A simple and effective multi-attribute decision-making method, named as BHARAT method, is proposed in Part-1 of this paper and the same method is used now as a multi- and many-objective decision-making method for evaluating the Pareto optimal solutions. The proposed BHARAT method is used to identify the best compromise Pareto solution. Based on their importance for the given optimization problem, the objectives are ranked, and the weights are assigned. The weights of the objectives and the normalized values of the objectives for different Pareto optimal solutions are used to compute the total scores. The total scores are used to differentiate the alternative optimal solutions and an alternative solution that gets the highest total score is suggested as the best compromise solution. Three case studies are presented to illustrate and validate the proposed BHARAT method. The case study 1 is a multi-objective optimization problem related to cloud manufacturing with 3 objectives and 20 alternative solutions; case study 2 is a many-objective optimization problem of electro-discharge machining process with 4 objectives and 50 alternative solutions; case study 3 is a many-objective optimization of milling process parameters with 4 objectives and 100 alternative solutions. The outcomes of the suggested BHARAT method are compared with those of the other popular decision-making approaches for each of the three case studies considered. The suggested simple and more logical BHARAT method can be used in multi- and many-objective optimization problems to select the best compromise solution.

A simple and effective multi-criteria decision-making methodology named as “Best Holistic Adaptable Ranking of Attributes Technique (BHARAT)” is proposed that can be used in single- as well as group decision-making scenarios of the industrial environment. The attributes data for various alternatives can be quantitative or qualitative (i.e., expressed in linguistic terms). This paper proposes to transform the qualitative attributes into quantitative attributes by means of simple linear scales rather than complex fuzzy scales. The proposed BHARAT method normalizes the data with reference to the “best” alternative corresponding to an attribute and the normalization procedure is repeated for all the attributes to get the normalized data. A group of decision-makers or a decision-maker assigns ranks to the attributes according to how important they are deemed to be, and these ranks are then transformed into the proper weights. The total scores of the alternatives are calculated by multiplying the weights of the attributes by the corresponding normalized data of the attributes for different alternatives. Four industrial case studies are presented to illustrate the potential of the suggested BHARAT method. The first case study deals with the problem of an automated warehouse selection for a large industrial plant involving a single decision-maker, 13 attributes, and 4 alternative warehouses; the second case study deals with the problem of sustainable maintenance service provider selection for a large petrochemical plant involving fuzzy group decision-making with 5 decision-makers, 9 attributes, and 4 alternative maintenance service providers; the third case study deals with the problem of alternative strategy selection for implementation of a make-to-order system for passenger car manufacturers involving 6 factors, 18 sub-factors, and 3 alternative strategies; and the fourth case study deals with the problem of process parameters selection in a sustainable high speed turning operation involving 4 attributes and 9 alternative sets of experimental conditions. The results of the proposed decision-making method and its second version are compared with the other popular decision-making methods. The proposed method and its another version are proved simple, effective, powerful, flexible, easy to apply, do not require the use of fuzzy logic, offer logical and consistent procedures to assign weights to the attributes, and are applicable to different decision-making scenarios of the industries. Part-1 of this paper describes the applications of the BHARAT method to multi-attribute decision-making problems and Part-2 describes the evaluation of Pareto solutions using the BHARAT method in multiple objective decision-making problems.

Three simple metaphor-less optimization algorithms are developed in this paper for solving the unconstrained and constrained optimization problems. These algorithms are based on the best and worst solutions obtained during the optimization process and the random interactions between the candidate solutions. These algorithms require only the common control parameters like population size and number of iterations and do not require any algorithm-specific control parameters. The performance of the proposed algorithms is investigated by implementing these on 23 benchmark functions comprising 7 unimodal, 6 multimodal and 10 fixed-dimension multimodal functions. Additional computational experiments are conducted on 25 unconstrained and 2 constrained optimization problems. The proposed simple algorithms have shown good performance and are quite competitive. The research community may take advantage of these algorithms by adapting the same for solving different unconstrained and constrained optimization problems.

A simple multi-attribute decision-making method based on ranking of alternatives and attributes is proposed in this paper. The method ranks the alternatives with respect to each of the attributes based on the corresponding performance measures. Similarly, the ranks are assigned to the attributes based on their importance as perceived by the decision maker. The ranks assigned to the alternatives with respect to each of the attributes and the ranks assigned to the attributes are converted to appropriate weights and the final composite scores of the alternatives are computed using these weights. An interesting feature of the proposed method is that the qualitative attributes (i.e. the attributes expressed in linguistic terms) need not require the use of fuzzy logic. The proposed method is very simple and useful in situations of limited time availability, presence of qualitative attributes, imprecise/incomplete/partial data, and decision maker’s limited attention and capability to process the information. The proposed method is proved easier and better compared to the other widely used decision-making methods. The proposed method will be tested further on more realistic problems of the industrial environment and the results will be reported soon.

A growing number of companies treat "sustainability" as an important objective in their strategy. Sustainable and green suppliers increase efficiency by reducing costs and waste in industries. Sustainable and green supplier selection is a critically important factor in moving forward along the path of sustainability. A fuzzy R-method is proposed in this paper based on ranking the fuzzy numbers of alternative suppliers and criteria. Triangular fuzzy membership function and different fuzzy scales are presented to demonstrate and validate the proposed method. Fuzzy composite scores are generated, and these scores are converted into crisp forms to evaluate the alternative suppliers. The novelty of the proposed method is that it is simple, can deal with qualitative and quantitative criteria of supplier selection, and requires less computational effort for evaluating and ranking the green and sustainable suppliers in fuzzy group decision-making situations. The weights of the criteria and alternative suppliers are generated using a simple equation and hence there is no need to apply different methods for weights generation and ranking. Furthermore, this method does not require normalization of the data. Two realistic group decision-making problems of green and sustainable supplier selection to test the method. Sensitivity analysis for the proposed method is also conducted to check the consistency of the proposed method to different weights of the criteria. The proposed method is effective, robust, and competitive to the existing multi-criteria decision making (MCDM) methods of sustainable supplier selection.