A Lagrangian based immune-inspired optimization framework for distributed systems

This paper presents a novel hybrid framework for cooperative conflict resolution in distributed system (DS) optimization problems that combines the Lagrangian decomposition (LD) method and the mechanisms offered by artificial immune systems. LD provides a means to derive simpler sub-problems by dropping complicated constraints, yet the challenge is to determine effective algorithms for updating the corresponding multipliers. After full decomposition of a single optimization problem derived from a DS into a number of sub-problems that are to be solved by individual intelligent agents, this paper introduces a distributed cooperative search framework (DCSF) whereby intelligent agents are designed for solving those sub-problems. The development of DCSF is inspired by the human immune system where algorithms of suppression and stimulation are formulated to compute the infeasibility (violation of relaxation constraints) and the affinity of candidate solutions individually. In this paper, DCSF is implemented on a distributed platform supported by Matlab to solve a generalized assignment problem (GAP) so as to demonstrate its behavior and performance in the realm of distributed combinatorial optimization.