Shanu Verma

Chemical plants, including petroleum refineries, generate and treat large volumes of wastewater, comprising complex mixtures of organic and inorganic contaminants. Managing treatment costs and freshwater use remains critical, particularly in water-scarce regions where industrial demand continues to strain freshwater supplies. Many existing water treatment network models employ simplified representations of treatment systems based on fixed removal efficiencies, single-stage treatment units, and uniform operating costs, while neglecting the influence of contaminant concentration on treatment performance and treatment economics. Such simplifications may limit the realism of the network designs and economic evaluations. To address these limitations, this work proposes a superstructure-based multistage water treatment network framework formulated as a mixed-integer nonlinear programming model. The framework incorporates concentration-range-dependent treatment-stage operation, stage-specific contaminant removal efficiencies, stage-specific treatment costs, and binary decision variables for the treatment-stage activation. The model minimizes total operating cost while determining freshwater consumption, internal water reuse, regeneration, discharge, and stream-blending decisions, all of which are subject to environmental and operational constraints. The effectiveness of the proposed framework is demonstrated through two case studies: a small-scale illustrative network and a petroleum refinery water-treatment network. The results reveal a trade-off between discharge stringency and operational expenditure, where stricter discharge limits require greater treatment intensity and higher treatment costs, whereas relaxed standards permit selective-stage deactivation and reduced regeneration requirements. By explicitly accounting for concentration-dependent treatment behavior and heterogeneous treatment costs, the proposed framework provides a flexible decision-support tool for industrial water network design and sustainable water management.

Selecting team players is a crucial and challenging task demanding a considerable amount of thinking and hard work by the selectors. The present study formulated the selection of an IPL squad as a multi-objective optimization problem with the objectives of maximizing the batting and bowling performance of the squad, in which a player’s performance is estimated using an efficient Batting Performance Factor and Combined Bowling Rate. Also, the proposed model tries to formulate a balanced squad by constraining the number of pure batters, pure bowlers, and all-rounders. Bounds are also considered on star players to enhance the performance of the squad and also from the income prospects of IPL. The problem in itself is treated as a 0/1 knapsack problem for which two combinatorial optimization algorithms, namely, BNSGA-II and INSGA-II, are developed. These algorithms were compared with existing modified NSGA-II for IPL team selection and three other popular multi-objective optimization algorithms, NSGA-II, NSDE, and MOPSO-CD, on the basis of standard performance metrics: hypervolume, inverted generational distance, and number of Pareto optimal solutions. Both algorithms performed well, with BNSGA-II performing better than all the other algorithms considered in this study. The IPL 2020 players’ data validated the applicability of the proposed model and algorithms. The trade-off squads contained players of each expertise in appropriate proportions. Further analysis of the trade-off squads demonstrated that many theoretically selected players performed well in IPL 2020 matches.

This paper provides an extensive review of the popular multi-objective optimization algorithm NSGA-II for selected combinatorial optimization problems viz. assignment problem, allocation problem, travelling salesman problem, vehicle routing problem, scheduling problem, and knapsack problem. It is identified that based on the manner in which NSGA-II has been implemented for solving the aforementioned group of problems, there can be three categories: Conventional NSGA-II, where the authors have implemented the basic version of NSGA-II, without making any changes in the operators; the second one is Modified NSGA-II, where the researchers have implemented NSGA-II after making some changes into it and finally, Hybrid NSGA-II variants, where the researchers have hybridized the conventional and modified NSGA-II with some other technique. The article analyses the modifications in NSGA-II and also discusses the various performance assessment techniques used by the researchers, i.e., test instances, performance metrics, statistical tests, case studies, benchmarking with other state-of-the-art algorithms. Additionally, the paper also provides a brief bibliometric analysis based on the work done in this study.