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A fuzzy multi-objective optimization approach for treated wastewater allocation

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Abstract

In face of the new climate and socio-environmental conditions, conventional sources of water are no longer reliable to supply all water demands. Different alternatives are proposed to augment the conventional sources, including treated wastewater. Optimal and objective allocation of treated wastewater to different stakeholders through an optimization process that takes into account multiple objectives of the system, unlike the conventional ground and surface water resources, has been widely unexplored. This paper proposes a methodology to allocate treated wastewater, while observing the physical constraints of the system. A multi-objective optimization model (MOM) is utilized herein to identify the optimal solutions on the pareto front curve satisfying different objective functions. Fuzzy transformation method (FTM) is utilized to develop different fuzzy scenarios that account for potential uncertainties of the system. Non-dominated sorting genetic algorithm II (NSGA-II) is then expanded to include the confidence level of fuzzy parameters, and thereby several trade-off curves between objective functions are generated. Subsequently, the best solution on each trade-off curve is specified with preference ranking organization method for enrichment evaluation (PROMETHEE). Sensitivity analysis of criteria’s weights in the PROMETHEE method indicates that the results are highly dependent on the weighting scenario, and hence weights should be carefully selected. We apply this framework to allocate projected treated wastewater in the planning horizon of 2031, which is expected to be produced by wastewater treatment plants in the eastern regions of Tehran province, Iran. Results revealed the efficiency of this methodology to obtain the most confident allocation strategy in the presence of uncertainties.

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Notes

  1. Treated wastewater production capacities in four regions

  2. Indifference threshold

  3. Strict preference threshold

  4. A value between s and t

  5. Million cubic meters (MCM)

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Authors and Affiliations

  1. School of Engineering, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran

    Saeid Tayebikhorami & Mohammad Reza Nikoo

  2. College of Engineering, Department of Civil Engineering, Boise State University, Boise, ID, USA

    Mojtaba Sadegh

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  1. Saeid Tayebikhorami
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  2. Mohammad Reza Nikoo
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  3. Mojtaba Sadegh
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Correspondence to Saeid Tayebikhorami or Mohammad Reza Nikoo.

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Appendices

Appendix 1

In this paper, fuzzy transformation method (FTM) is utilized to incorporate the uncertainties associated with treated wastewater production capacities. According to the “Case study” section, the eastern part of Tehran province is divided into four separate regions, namely, Firouzkooh county region, Latyan dam region, Mamlou dam region, and Varamin plain region. The capacities of wastewater treatment plants are estimated in the planning horizon of 2031 and are used as the main fuzzy parameters in this study. In order to consider the uncertainties, the range of variation for the fuzzy triangular membership function is considered to be 20% in FTM. Three α-cut levels (0, 0.5, and 1) are utilized to decompose the fuzzy inputs, and various fuzzy scenarios are developed. In Table 9, fuzzy scenarios are introduced and the fuzzy parameters are determined in each scenario.

Table 9 Fuzzy scenarios and fuzzy values for treated wastewater capacities of four eastern regions of Tehran Province, Iran, in the planning horizon of 2031
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Appendix 2

The PROMETHEE method is used in this study to locate the most preferable solution among the optimal solutions that are generated in a trade-off using the optimization model. In this method, preference indices are calculated with pairwise comparison for each of the two solutions on the trade-off curve. Afterwards, the entering and leaving flows (φ+, φ−) are determined, and solutions are ranked based on net outranking flows. As an example, calculations and ranking procedure of a specific trade-off curve, which is shown in Fig. 7, are demonstrated in Table 10. As it clearly indicates, the 1st, 19th, and 23rd solutions are the most preferred answers.

Table 10 PROMETHEE preference indices for the trade-off curve shown in Fig. 7
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Tayebikhorami, S., Nikoo, M.R. & Sadegh, M. A fuzzy multi-objective optimization approach for treated wastewater allocation. Environ Monit Assess 191, 468 (2019). https://doi.org/10.1007/s10661-019-7557-2

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