Constraint Consensus Based Artificial Bee Colony Algorithm for Constrained Optimization Problems

Over the last few decades, evolutionary algorithms (EAs) have been widely adopted to solve complex optimization problems. However, EAs are powerless to challenge the constrained optimization problems (COPs) because they do not directly act to reduce constraint violations of constrained problems. In this paper, the robustly global optimization advantage of artificial bee colony (ABC) algorithm and the stably minor calculation characteristic of constraint consensus (CC) strategy for COPs are integrated into a novel hybrid heuristic algorithm, named ABCCC. CC strategy is fairly effective to rapidly reduce the constraint violations during the evolutionary search process. The performance of the proposed ABCCC is verified by a set of constrained benchmark problems comparing with two state-of-the-art CC-based EAs, including particle swarm optimization based on CC (PSOCC) and differential evolution based on CC (DECC). Experimental results demonstrate the promising performance of the proposed algorithm, in terms of both optimization quality and convergence speed.

Constraint consensus of heterogeneous multi-agent systems

In this brief paper, we study the constraint consensus problem of heterogeneous multi-agent systems. First, we provide an invariant set, which can be exactly obtained by solving linear equations. Then, a virtual system is defined on this invariant set such that it is the largest common embedded system of all the individual agents. Afterwards, a linear consensus protocol is proposed with the corresponding constraint consensus criterion. In particular, the above virtual system can reveal all the asymptotic dynamical behaviors if heterogeneous multi-agent systems achieve consensus. Finally, an example with numerical simulations is given to illustrate the validity of our criterion.

Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities

We give algorithms for solving the strict feasibility problem for linear matrix inequalities. These algorithms are based on John Chinneck’s constraint consensus methods, in particular, the method of his original paper and the modified DBmax constraint consensus method from his paper with Ibrahim. Our algorithms start with one of these methods as “Phase 1.” Constraint consensus methods work for any differentiable constraints, but we take advantage of the structure of linear matrix inequalities. In particular, for linear matrix inequalities, the crossing points of each constraint boundary with the consensus ray can be calculated. In this way we check for strictly feasible points in “Phase 2” of our algorithms. We present four different algorithms, depending on whether the original (basic) or DBmax constraint consensus vector is used in Phase 1 and, independently, in Phase 2. We present results of numerical experiments that compare the four algorithms. The evidence suggests that one of our algorithms is the best, although none of them are guaranteed to find a strictly feasible point after a given number of iterations. We also give results of numerical experiments indicating that our best method compares favorably to a new variant of the method of alternating projections.