Solving low-rank semidefinite programs via manifold optimization

We propose a manifold optimization approach to solve linear semidefinite programs (SDP) with low-rank solutions. This approach incorporates the augmented Lagrangian method and the Burer-Monteiro factorization, and features the adaptive strategies for updating the factorization size and the penalty parameter. We prove that the present algorithm can solve SDPs to global optimality, despite of the … Read more

Effective matrix adaptation strategy for noisy derivative-free optimization

In this paper, we introduce a new effective matrix adaptation evolution strategy (MADFO) for noisy derivative-free optimization problems. Like every MAES solver, MADFO consists of three phases: mutation, selection and recombination. MADFO improves the mutation phase by generating good step sizes, neither too small nor too large, that increase the probability of selecting mutation points … Read more

Orbital Crossover

Symmetry in optimization has been known to wreak havoc in optimization algorithms. Often, some of the hardest instances are highly symmetric. This is not the case in linear programming, as symmetry allows one to reduce the size of the problem, possibly dramatically, while still maintaining the same optimal objective value. This is done by aggregating … Read more

Efficient composite heuristics for integer bound constrained noisy optimization

This paper discusses a composite algorithm for bound constrained noisy derivative-free optimization problems with integer variables. This algorithm is an integer variant of the matrix adaptation evolution strategy. An integer derivative-free line search strategy along affine scaling matrix directions is used to generate candidate points. Each affine scaling matrix direction is a product of the … Read more

OPM, a collection of Optimization Problems in Matlab

OPM is a small collection of CUTEst unconstrained and bound-constrained nonlinear optimization problems, which can be used in Matlab for testing optimization algorithms directly (i.e. without installing additional software). Article Download View OPM, a collection of Optimization Problems in Matlab

EETTlib – Energy-Efficient Train Timetabling Library

We introduce EETTlib, an instance library for the Energy-Efficient Train Timetabling problem. The task in this problem is to adjust a given timetable draft such that several key indicators relating to the energy consumption of the resulting railway traffic are minimized. These include peak power consumption, total energy consumption, loss in recuperation energy, fluctuation in … Read more

A developed randomized algorithm with noise level tuning for large-scale noisy unconstrained DFO problems and its real-life applications

In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization problems is discussed. Complexity results in the presence of noise for nonconvex, convex, and strongly convex functions are studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined … Read more

The confined primal integral

It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more

A Restricted Dual Peaceman-Rachford Splitting Method for QAP

We revisit and strengthen splitting methods for solving doubly nonnegative, DNN, relaxations of the quadratic assignment problem, QAP. We use a modified restricted contractive splitting method, rPRSM, approach. Our strengthened bounds and new dual multiplier estimates improve on the bounds and convergence results in the literature. Citation Department of Combinatorics & Optimization, University of Waterloo, … Read more

A new interior-point approach for large two-stage stochastic problems

Two-stage stochastic models give rise to very large optimization problems. Several approaches have been devised for efficiently solving them, including interior-point methods (IPMs). However, using IPMs, the linking columns associated to first-stage decisions cause excessive fill-in for the solution of the normal equations. This downside is usually alleviated if variable splitting is applied to first-stage … Read more