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 new ant colony optimization model for complex graph-based problems

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de lectura: julio de 2014Nowadays, there is a huge number of problems that due to their complexity have employed heuristic-based algorithms to search for near-to-optimal (or even optimal) solutions. These problems are usually NP-complete, so classical algorithms are not the best candidates to address these problems because they need a large amount of computational resources, or they simply cannot find any solution when the problem grows. Some classical examples of these kind of problems are the Travelling Salesman Problem (TSP) or the N-Queens problem. It is also possible to find examples in real and industrial domains related to the optimization of complex problems, like planning, scheduling, Vehicle Routing Problems (VRP), WiFi network Design Problem (WiFiDP) or behavioural pattern identification, among others. Regarding to heuristic-based algorithms, two well-known paradigms are Swarm Intelligence and Evolutionary Computation. Both paradigms belongs to a subfield from Artificial Intelligence, named Computational Intelligence that also contains Fuzzy Systems, Artificial Neural Networks and Artificial Immune Systems areas. Swarm Intelligence (SI) algorithms are focused on the collective behaviour of selforganizing systems. These algorithms are characterized by the generation of collective intelligence from non-complex individual behaviour and the communication schemes amongst them. Some examples of SI algorithms are particle swarm optimization, ant colony optimization (ACO), bee colony optimization o bird flocking. Ant Colony Optimization (ACO) are based on the foraging behaviour of these insects. In these kind of algorithms, the ants take different decisions during their execution that allows them to build their own solution to the problem. Once any ant has finished its execution, the ant goes back through the followed path and it deposits, in the environment, pheromones that contains information about the built solution. These pheromones will influence the decision of future ants, so there is an indirect communication through the environment called stigmergy. When an ACO algorithm is applied to any of the optimization problems just described, the problem is usually modelled into a graph. Nevertheless, the classical graph-based representation is not the best one for the execution of ACO algorithms because it presents some important pitfalls. The first one is related to the polynomial, or even exponential, growth of the resulting graph. The second pitfall is related to those problems that needs from real variables because these problems cannot be modelled using the classical graph-based representation. On the other hand, Evolutionary Computation (EC) are a set of population-based algorithms based in the Darwinian evolutionary process. In this kind of algorithms there is one (or more) population composed by different individuals that represent a possible solution to the problem. For each iteration, the population evolves by the use of evolutionary procedures which means that better individuals (i.e. better solutions) are generated along the execution of the algorithm. Both kind of algorithms, EC and SI, have been traditionally applied in previous NP-hard problems. Different population-based strategies have been developed, compared and even combined to design hybrid algorithms. This thesis has been focused on the analysis of classical graph-based representations and its application in ACO algorithms into complex problems, and the development of a new ACO model that tries to take a step forward in this kind of algorithms. In this new model, the problem is represented using a reduced graph that affects to the ants behaviour, which becomes more complex. Also, this size reduction generates a fast growth in the number of pheromones created. For this reason, a new metaheuristic (called Oblivion Rate) has been designed to control the number of pheromones stored in the graph. In this thesis different metaheuristics have been designed for the proposed system and their performance have been compared. One of these metaheuristics is the Oblivion Rate, based on an exponential function that takes into account the number of pheromones created in the system. Other Oblivion Rate function is based on a bioinspired swarm algorithm that uses some concepts extracted from the evolutionary algorithms. This bio-inspired swarm algorithm is called Coral Reef Opmization (CRO) algorithm and it is based on the behaviour of the corals in a reef. Finally, to test and validate the proposed model, different domains have been used such as the N-Queens Problem, the Resource-Constraint Project Scheduling Problem, the Path Finding problem in Video Games, or the Behavioural Pattern Identification in users. In some of these domains, the performance of the proposed model has been compared against a classical Genetic Algorithm to provide a comparative study and perform an analytical comparison between both approaches.En la actualidad, existen un gran número de problemas que debido a su complejidad necesitan algoritmos basados en heurísticas para la búsqueda de solucionas subóptimas (o incluso óptimas). Normalmente, estos problemas presentan una complejidad NP-completa, por lo que los algoritmos clásicos de búsqueda de soluciones no son apropiados ya que necesitan una gran cantidad de recursos computacionales, o