-bus distribution network with large number of distributed resources is used.

Real-time Energy Resource Scheduling considering a Real Portuguese Scenario

The development in power systems and the introduction of decentralized generation and Electric Vehicles (EVs), both connected to distribution networks, represents a major challenge in the planning and operation issues. This new paradigm requires a new energy resources management approach which considers not only the generation, but also the management of loads through demand response programs, energy storage units, EVs and other players in a liberalized electricity markets environment. This paper proposes a methodology to be used by Virtual Power Players (VPPs), concerning the energy resource scheduling in smart grids, considering day-ahead, hour-ahead and real-time scheduling. The case study considers a 33-bus distribution network with high penetration of distributed energy resources. The wind generation profile is based on a real Portuguese wind farm. Four scenarios are presented taking into account 0, 1, 2 and 5 periods (hours or minutes) ahead of the scheduling period in the hour-ahead and realtime scheduling.

A New Heuristic Providing an Effective Initial Solution for a Simulated Annealing approach to Energy Resource Scheduling in Smart Grids

An intensive use of dispersed energy resources is expected for future power systems, including distributed generation, especially based on renewable sources, and electric vehicles. The system operation methods and tool must be adapted to the increased complexity, especially the optimal resource scheduling problem. Therefore, the use of metaheuristics is required to obtain good solutions in a reasonable amount of time. This paper proposes two new heuristics, called naive electric vehicles charge and discharge allocation and generation tournament based on cost, developed to obtain an initial solution to be used in the energy resource scheduling methodology based on simulated annealing previously developed by the authors. The case study considers two scenarios with 1000 and 2000 electric vehicles connected in a distribution network. The proposed heuristics are compared with a deterministic approach and presenting a very small error concerning the objective function with a low execution time for the scenario with 2000 vehicles.