Nonlinear displacement analysis of trusses using ant colony optimization

Abstract

For linear analysis of trusses, a linear matrix equation is solved. Nonlinear analysis of trusses requires a nonlinear matrix equation to be solved where the coefficient matrix depends on both the load vector and displacement vector. Such problems are often attacked by successive iterations and searching for local optimum. Such a brute force attack does not only require too much computing power and time, it also has risk of being stuck in the local minimum. A better approach could be using one of the Nature Inspired Algorithms; Ant Colony Optimization which is an optimization method often used for discrete problems. Both of the methods can be based on the principle of minimum energy. This principle states that for a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium. Ant Colony Optimization is a technique for optimization introduced in the early 1990's. Ant Colony Optimization is inspired from the real ant colonies. In the real world, ants initially wander randomly, and upon finding food return to their colony while laying down chemical pheromone trails to inform other ants indirectly about the path found. If other ants find such a path, they are likely not to keep travelling at random, but to instead follow the trail, returning and reinforcing it if they eventually find food. As the time passes and larger number of ants is wandering, the optimum path for the food source becomes clearer. The ants are likely to move through the trail with more pheromone, but there is no guarantee for that, any ant can choose finding another path. This behavior of ants allows optimization problems to escape from being stuck in the local minimum and missing better solutions. iii In this study, the goal is to analyze the nonlinear displacement of trusses using ant colony optimization. The continuous truss data is discretized to be solved by Ant Colony Optimization. The virtual ants are wandering on the solution space, trying to find the optimum solution(s) with the minimum energy. More pheromone will remain in the better paths, indicating best solution(s). The study intents to shorten the computing time and decrease the chance of being stuck in local optimum in truss displacement analysis.