simplemente, no son capaces de encontrar alguna solución cuando el problema crece. Ejemplos clásicos de este tipo de problemas son el problema del vendedor viajero (o TSP del inglés Travelling Salesman Problem) o el problema de las N-reinas. También se pueden encontrar ejemplos en dominios reales o industriales que generalmente están ligados a temas de optimización de sistemas complejos, como pueden ser problemas de planificación, scheduling, problemas de enrutamiento de vehículos (o VRP del inglés Vehicle Routing Problem), el diseño de redes Wifi abiertas (o WiFiDP del inglés WiFi network Design Problem), o la identificación de patrones de comportamiento, entre otros. En lo referente a los algoritmos basados en heuristicas, dos paradigmas muy conocidos son los algoritmos de enjambre (Swarm Intelligence) y la computación evolutiva (Evolutionary Computation). Ambos paradigmas pertencen al subárea de la Inteligencia Artificial denominada Inteligencia Computacional, que además contiene los sistemas difusos, redes neuronales y sistemas inmunológicos artificiales. Los algoritmos de inteligencia de enjambre, o Swarm Intelligence, se centran en el comportamiento colectivo de sistemas auto-organizativos. Estos algoritmos se caracterizan por la generación de inteligencia colectiva a partir del comportamiento, no muy complejo, de los individuos y los esquemas de comunicación entre ellos. Algunos ejemplos son particle swarm optimization, ant colony optimization (ACO), bee colony optimization o bird flocking. Los algoritmos de colonias de hormigas (o ACO del inglés Ant Colony Optimization) se basan en el comportamiento de estos insectos en el proceso de recolección de comida. En este tipo de algoritmos, las hormigas van tomando decisiones a lo largo de la simulación que les permiten construir su propia solución al problema. Una vez que una hormiga termina su ejecución, deshace el camino andado depositando en el entorno feronomas que contienen información sobre la solución construida. Estas feromonas influirán en las decisiones de futuras hormigas, por lo que produce una comunicación indirecta utilizando el entorno. A este proceso se le llama estigmergia. Cuando un algoritmo de hormigas se aplica a alguno de los problemas de optimización descritos anteriormente, se suele modelar el problema como un grafo sobre el cual se ejecutarán las hormigas. Sin embargo, la representación basada en grafos clásica no parece ser la mejor para la ejecución de algoritmos de hormigas porque presenta algunos problemas importantes. El primer problema está relacionado con el crecimiento polinómico, o incluso expnomencial, del grafo resultante. El segundo problema tiene que ver con los problemas que necesitan de variables reales, o de coma flotante, porque estos problemas, con la representación tradicional basada en grafos, no pueden ser modelados. Por otro lado, los algoritmos evolutivos (o EC del inglés Evolutionary Computation) son un tipo de algoritmos basados en población que están inspirados en el proceso evolutivo propuesto por Darwin. En este tipo de algoritmos, hay una, o varias, poblaciones compuestas por individuos diferentes que representan problems solutiones al problema modelado. Por cada iteración, la población evoluciona mediante el uso de procedimientos evolutivos, lo que significa que mejores individuos (mejores soluciones) son creados a lo largo de la ejecución del algoritmo. Ambos tipos de algorithmos, EC y SI, han sido tradicionalmente aplicados a los problemas NPcompletos descritos anteriormente. Diferentes estrategias basadas en población han sido desarrolladas, comparadas e incluso combinadas para el diseño de algoritmos híbridos. Esta tesis se ha centrado en el análisis de los modelos clásicos de representación basada en grafos de problemas complejos para la posterior ejecución de algoritmos de colonias de hormigas y el desarrollo de un nuevo modelo de hormigas que pretende suponer un avance en este tipo de algoritmos. En este nuevo modelo, los problemas son representados en un grafo más compacto que afecta al comportamiento de las hormigas, el cual se vuelve más complejo. Además, esta reducción en el tamaño del grafo genera un rápido crecimiento en el número de feronomas creadas. Por esta razón, una nueva metaheurística (llamada Oblivion Rate) ha sido diseñada para controlar el número de feromonas almacenadas en el grafo. En esta tesis, varias metaheuristicas han sido diseñadas para el sistema propuesto y sus rendimientos han sido comparados. Una de estas metaheurísticas es la Oblivion Rate basada en una función exponencial que tiene en cuenta el número de feromonas creadas en el sistema. Otra Oblivion Rate está basada en un algoritmo de enjambre bio-inspirado que usa algunos conceptos extraídos de la computación evolutiva. Este algoritmo de enjambre bio-inspirado se llama Optimización de arrecifes de corales (o CRO del inglés Coral Reef Optimization) y está basado en el comportamiento de los corales en el arrecife. Finalmente, para validar y testear el modelo propuesto, se han utilizado diversos dominios de aplicación como son el problema de las N-reinas, problemas de planificación de proyectos con restricciones de recursos, problemas de búsqueda de caminos en entornos de videojuegos y la identificación de patrones de comportamiento de usuarios. En algunos de estos dominios, el rendimiento del modelo propuesto ha sido comparado contra un algoritmo genético clásico para realizar un estudio comparativo, y analítico, entre ambos enfoques

