Analysis of Weighting and Selection Methods for Pareto-Optimal Solutions of Multiobjective Optimization in Chemical Engineering Applications

Abstract

Optimization in chemical engineering often involves two or more objectives, which are conflicting. Multiobjective optimization (MOO) generates a set of equally good solutions from the perspective of objectives used; these solutions are known as nondominated or Paretooptimal solutions. Although MOO has become popular in chemical engineering in the past 20 years, majority of studies are limited to finding Pareto-optimal solutions and only some papers discussed the selection of one nondominated solution for implementation. Thus, the main research gap in the application of MOO in chemical engineering is the very limited use of selection or ranking methods. To address this gap, 8 weighting methods and 4 more selection methods (besides 10 methods analyzed by Wang and Rangaiah) are carefully chosen and implemented in an MS Excel-based program. Then, all these methods are applied to 12 mathematical and 13 chemical engineering problems. The results of this extensive analysis indicate that the entropy method, criteria importance through intercriteria correlation method, and best− worst method are better for determining weights for objectives. Further, out of the four additional selection methods tested, multiattributive border approximation area comparison is suggested for ranking Pareto-optimal solutions.

Analysis on Project Portfolio Management Practices in Indian Construction Industry

“…Similarly for the same parameters adopted in this research study values mentioned in the The chart in Figure 2 showing the comparison of the SAW amd CODAS ranking of PPM practices in Manpower Management, Regulatory Mechanism, Organising Skills, Project Proposal Related to Investment [19,20] respectively. The Figure 2 (four important criteria of project portfolio management which includes Manpower Management, Regulatory Mechanism, Organising skills, Project Proposal related to Investment) represents number of paramneters choosen in each criteriaVs rank in codas and saw are portrayed in Figure 2.…”

Preference Ranking on the Basis of Ideal-Average Distance Method for Multi-Criteria Decision-Making

“…Then, weights for each of the objectives are given by decision makers or calculated using one of the weighting methods. 30 The final step is ranking the optimal solutions and selecting the top ranked solution.…”

“…Thereafter, the normalized objective matrix, as shown on the left of Table 2, can be constructed according to Step 1 of the proposed PROBID method to rank and choose 1 of the 11 solutions for implementation. The CRITIC method, 41 recommended by Wang et al 30 because of its holistic consideration of the standard deviation of objectives and pairwise correlation between them, is utilized in this study to find the weights of objectives, which are given in the last row of Table 2. Multiplying weights with the normalized objective values (Step 2) will create the weighted normalized objective matrix, presented on the right of Table 2.…”

“…Alternatively, there are many weighting methods to find objective weights, and they can be put into two main groups: subjective-and objective-weighting methods. In the phrase "objective-weighting methods", objective is the adjective to describe those methods that are not influenced by personal opinions, and it is entirely different from objectives (or criteria) in the optimization problem (see Wang et al 30 for more details about weighting methods). To study the effect of changing weights on the ranking of non-dominated solutions, 11 weighting cases are systematically created; for this, weight assigned to NPW is changed from 0 to 1 in steps of 0.1, and the remaining weight is distributed equally for the 4 environmental objectives.…”

“…Hafezalkotob et al 29 provided an overview of weighting and MCDM methods, as well as their use in the literature, with a comparison of six MCDM methods. In a sequel to Wang and Rangaiah, 27 Wang et al 30 analyzed many weighting and MCDM methods by applying them to 12 mathematical and 13 chemical engineering problems; they suggested the entropy method, CRITIC (criteria importance through intercorrelation) and best−worst methods for determining weights for objectives, and TOPSIS, SAW, GRA, and MABAC (multi-attributive border approximation area comparison) for selecting one of the Paretooptimal solutions.…”