Mathematical Derives of Evolutionary Algorithms for Multiple Criteria Decision Making

In multiple criteria decision making (MCDM) with interval-valued belief distributions (IVBDs), individual IVBDs on multiple criteria are combined explicitly or implicitly to generate the expected utilities of alternatives which can be used to make decisions with the aid of decision rules. Optimization models are usually constructed to implement such combination. To analyze a MCDM problem with a large number of criteria and grades used to profile IVBDs, effective algorithms are required to find the solutions to the optimization models within a large feasible region. We anticipate experimental results will indicate that particle swarm optimization algorithm is the best one to combine individual IVBDs and generate the minimum and maximum expected utilities of alternatives among the four algorithms.