Time-Cost Tradeoff and Resource-Scheduling Problems in Construction: A State-of-the-Art Review

Duration, cost, and resources are defined as constraints in projects. Consequently, Construction manager needs to balance between theses constraints to ensure that project objectives are met. Choosing the best alternative of each activity is one of the most significant problems in construction management to minimize project duration, project cost and also satisfies resources constraints as well as smoothing resources. Advanced computer technologies could empower construction engineers and project managers to make right, fast and applicable decisions based on accurate data that can be studied, optimized, and quantified with great accuracy. This article strives to find the recent improvements of resource-scheduling problems and time-cost trade off and the interacting between them which can be used in innovating new approaches in construction management. To achieve this goal, a state-of-the-art review, is conducted as a literature sample including articles implying three areas of research; time-cost trade off, constrained resources and unconstrained resources. A content analysis is made to clarify contributions and gaps of knowledge to help suggesting and specifying opportunities for future research

Optimized Resource-Constrained Method for Project Schedule Compression

Construction projects are unique and can be executed in an accelerated manner to meet market conditions. Accordingly, contractors need to compress project durations to meet client changing needs and related contractual obligations and recover from delays experienced during project execution. This acceleration requires resource planning techniques such as resource leveling and allocation. Various optimization methods have been proposed for the resource-constrained schedule compression and resource allocation and leveling individually. However, in real-world construction projects, contractors need to consider these aspects concurrently. For this purpose, this study proposes an integrated method that allows for joint consideration of the above two aspects. The method aims to optimize project duration and costs through the resources and cost of the execution modes assigned to project activities. It accounts for project cost and resource-leveling based on costs and resources imbedded in these modes of execution. The method's objective is to minimize the project duration and cost, including direct cost, indirect cost, and delay penalty, and strike a balance between the cost of acquiring and releasing resources on the one hand and the cost of activity splitting on the other hand. The novelty of the proposed method lies in its capacity to consider resource planning and project scheduling under uncertainty simultaneously while accounting for activity splitting. The proposed method utilizes the fuzzy set theory (FSs) for modeling uncertainty associated with the duration and cost of project activities and genetic algorithm (GA) for scheduling optimization. The method has five main modules that support two different optimization methods: modeling uncertainty and defuzzification module; scheduling module; cost calculations module; sensitivity IV analysis module; and decision-support module. The two optimization methods use the genetic algorithm as an optimization engine to find a set of non-dominated solutions. One optimization method uses the elitist non-dominated sorting genetic algorithm (NSGA-II), while the other uses a dynamic weighted optimization genetic algorithm. The developed scheduling and optimization method is coded in python as a stand-alone automated computerized tool to facilitate the needed iterative rescheduling of project activities and project schedule optimization. The developed method is applied to a numerical example to demonstrate its use and to illustrate its capabilities. Since the adopted numerical example is not a resource-constrained optimization example, the proposed optimization methods are validated through a multi-layered comparative analysis that involves performance evaluation, statistical comparisons, and performance stability evaluation. The performance evaluation results demonstrated the superiority of the NSGA-II against the dynamic weighted optimization genetic algorithm in finding better solutions. Moreover, statistical comparisons, which considered solutions’ mean, and best values, revealed that both optimization methods could solve the multi-objective time-cost optimization problem. However, the solutions’ range values indicated that the NSGA-II was better in exploring the search space before converging to a global optimum; NSGA-II had a trade-off between exploration (exploring the new search space) and exploitation (using already detected points to search the optimum). Finally, the coefficient of variation test revealed that the NSGA-II performance was more stable than that of the dynamic weighted optimization genetic algorithm. It is expected that the developed method can assist contractors in preparation for efficient schedule compression, which optimizes schedule and ensures efficient utilization of their resources

