Major applications of mixed-integer quadratically-constrained quadratic programs (MIQCQP) include quality blending in process networks, separating objects in computational geometry, and portfolio optimization in finance. Specific instantiations of MIQCQP in process networks optimization problems include: pooling problems, distillation sequences, wastewater treatment and total water systems, hybrid energy systems, heat exchanger networks, reactor-separator-recycle systems, separation systems, data reconciliation, batch processes, crude oil scheduling, and natural gas production. Computational geometry problems formulated as MIQCQP include: point packing, cutting convex shapes from rectangles, maximizing the area of a convex polygon, and chip layout and compaction. Portfolio optimization in financial engineering can also be formulated as MIQCQP. MIQCQP is mathematically defined:
where C, B, I, and M represent the number of continuous variables, binary variables, integer variables, and constraints, respectively. We assume that it is possible to infer finite bounds on the variables participating in nonlinear terms.
|Time||Percent gap remaining|
GloMIQO is the fastest solver for ≈ 48% of the test cases and can address ≈ 70% of the test cases within the time limit. Additionally, GloMIQO generally closes more of the optimality gap. The success of GloMIQO is a direct result of finding and exploiting an array of special structure components within MIQCQP.