Table 5 Overview of optimization research in industrial integrated energy systems

⁶⁴

Electricity, heat, compressed air

×

×

×

√

√

LP

Carbon flow tracing of the steel industry

¹⁰⁴

Electricity, heat

×

√

×

√

√

MILP

Flexibility evaluation of the steel refining process

¹⁰⁹

Electricity, heat, hydrogen

√

×

×

√

√

MINLP & Stochastic programming

Material–energy coupling optimization for refineries

¹¹⁶

Electricity, heat

√

×

√

×

√

Robust optimization

Production plan and energy management in the steel industry

²⁰²

Electricity, gas, cooling, heat

×

×

×

√

×

MILP

Low-carbon economic operation of energy hubs

²⁰¹

Electricity, heat

√

×

×

√

√

MILFP using the Charnes–Cooper transformation

Emission intensity optimization for electrolytic aluminum based on STN

²⁰⁰

Electricity, gas

×

√

√

√

√

MILP

Production scheduling considering carbon policy

¹⁰³

Electricity, heat

×

√

×

×

√

MILP

Demand response in the cement industry

²⁰⁷

Electricity

×

√

√

√

√

Enhanced memetic algorithm

Flexible job shop scheduling considering machine restart

²⁰⁹

Electricity

×

√

×

√

√

Improved evolutionary algorithm

Low-carbon flexible job shop scheduling

¹⁰⁵

Electricity, heat, cooling

√

√

√

√

×

KKT and binary expansion method

Multi-time scale demand response for manufacturing

²⁰³

Electricity, gas, hydrogen

√

√

×

√

√

Lagrangian benders decomposition

Low-carbon dispatch in the steel industry, coupled with hydrogen

²⁰⁴

Electricity, heat, gas, compressed air

×

√

×

√

√

Relaxation and heuristic algorithms

Carbon flow tracing and coordinated scheduling of energy-material flows