A Method for Solving Optimization Problems in Continuous Space Using Ant Colony Algorithm

Abstract

We state our algorithm using the nonlinear programming (NLP) problem, objective function G is a given non-linear function. Constraint conditions that represented by a set of inequalities form a convex domain of R ⁿ. We can obtain the minimal n-d hypercube that can be defined as the following inequalities: l _i≤x _i≤U _i (I = 1, 2, …, n). Let the total number of ants be m and the m initial solution vectors are chosen at random. All the ith components of these initial solution vectors construct a group of candidate values of the ith component of solution vector. If we use n vertices to represent the n components and the edges between vertex i and vertex i+1 to represent the candidate values of component i, a path from the start vertex to the last vertex represents a solution vector whose n edges represent n components. We denote the jth edge between vertices i and i+1 as (i ,j) and its intensity of trail information at time t as τ_ij(t).