The Project Scheduling Problem with Non-Deterministic Activities Duration: A Literature Review

Purpose: The goal of this article is to provide an extensive literature review of the models and solution procedures proposed by many researchers interested on the Project Scheduling Problem with nondeterministic activities duration. Design/methodology/approach: This paper presents an exhaustive literature review, identifying the existing models where the activities duration were taken as uncertain or random parameters. In order to get published articles since 1996, was employed the Scopus database. The articles were selected on the basis of reviews of abstracts, methodologies, and conclusions. The results were classified according to following characteristics: year of publication, mathematical representation of the activities duration, solution techniques applied, and type of problem solved. Findings: Genetic Algorithms (GA) was pointed out as the main solution technique employed by researchers, and the Resource-Constrained Project Scheduling Problem (RCPSP) as the most studied type of problem. On the other hand, the application of new solution techniques, and the possibility of incorporating traditional methods into new PSP variants was presented as research trends. Originality/value: This literature review contents not only a descriptive analysis of the published articles but also a statistical information section in order to examine the state of the research activity carried out in relation to the Project Scheduling Problem with non-deterministic activities duration.Peer Reviewe

A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems

This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA–PS–SQP algorithm is very efficient in solving power system economic dispatch problem

Solution of Different Types of Economic Load Dispatch Problems Using a Pattern Search Method

Direct search (DS) methods are evolutionary algorithms used to solve constrained optimization problems. DS methods do not require information about the gradient of the objective function when searching for an optimum solution. One such method is a pattern search (PS) algorithm. This study presents a new approach based on a constrained PS algorithm to solve various types of power system economic load dispatch (ELD) problems. These problems include economic dispatch with valve point (EDVP) effects, multi-area economic load dispatch (MAED), companied economic-environmental dispatch (CEED), and cubic cost function economic dispatch (QCFED). For illustrative purposes, the proposed PS technique has been applied to each of the above dispatch problems to validate its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method has been assessed and investigated through comparison with results reported in literature. The outcome is very encouraging and suggests that PS methods may be very efficient when solving power system ELD problems

Preconditioners for state constrained optimal control problems with Moreau-Yosida penalty function

Optimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau-Yosida regularization technique. This method has been studied recently and has proven to be advantageous compared to other approaches. In this paper we develop robust preconditioners for the efficient solution of the Newton steps associated with solving the Moreau-Yosida regularized problem. Numerical results illustrate the efficiency of our approach

Resource dedication problem in a multi-project environment

There can be different approaches to the management of resources within the context of multi-project scheduling problems. In general, approaches to multiproject scheduling problems consider the resources as a pool shared by all projects. On the other hand, when projects are distributed geographically or sharing resources between projects is not preferred, then this resource sharing policy may not be feasible. In such cases, the resources must be dedicated to individual projects throughout the project durations. This multi-project problem environment is defined here as the resource dedication problem (RDP). RDP is defined as the optimal dedication of resource capacities to different projects within the overall limits of the resources and with the objective of minimizing a predetermined objective function. The projects involved are multi-mode resource constrained project scheduling problems with finish to start zero time lag and non-preemptive activities and limited renewable and nonrenewable resources. Here, the characterization of RDP, its mathematical formulation and two different solution methodologies are presented. The first solution approach is a genetic algorithm employing a new improvement move called combinatorial auction for RDP, which is based on preferences of projects for resources. Two different methods for calculating the projects’ preferences based on linear and Lagrangian relaxation are proposed. The second solution approach is a Lagrangian relaxation based heuristic employing subgradient optimization. Numerical studies demonstrate that the proposed approaches are powerful methods for solving this problem

Proposal and Comparative Study of Evolutionary Algorithms for Optimum Design of a Gear System

This paper proposes a novel metaheuristic framework using a Differential Evolution (DE) algorithm with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Both algorithms are combined employing a collaborative strategy with sequential execution, which is called DE-NSGA-II. The DE-NSGA-II takes advantage of the exploration abilities of the multi-objective evolutionary algorithms strengthened with the ability to search global mono-objective optimum of DE, that enhances the capability of finding those extreme solutions of Pareto Optimal Front (POF) difficult to achieve. Numerous experiments and performance comparisons between different evolutionary algorithms were performed on a referent problem for the mono-objective and multi-objective literature, which consists of the design of a double reduction gear train. A preliminary study of the problem, solved in an exhaustive way, discovers the low density of solutions in the vicinity of the optimal solution (mono-objective case) as well as in some areas of the POF of potential interest to a decision maker (multi-objective case). This characteristic of the problem would explain the considerable difficulties for its resolution when exact methods and/or metaheuristics are used, especially in the multi-objective case. However, the DE-NSGA-II framework exceeds these difficulties and obtains the whole POF which significantly improves the few previous multi-objective studies.Fil: Méndez Babey, Máximo. Universidad de Las Palmas de Gran Canaria; EspañaFil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: González, Begoña. Universidad de Las Palmas de Gran Canaria; EspañaFil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin