jective FLP. Generally, quantitative factors are considered as material handling cost, time, etc., and qualitative factors are considered as closeness rating, hazardous movement between the facilities, etc. For solving and optimizing two or more objectives, two methods are available. First is weight approach method and second is non-dominated sorting method. In the former method, suitable weights are given to each objective and combined in a single objective function; while in later method, the objectives are defined separately and by making comparison of the solutions on the non-dominance criteria, best Pareto-optimal solutions are obtained. In this paper, equal area multi-objective FLPs which are formulated as quadratic assignment problem (QAP) are considered and optimized using biogeography based optimization (BBO) algorithm and non-dominated sorting BBO (NSBBO) algorithm. BBO is one of the efficient metaheuristic techniques, developed to solve complex optimization problems. Computational results of BBO algorithm using weight approach illustrate its better performance compared to other methods while solving multi-objective FLPs. Furthermore to obtain Pareto optimal solutions, NSBBO algorithm is implemented.

A non-dominated sorting genetic algorithm (NSGA-II) is applied to obtain Pareto optimal solutions in widely used advanced machining processes, i.e., electric discharge machining, electrochemical micromachining, ultrasonic machining, abrasive water jet machining. The solutions obtained using the proposed method is in the form of the Pareto-optimal front, thus, any solution is acceptable and can be utilized to obtain optimum performance of the considered processes. The obtained results using NSGA-II show good agreement with the results of previous researchers. Implementation of the proposed method shows benefits to the process engineer of the industries as they can select alternative parameters based on the requirement.

The selection of appropriate alternative in the industrial environment is an important but, at the same time, a complex and difficult problem because of the availability of a wide range of alternatives and similarity among them. Therefore, there is a need for simple, systematic, and logical methods or mathematical tools to guide decision makers in considering a number of selection attributes and their interrelations. In this paper, a hybrid decision making method of graph theory and matrix approach (GTMA) and analytical hierarchy process (AHP) is proposed. Three examples are presented to illustrate the potential of the proposed GTMA-AHP method and the results are compared with the results obtained using other decision making methods.