Bat algorithm assisted by ordinal optimization for solving discrete probabilistic bicriteria optimization problems

The discrete probabilistic bicriteria optimization problem (DPBOP) is a discrete optimization problem with probabilistic criteria which should be optimized simultaneously. The DPBOP belongs to a class of NP-hard problems because the computing time increases much faster when the size of the solution space increases. To solve the DPBOP efficiently, an algorithm that used bat algorithm (BA) assisted by ordinal optimization (OO), abbreviated as BAOO, is proposed to determine an outstanding solution within an acceptable time. The BAOO algorithm comprises three parts, surrogate model, exploration and exploitation. In surrogate model, the support vector regression is utilized as a fitness evaluation of a solution. In exploration, an amended bat algorithm is adopted to select N superior solutions from the whole solution space. In exploitation, an intensified optimal computing budget allocation scheme is adopted to decide an outstanding solution from the N superior solutions. The above three parts substantially decrease the required computing overhead of DPBOP. Finally, the BAOO algorithm is applied to a facility-sizing optimization problem in factory, which is formulated as a DPBOP. Three different size problems are considered as test examples. The BAOO algorithm is compared with three general optimization methods, particle swarm optimization, genetic algorithm and evolutionary strategy. Experimental results illustrate that the BAOO algorithm yields an outstanding solution with a higher quality and efficiency than three general optimization methods.