A linearization and parameterization approach to tri-objective linear programming problems for power generation expansion planning

The present study proposed a new solution to a tri-objective linear programming problem for generation expansion planning by converting the tri-objective linear programming problem (i.e. simultaneously maximizing the total power generation, minimizing the total system cost, and minimizing the total CO2 emission) into an equivalent bi-objective linear fractional programming problem (i.e. simultaneously maximizing the ratio of the total power generation to the total system cost, and the ratio of the total power generation to the total CO2 emission) to produce a better nondominated solution without any preference information from a decision maker. An approach for solving the bi-objective linear fractional programming problem is a newly developed linearization and parameterization approach based on Dinkelbach's theorem and Güzel's approach, which transforms all of linear fractional objective functions into a single objective linear programming problem. The proposed bi-objective fractional programming method was applied to a case study of power generation expansion planning problem. Moreover, comparison of the solutions generated by the proposed linearization and parameterization approach and a traditional weighted sum approach has been conducted to demonstrate the effectiveness of the proposed approach in reflecting the trade-offs among the total power generation, the total system cost and the total CO2 emission.