Soft constraint handling for a real-world multiobjective energy distribution problem

Abstract

Real-world optimisation problems usually involve some conflicting objectives and a number of constraints. In such cases, finding a feasible, Pareto-optimal solution poses a demanding challenge. In reality, constraints bear different importance levels to these conflicting objectives. If some constraints are relaxed within an acceptable degree, quality infeasible solutions could be found on the boundary from the infeasible side of the searching region. This paper formulates an energy distribution problem arising from a real-world iron and steel production as a multiobjective optimisation problem. During the course of the optimisation search, this paper attempts to handle certain constraints in a soft manner to find solutions with good balance among objective and constraints violation. Based on the analysis of constraints from the real-world perspective, different tolerance values are defined. The proposed constraint violation degree-based soft handling approach is incorporated into the advanced version of non-dominated sorting genetic algorithm framework, as a case study, to examine the efficiency of the proposed soft constraint handling approach for a real-world energy distribution problem. The proposed approach is also implemented in different ways of constraint handling and tested on some benchmark functions to further demonstrate the performance of soft constraint handling for multiobjective optimisation problems.

Keywords:

• Multiobjective optimisation
• soft constraint handling
• iron and steel production
• energy distribution

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Yanyan Zhang and Lixin Tang was supported by the National Key R&D Program of China [grant number 2016YFB0901900], the Innovative Research Groups of the National Natural Science Foundation of China [grant number 71621061], the National Natural Science Foundation of China [grant number 71302161], the Major International Joint Research Project of the National Natural Science Foundation of China [grant number 71520107004], the Major Program of National Natural Science Foundation of China [grant number 71790614], and the 111 Project [grant number B16009].