arXiv subjects

Georgia Kouyialis

Publications and source records attributed to Georgia Kouyialis.

3 recordsLinked to original sources

arXiv2019

Symmetry Detection for Quadratically Constrained Quadratic Programs Using Binary Layered Graphs

Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple equivalent solutions, i.e. with the same optimal value. Dealing with symmetry requires detecting and classifying it first. This work develops methods for detecting groups of symmetry in the formulation of quadratically constrained quadratic optimisation problems via adjacency matrices. Using graph theory, we transform these matrices into Binary Layered Graphs (BLG) and enter them into the software package nauty. Nauty generates important symmetric properties of the original problem.

math.OC↗

arXiv2018

Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an NP-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods.

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arXiv2017

Detecting Symmetry in Designing Heat Exchanger Networks

Symmetry in mathematical optimisation is of broad and current interest. In problem classes such as mixed-integer linear programming (MILP), equivalent solutions created by symmetric variables and constraints may combinatorially increase the search space. Identifying problem symmetries is an important step towards expediting tree-based algorithms such as branch-and-cut because computationally classifying equivalence allows state-of-the-art solver software to omit symmetric solutions. But symmetry has not been characterised in several critically important process systems engineering applications such as heat exchanger network synthesis; neither do current MILP solvers detect or use symmetries for these energy efficiency problems. This paper uses group theory to study the MILP transshipment model of heat exchanger network synthesis and identifies several types of symmetry arising in the problem.

math.OC↗