Discrete Equilibrium Optimizer Combined with Simulated Annealing for Feature Selection

This paper proposes a binary adaptation of the recently proposed meta-heuristic, Equilibrium Optimizer (EO), called Discrete EO (DEO) to solve binary optimization problems. A U-shaped transfer function has been used to map the continuous values of EO into the binary domain. To further improve the exploitation capability of DEO, Simulated Annealing (SA) has been used as a local search procedure and the combination has been named as DEOSA. The proposed DEOSA algorithm has been applied over 18 well-known UCI datasets and compared with a wide range of algorithms. The results have been statistically validated using Wilcoxon rank-sum test. In order to test the scalability and robustness of DEOSA, it has been additionally tested over 7 high-dimensional Microarray datasets and 25 binary Knapsack problems. The results clearly demonstrate the superiority and merits of DEOSA when solving binary optimization problems.

VESPA: static profiling for binary optimization

Over the past few years, there has been a surge in the popularity of binary optimizers such as BOLT, Propeller, Janus and HALO. These tools use dynamic profiling information to make optimization decisions. Although effective, gathering runtime data presents developers with inconveniences such as unrepresentative inputs, the need to accommodate software modifications, and longer build times. In this paper, we revisit the static profiling technique proposed by Calder et al. in the late 90’s, and investigate its application to drive binary optimizations, in the context of the BOLT binary optimizer, as a replacement for dynamic profiling. A few core modifications to Calder et al.’s original proposal, consisting of new program features and a new regression model, are sufficient to enable some of the gains obtained through runtime profiling. An evaluation of BOLT powered by our static profiler on four large benchmarks (clang, GCC, MySQL and PostgreSQL) yields binaries that are 5.47 % faster than the executables produced by clang -O3.

Decomposition-Based Approaches for a Class of Two-Stage Robust Binary Optimization Problems

In this paper, we study a class of two-stage robust binary optimization problems with objective uncertainty, where recourse decisions are restricted to be mixed-binary. For these problems, we present a deterministic equivalent formulation through the convexification of the recourse-feasible region. We then explore this formulation under the lens of a relaxation, showing that the specific relaxation we propose can be solved by using the branch-and-price algorithm. We present conditions under which this relaxation is exact and describe alternative exact solution methods when this is not the case. Despite the two-stage nature of the problem, we provide NP-completeness results based on our reformulations. Finally, we present various applications in which the methodology we propose can be applied. We compare our exact methodology to those approximate methods recently proposed in the literature under the name [Formula: see text]adaptability. Our computational results show that our methodology is able to produce better solutions in less computational time compared with the [Formula: see text]adaptability approach, as well as to solve bigger instances than those previously managed in the literature. Summary of Contribution: Our manuscript describes an exact solution approach for a class of robust binary optimization problems with mixed-binary recourse and objective uncertainty. Its development reposes first on a reformulation of the problem, then a carefully constructed relaxation of this reformulation. Our solution approach is designed to exploit the two-stage and binary structure of the problem for effective resolution. In its execution, it relies on the branch-and-price algorithm and its efficient implementation. With our computational experiments, we show that our proposed exact solution method outperforms the existing approximate methodologies and, therefore, pushes the computational envelope for the class of problems considered.

Template-Based Minor Embedding for Adiabatic Quantum Optimization

Quantum annealing (QA) can be used to quickly obtain near-optimal solutions for quadratic unconstrained binary optimization (QUBO) problems. In QA hardware, each decision variable of a QUBO should be mapped to one or more adjacent qubits in such a way that pairs of variables defining a quadratic term in the objective function are mapped to some pair of adjacent qubits. However, qubits have limited connectivity in existing QA hardware. This has spurred work on preprocessing algorithms for embedding the graph representing problem variables with quadratic terms into the hardware graph representing qubits adjacencies, such as the Chimera graph in hardware produced by D-Wave Systems. In this paper, we use integer linear programming to search for an embedding of the problem graph into certain classes of minors of the Chimera graph, which we call template embeddings. One of these classes corresponds to complete bipartite graphs, for which we show the limitation of the existing approach based on minimum odd cycle transversals (OCTs). One of the formulations presented is exact and thus can be used to certify the absence of a minor embedding using that template. On an extensive test set consisting of random graphs from five different classes of varying size and sparsity, we can embed more graphs than a state-of-the-art OCT-based approach, our approach scales better with the hardware size, and the runtime is generally orders of magnitude smaller. Summary of Contribution: Our work combines classical and quantum computing for operations research by showing that integer linear programming can be successfully used as a preprocessing step for adiabatic quantum optimization. We use it to determine how a quadratic unconstrained binary optimization problem can be solved by a quantum annealer in which the qubits are coupled as in a Chimera graph, such as in the quantum annealers currently produced by D-Wave Systems. The paper also provides a timely introduction to adiabatic quantum computing and related work on minor embeddings.

Automatic Design of Heuristic Algorithms for Binary Optimization Problems

In this work we present AutoBQP, a heuristic solver for binary optimization problems. It applies automatic algorithm design techniques to search for the best heuristics for a given optimization problem. Experiments show that the solver can find algorithms which perform better than or comparable to state-of-the-art methods, and can even find new best solutions for some instances of standard benchmark sets.