limits and potentials of mixed integer linear programming methods for optimization of polygeneration energy systems

Abstract The simultaneous production of different energy vectors from hybrid polygeneration plants is a promising way to increase energy efficiency and facilitate the development of distributed energy systems. The inherent complexity of polygeneration energy systems makes their economic, environmental and energy performance highly dependent on system synthesis, equipment selection and capacity, and operational strategy. Mixed Integer Linear Programming (MILP) is the state of the art approach to tackle the optimization problem of polygeneration systems. The guarantee of finding global optimality in linear problems and the effectiveness of available commercial solvers make MILP very attractive and widely used in optimization problems of polygeneration systems. Nevertheless, several drawbacks affect the MILP formulation, such as: the impossibility of taking into account nonlinear effects; the necessity of considering all the time periods at once; the risk of high-dimensionality of the problem. To tackle these limitations, several techniques have been developed, such as: piecewise linearization methods; rolling horizon approaches; dimensionality reduction by means of energy demands clustering algorithms. In this paper, limits and potentials of MILP methods for the optimization problem of polygeneration energy systems are reviewed and discussed

Off-the-shelf solvers for mixed-integer conic programming: insights from a computational study on congested capacitated facility location instances

This paper analyzes the performance of five well-known off-the-shelf optimization solvers on a set of mixed-integer conic programs proposed for the congested capacitated facility location problem. We aim to compare the computational efficiency of the solvers and examine the solution strategies they adopt when solving instances with different sizes and complexity. The solvers we compare are Gurobi, Cplex, Mosek, Xpress, and Scip. We run extensive numerical tests on a testbed of 30 instances from the literature. Our results show that Mosek and Gurobi are the most competitive solvers, as they achieve better time and gap performance, solving most instances within the time limit. Mosek outperforms Gurobi in large-size problems and provides more accurate solutions in terms of feasibility. Xpress solves to optimality about half of the instances tested within the time limit, and in this half, it achieves performance similar to that of Gurobi and Mosek. Cplex and Scip emerge as the least competitive solvers. The results provide guidelines on how each solver behaves on this class of problems and highlight the importance of choosing a solver suited to the problem type

QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary Optimization

We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of JuMP problems for straightforward application in many physics and physics-inspired solution methods whose standard optimization form is equivalent to the QUBO. These methods include quantum annealing, quantum gate-circuit optimization algorithms (Quantum Optimization Alternating Ansatz, Variational Quantum Eigensolver), other hardware-accelerated platforms, such as Coherent Ising Machines and Simulated Bifurcation Machines, and more traditional methods such as simulated annealing. Besides working with reformulations, QUBO.jl allows its users to interface with the aforementioned hardware, sending QUBO models in various file formats and retrieving results for subsequent analysis. QUBO.jl was written as a JuMP / MathOptInterface (MOI) layer that automatically maps between the input and output frames, thus providing a smooth modeling experience

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design