“…,Liao et al (2008),Feng et al (2009),Kim et al (2009) Liao et al (2011),Boix et al (2011a),Boix et al (2011b),Yang and Grossmann (2011),Boix et al (2012),,Ahmetović and Kravanja (2012a,b,c, 2013,Ibrić et al (2012Ibrić et al ( , 2013aIbrić et al ( , 2014b,,Li and Yin (2013),Yang and Grossmann (2013),,Kermani et al (2014),Chen et al (2014) State-space representationBagajewicz (2000),Bagajewicz et al (2002) Dong et al (2008) Chen et al (2014) Source-demand or source-sink representation Renard et al (2012), Tan et al (2012), Rojas-Torres et al (2013), Jiménez-Gutiérrez et al (2014), Kermani et al (2014) Heat-integrated water-using, and wastewater treatments networks (HIWTNs) Dong et al (2008), Bogataj and Bagajewicz (2008), Chen et al (2010b) Yang and Grossmann (2011), Yang and Grossmann (2013), Ibrić et al (2013b, 2014a,c), Ahmetović et al (2014) Multi-scale state-space representation Zhou et al (2012a,b) Mathematical models and solution strategies Sequential: WN design → HEN design Water and energy targeting models (LP) → MILP Bagajewicz (2000), Bagajewicz et al (2002) NLP → MINLP Du et al (2003) Ahmetović and Kravanja (2012a), Li and Yin (2013) MILP → MINLP Liao et al (2011), Boix et al (2012) MILP/integer cut constraint (ICC) Kermani et al (2014) LP/MILP/LP → MILP Li et al (2013) MINLP → MINLP Du et al (2004) Chen et al (2010b) Ibrić et al (2012) Water and energy targeting models → MINLP Liao et al (2008) Chen et al (2014) Simultaneous: initialisation → WN + HEN design MINLP Du et al (2004) Jiménez-Gutiérrez et al (2014), Zhou et al (2015) Stochastic perturbation procedure → MINLP Dong et al (2008) NLP → MINLP Bogataj and Bagajewicz (2007), Bogataj and Bagajewicz (2008) NLP (WN + HI models) → MINLP Ibrić et al (2013a, 2014a,b,c) MILP → MINLP Leewongwanawit et al (2004), Leewongtanawit and Kim (2004a) MINLP (WN model) → MINLP Ahmetović and Kravanja (2012a,b,c, 2013, 2014), Ahmetović et al (2013), Ahmetović et al (2014) MINLP (WN + HI models) MINLP Ibrić et al (2013b, 2014a) Initial guesses and random perturbations → MINLP (MILPs → NLPs) Zhou et al (2012a,b) MINLP (MILP → NLP by iterative consumption and global equivalent cost Boix et al (2011a) WN targeting − minimum number of temperature local fluctuations (MINLP) Feng et al (2009) Identification of hot and cold streams for HEN Bogataj and Bagajewicz (2008) Liao et al (2011), Ahmetović and Kravanja (2013), Ibrić et al (2013a), Chen et al (2014)…”