The efficient numerical treatment of convex quadratic mixed-integer optimization poses a challenging problem for present branch-and-bound algorithms. We introduce a method based on the duality principle for nonlinear convex problems to derive suitable bounds that can be directly exploit to improve heuristic branching rules. Numerical results indicate that the bounds allow the branch-and-bound t...

Given rational numbers C0, . . . , Cm and b0, . . . , bm, the mixing set with arbitrary capacities is the mixed-integer set defined by conditions s + Ctzt ≥ bt, 0 ≤ t ≤ m, s ≥ 0, zt integer, 0 ≤ t ≤ m. Such a set has applications in lot-sizing problems. We study the special case of divisible capacities, i.e. Ct/Ct−1 is a positive integer for 1 ≤ t ≤ m. Under this assumption, we give an extended...

In this paper, we study how well one can approximate arbitrary polytopes using sparse inequalities. Our motivation comes from the use of sparse cutting-planes in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch&-bound more efficiently. However, how well can we approximate the integer hull by just using sparse cutting-planes? In ord...

Multi-choice programming problems arise due to diverse needs of people. In this paper, multi-choice optimisation is applied bilevel transportation problem. This problem deals with at both the levels, upper as well lower. There are multiple choices for demand and supply parameters. The parameters respective levels converted into polynomials which transmute defined a mixed integer objective paper...

Sparse cutting-planes are often the ones used in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch-&-bound more efficiently. However, how well can we approximate the integer hull by just using sparse cuttingplanes? In order to understand this question better, given a polyope P (e.g. the integer hull of a MIP), let P be its best appr...

Let (QP ) be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. In this paper, we present several linearizations of (QP ). Many linearization methods for the quadratic 0-1 programs are known. A natural approach when considering (QP ) is to reformulate it into a quadratic 0-1 program. However, this method, that we denote BBL (Binary Binar...

Because of the coupling CO 2 absorption and treatment, conventional carbon capture power plants lack flexibility plant operation. This paper provides a liquid storage (LSCCPP) with solution storage, analyzes “energy time-shift” features creates joint operating model LSCCPP Power to Gas(P2G) based on this. Taking into account market trading mechanism, this develops low-carbon economic dispatch f...

In this paper, an optimization-based approach is proposed using a mixed integer quadratic programming model for the economic dispatch of electrical power generators with prohibited zones of operation. The main advantage of the proposed approach is its capability to solve case studies from the literature to global optimality quickly and without any targeting of solution procedures.