satisfactory solutions for resource-leveling problem in modern construction projects.
Symbiotic Organisms Search Algorithm
The SOS algorithm is a new metaheuristic algorithm developed by Cheng and Prayogo (2014). It was inspired by the dependencybased interactions seen among organisms in nature, which are known as symbiosis. Like most population-based metaheuristic algorithms, SOS has the following features: (1) it uses a population of organisms that contains candidate solutions used to seek the global solution over the search space; (2) it has special operators that use the candidate solutions to guide the search process; (3) it uses a selection mechanism to preserve the better solutions; and (4) it requires the proper setting of common control parameters such as population size and maximum number of evaluations.
However, unlike most metaheuristic algorithms that have additional control parameters (e.g., GA has crossover and mutation rates; PSO has inertia weight, cognitive factors, and social factors), SOS requires no algorithm-specific parameters. This is considered an advantage over competing algorithms because SOS does not need to perform parameter tuning . Improper tuning related to algorithm-specific parameters might increase computational time and produce local optima solutions.
In the early stage, a random ecosystem (population) matrix is created, each row representing a candidate solution to the corresponding problem. The number of organisms in the ecosystem, the so-called ecosystem size, is predetermined by the user. The rows in the matrix are called organisms, as in other metaheuristic algorithms. Each virtual organism represents a candidate solution to the corresponding problem or objective. The search begins after the initial ecosystem has been generated. During the search process, each organism benefits from continuous interaction with others in three different phases:
• Mutualism: one organism develops a relationship that benefits itself and the other—a classic example is the interaction between bees and flowers;
• Commensalism: one organism develops a relationship that benefits itself but does not impact the other—an example is the relationship between remora fish and sharks; and
• Parasitism: one organism develops a relationship that benefits itself but harms the other—an example is the plasmodium parasite, which uses its relationship with the anopheles mosquito to transfer between human hosts.
The three phases are adopted from the most common symbioses used by organisms to increase their fitness and survival advantage over the long term. During the interaction, the one that receives a benefit evolves to a fitter organism whereas the one who is harmed perishes. The mechanisms for updating the best organism are conducted after one generation of organisms has completed its three phases. The phases are repeated until the stopping criterion is achieved. The pseudocode shown in Fig. 1 summarizes the basic step of the SOS optimization procedure:
Discrete Symbiotic Organisms Search for
Multiple-Resources Leveling in Multiple Projects—the DSOS-MRLMP Model