Enhancing the Performance of Search Heuristics. Variable Fitness Functions and other Methods to Enhance Heuristics for Dynamic Workforce Scheduling.

Scheduling large real world problems is a complex process and finding high quality solutions is not a trivial task. In cooperation with Trimble MRM Ltd., who provide scheduling solutions for many large companies, a problem is identified and modelled. It is a general model which encapsulates several important scheduling, routing and resource allocation problems in literature. Many of the state-of-the-art heuristics for solve scheduling problems and indeed other problems require specialised heuristics tailored for the problem they are to solve. While these provide good solutions a lot of expert time is needed to study the problem, and implement solutions. This research investigates methods to enhance existing search based methods. We study hyperheuristic techniques as a general search based heuristic. Hyperheuristics raise the generality of the solution method by using a set of tools (low level heuristics) to work on the solution. These tools are problem specific and usually make small changes to the problem. It is the task of the hyperheuristic to determine which tool to use and when. Low level heuristics using exact/heuristic hybrid method are used in this thesis along with a new Tabu based hyperheuristic which decreases the amount of CPU time required to produce good quality solutions. We also develop and investigate the Variable Fitness Function approach, which provides a new way of enhancing most search-based heuristics in terms of solution quality. If a fitness function is pushing hard in a certain direction, a heuristic may ultimately fail because it cannot escape local minima. The Variable Fitness Function allows the fitness function to change over the search and use objective measures not used in the fitness calculation. The Variable Fitness Function and its ability to generalise are extensively tested in this thesis. The two aims of the thesis are achieved and the methods are analysed in depth. General conclusions and areas of future work are also identified

Meta-RaPS Hybridization with Machine Learning Algorithms

This dissertation focuses on advancing the Metaheuristic for Randomized Priority Search algorithm, known as Meta-RaPS, by integrating it with machine learning algorithms. Introducing a new metaheuristic algorithm starts with demonstrating its performance. This is accomplished by using the new algorithm to solve various combinatorial optimization problems in their basic form. The next stage focuses on advancing the new algorithm by strengthening its relatively weaker characteristics. In the third traditional stage, the algorithms are exercised in solving more complex optimization problems. In the case of effective algorithms, the second and third stages can occur in parallel as researchers are eager to employ good algorithms to solve complex problems. The third stage can inadvertently strengthen the original algorithm. The simplicity and effectiveness Meta-RaPS enjoys places it in both second and third research stages concurrently. This dissertation explores strengthening Meta-RaPS by incorporating memory and learning features. The major conceptual frameworks that guided this work are the Adaptive Memory Programming framework (or AMP) and the metaheuristic hybridization taxonomy. The concepts from both frameworks are followed when identifying useful information that Meta-RaPS can collect during execution. Hybridizing Meta-RaPS with machine learning algorithms helped in transforming the collected information into knowledge. The learning concepts selected are supervised and unsupervised learning. The algorithms selected to achieve both types of learning are the Inductive Decision Tree (supervised learning) and Association Rules (unsupervised learning). The objective behind hybridizing Meta-RaPS with an Inductive Decision Tree algorithm is to perform online control for Meta-RaPS\u27 parameters. This Inductive Decision Tree algorithm is used to find favorable parameter values using knowledge gained from previous Meta-RaPS iterations. The values selected are used in future Meta-RaPS iterations. The objective behind hybridizing Meta-RaPS with an Association Rules algorithm is to identify patterns associated with good solutions. These patterns are considered knowledge and are inherited as starting points for in future Meta-RaPS iteration. The performance of the hybrid Meta-RaPS algorithms is demonstrated by solving the capacitated Vehicle Routing Problem with and without time windows