Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

A random key based genetic algorithm for the resource constrained project scheduling problem

This paper presents a genetic algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities of the activities are defined by the genetic algorithm. The heuristic generates parameterized active schedules. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

An optimization approach for the job shop scheduling problem

This paper presents an optimization approach for the job shop scheduling problem (JSSP). The JSSP is a difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms. The proposed approach is based on a genetic algorithm technique. The scheduling rules such as SPT and MWKR are integrated into the process of genetic evolution. The chromosome representation of the problem is based on random keys. The schedules are constructed using a priority rule in which the priorities and delay times of the operations are defined by the genetic algorithm. Schedules are constructed using a procedure that generates parameterized active schedules. After a schedule is obtained a local search heuristic is applied to improve the solution. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed approach.

Simulação de um Pool Simétrico com validação técnica do despacho provisório e apresentação de medidas corretivas baseadas num despacho ótimo

Os mercados de energia elétrica são atualmente uma realidade um pouco por todo o mundo. Contudo, não é consensual o modelo regulatório a utilizar, o que origina a utilização de diferentes modelos nos diversos países que deram início ao processo de liberalização e de reestruturação do sector elétrico. A esses países, dado que a energia elétrica não é um bem armazenável, pelo menos em grandes quantidades, colocam-se questões importantes relacionadas com a gestão propriamente dita do seu sistema elétrico. Essas questões implicam a adoção de regras impostas pelo regulador que permitam ultrapassar essas questões. Este trabalho apresenta um estudo feito aos mercados de energia elétrica existentes um pouco por todo o mundo e que o autor considerou serem os mais importantes. Foi também feito um estudo de ferramentas de otimização essencialmente baseado em meta-heurísticas aplicadas a problemas relacionados com a operação dos mercados e com os sistemas elétricos de energia, como é o exemplo da resolução do problema do Despacho Económico. Foi desenvolvida uma aplicação que simula o funcionamento de um mercado que atua com o modelo Pool Simétrico, em que são transmitidas as ofertas de venda e compra de energia elétrica por parte dos produtores, por um lado, e dos comercializadores, consumidores elegíveis ou intermediários financeiros, por outro, analisando a viabilidade técnica do Despacho Provisório. A análise da viabilidade técnica do Despacho Provisório é verificada através do modelo DC de trânsito de potências. No caso da inviabilidade do Despacho Provisório, por violação de restrições afetas ao problema, são determinadas medidas corretivas a esse despacho, com base nas ofertas realizadas e recorrendo a um Despacho Ótimo. Para a determinação do Despacho Ótimo recorreu-se à meta-heurística Algoritmos Genéticos. A aplicação foi desenvolvida no software MATLAB utilizando a ferramenta Graphical User Interfaces. A rede de teste utilizada foi a rede de 14 barramentos do Institute of Electrical and Electronics Engineers (IEEE). A aplicação mostra-se competente no que concerne à simulação de um mercado com tipo de funcionamento Pool Simétrico onde são efetuadas ofertas simples e onde as transações ocorrem no mercado diário, porém, não reflete o problema real relacionado a este tipo de mercados. Trata-se, portanto, de um simulador básico de um mercado de energia cujo modelo de funcionamento se baseia no tipo Pool Simétrico.

Trajectory planning of redundant manipulators using genetic algorithms

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms. The results are compared with a genetic algorithm that adopts the direct kinematics. In both cases the trajectory planning is formulated as an optimization problem with constraints.

Discretization of complex-order algorithms for control applications

In this article we describe several methods for the discretization of the differintegral operator sa, where α = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.

Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena

The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.

Multi-agent system for distributed manufacturing scheduling with genetic algorithms and tabu search

Computerized scheduling methods and computerized scheduling systems according to exemplary embodiments. A computerized scheduling method may be stored in a memory and executed on one or more processors. The method may include defining a main multi-machine scheduling problem as a plurality of single machine scheduling problems; independently solving the plurality of single machine scheduling problems thereby calculating a plurality of near optimal single machine scheduling problem solutions; integrating the plurality of near optimal single machine scheduling problem solutions into a main multi-machine scheduling problem solution; and outputting the main multi-machine scheduling problem solution.

A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions

The container loading problem (CLP) is a combinatorial optimization problem for the spatial arrangement of cargo inside containers so as to maximize the usage of space. The algorithms for this problem are of limited practical applicability if real-world constraints are not considered, one of the most important of which is deemed to be stability. This paper addresses static stability, as opposed to dynamic stability, looking at the stability of the cargo during container loading. This paper proposes two algorithms. The first is a static stability algorithm based on static mechanical equilibrium conditions that can be used as a stability evaluation function embedded in CLP algorithms (e.g. constructive heuristics, metaheuristics). The second proposed algorithm is a physical packing sequence algorithm that, given a container loading arrangement, generates the actual sequence by which each box is placed inside the container, considering static stability and loading operation efficiency constraints.

Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising two different types of processors—such a platform is referred to as two-type platform. We present two low degree polynomial time-complexity algorithms, SA and SA-P, each providing the following guarantee. For a given two-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then (i) using SA, it is guaranteed to find such an assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which processors are 1+α times faster. The parameter 0<α≤1 is a property of the task set; it is the maximum of all the task utilizations that are no greater than 1. We evaluate average-case performance of both the algorithms by generating task sets randomly and measuring how much faster processors the algorithms need (which is upper bounded by 1+α/2 for SA and 1+α for SA-P) in order to output a feasible task assignment (intra-migrative for SA and non-migrative for SA-P). In our evaluations, for the vast majority of task sets, these algorithms require significantly smaller processor speedup than indicated by their theoretical bounds. Finally, we consider a special case where no task utilization in the given task set can exceed one and for this case, we (re-)prove the performance guarantees of SA and SA-P. We show, for both of the algorithms, that changing the adversary from intra-migrative to a more powerful one, namely fully-migrative, in which tasks can migrate between processors of any type, does not deteriorate the performance guarantees. For this special case, we compare the average-case performance of SA-P and a state-of-the-art algorithm by generating task sets randomly. In our evaluations, SA-P outperforms the state-of-the-art by requiring much smaller processor speedup and by running orders of magnitude faster.

Task Assignment Algorithms for Heterogeneous Multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising a constant number (denoted by t) of distinct types of processors—such a platform is referred to as a t-type platform. We present two algorithms, LPGIM and LPGNM, each providing the following guarantee. For a given t-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet their deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then: (i) LPGIM succeeds in finding such an assignment where the same restriction on task migration applies (intra-migrative) but given a platform in which only one processor of each type is 1 + α × t-1/t times faster and (ii) LPGNM succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which every processor is 1 + α times faster. The parameter α is a property of the task set; it is the maximum of all the task utilizations that are no greater than one. To the best of our knowledge, for t-type heterogeneous multiprocessors: (i) for the problem of intra-migrative task assignment, no previous algorithm exists with a proven bound and hence our algorithm, LPGIM, is the first of its kind and (ii) for the problem of non-migrative task assignment, our algorithm, LPGNM, has superior performance compared to state-of-the-art.

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.

On the Scalability of Constructive Interference in Low-Power Wireless Networks

12th European Conference on Wireless Sensor Networks (EWSN 2015). 9 to 11, Feb, 2015. Porto, Portugal