Kelley (1961), Fulkerson (1961), Siemens (1971), Salem & Elmaghraby (1994), Hendrickson & Au (1989), Tareghian & Taheri (2006), and Chen & Tsai (2011) put forward linear approaches for time-cost problems. Linear time-cost relationship is a conventional deterministic model for defining the time-cost problems and numerous studies have been presented in the literature formerly. The most traditional form of time-cost relationship is expressed as linear. On the other hand, different time-cost relationships can occur depending on the cost components of the project. Undoubtedly, the duration has a strong relation with the resource and they act each other inversely proportional. This acceleration called crashing which can be achieved by additional resources or new technological changes, but they always cause increases in cost. For this purpose, some of the activities must be accelerated to reduce the total project duration. However, the decision makers sometimes have to complete the project earlier due to various reasons such as unforeseen delays, incentive contracts, imposed deadlines, contract commitments, overhead costs and pressure to move resources to other project. Generally, all activities are considered with normal durations in traditional project planning ( Klerides & Hadjiconstantinou, 2015).

Palabras clave: Algoritmo híbrido método metaheurístico planificación de proyectos compensación de tiempo-costo La comparación de resultados numéricos con diferentes algoritmos metaheurísticos demuestra la efectividad y eficiencia de F-PSO con respecto a la optimización de los resultados de tiempo y costo. La aplicabilidad y validez del método propuesto se confirma realizando un proyecto de 18 actividades como un problema de referencia. En este método, el problema se modela con varios modos de ejecución para seleccionar el óptimo para cada actividad. Este artículo presenta un nuevo algoritmo llamado F-PSO que consiste en hibridar el Algoritmo Firefly (FA) con la Optimización de Enjambre de Partículas (PSO). En los últimos años, los algoritmos metaheurísticos son métodos sobresalientes en este campo debido a su estructura flexible y adaptable.

Además de ser uno de los temas más importantes de la gestión de la construcción, este problema se llama compensación - tiempo-costo (TCTO), que es extremadamente difícil de resolver con métodos matemáticos tradicionales. En general, quienes toman las decisiones generalmente buscan diferentes alternativas que reduzcan el tiempo y el costo. Recientemente, los gerentes de proyecto tienen que disminuir la duración total y los costos de los proyectos más que antes debido al entorno competitivo. La finalización de las actividades en un tiempo y costo óptimos desempeña un papel importante en los proyectos de construcción. Key words: Hybrid algorithm metaheuristic method project planning time-cost trade-off Comparison of numerical results with different metaheuristic algorithms demonstrates the effectiveness and efficiency of F-PSO with regard to optimality of time and cost outcomes. The applicability and validity of the proposed method is confirmed by performing 18-activity project as a benchmark problem. In this method, the problem is modelled with various execution modes to select the optimal one for each activity. This paper presents a new algorithm called F-PSO which consists of hybridizing Firefly Algorithm (FA) with Particle Swarm Optimization (PSO). In recent years, metaheuristic algorithms are outstanding methods in this field due to their flexible and adaptable structure. As well as being one of the most major topics of construction management, this problem called time-cost trade-off (TCTO) which is extremely difficult to solve with traditional mathematical methods.

Mostly, decision makers usually seek different alternatives which reduce time and cost. Recently, project managers have to decrease the total durations and costs of the projects more than before due to the competitive environment. Completion of the activities within optimal time and cost plays a significant role in construction projects.

Costo harmony test