An efficient envelope-based Branch and Bound algorithm for non-convex combined heat and power production planning

Aiying Rong*, Risto Lahdelma

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

95 Citations (Scopus)


Combined heat and power (CHP) production is universally accepted as one of the most energy-efficient technologies to produce energy with lower fuel consumption and fewer emissions. In CHP technology, heat and power generation follow a joint characteristic. Traditional CHP production is usually applied in backpressure plants, where the joint characteristic can often be represented by a convex model. Advanced CHP production technologies such as backpressure plants with condensing and auxiliary cooling options, gas turbines, and combined gas and steam cycles may require non-convex models. Cost-efficient operation of a CHP system can be planned using an optimization model based on forecasts for heat load and power price. A long-term planning model decomposes into thousands of single-period models, which can be formulated in the convex case as linear programming (LP) problems, and in the non-convex case as mixed integer programming (MIP) problems. In this paper, we introduce EBB algorithm, for solving the non-convex single-period CHP models of a long-term planning problem under the deregulated power market. EBB is based on the Branch and Bound (B&B) algorithm where tight lower bounds are computed analytically for pruning the search tree and the LP sub-problems are solved through an efficient envelope-based dual algorithm. We compare the performance of EBB with realistic models against the ILOG CPLEX 9.0 MIP solver and the Power Simplex (PS)-based B&B algorithm (PBB). PS is an efficient specialized primal-based Simplex algorithm developed for convex CHP planning problems. EBB is from 661 to 955 times (with average 785) faster than CPLEX and from 11 to 31 times (with average 24) faster than PBB.

Original languageEnglish
Pages (from-to)412-431
Number of pages20
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 16 Nov 2007
MoE publication typeA1 Journal article-refereed


  • Branch and Bound
  • Combined heat and power production
  • Energy optimization
  • Envelope
  • Mixed integer programming


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