Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange.

Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications. Part I focused on the Quadratic Unconstrained Binary Optimization (QUBO) model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems. Part II (the present paper) introduces the domain of QUBO-Plus models that enables a larger range of problems to be handled effectively. After illustrating the scope of these QUBO-Plus models with examples, we give special attention to an important instance of these models called the Asset Exchange Problem (AEP). Solutions to the AEP enable market players to identify exchanges of assets that benefit all participants. Such exchanges are generated by a combination of two optimization technologies for this class of QUBO-Plus models, one grounded in network optimization and one based on a new metaheuristic optimization approach called combinatorial chaining. This combination opens the door to expanding the links to quantum computing applications established by QUBO models through the Quantum Bridge Analytics perspective. We show how the modeling and solution capability for the AEP instance of QUBO-Plus models provides a framework for solving a broad range of problems arising in financial, industrial, scientific, and social settings.

Memetic Search for Identifying Critical Nodes in Sparse Graphs.

Critical node problems (CNPs) involve finding a set of critical nodes from a graph whose removal results in optimizing a predefined measure over the residual graph. As useful models for a variety of practical applications, these problems are computationally challenging. In this paper, we study the classic CNP and introduce an effective memetic algorithm for solving CNP. The proposed algorithm combines a double backbone-based crossover operator (to generate promising offspring solutions), a component-based neighborhood search procedure (to find high-quality local optima), and a rank-based pool updating strategy (to guarantee a healthy population). Extensive evaluations on 42 synthetic and real-world benchmark instances show that the proposed algorithm discovers 24 new upper bounds and matches 15 previous best-known bounds. We also demonstrate the relevance of our algorithm for effectively solving a variant of the classic CNP, called the cardinality-constrained CNP. Finally, we investigate the usefulness of each key algorithmic component.

Dealing with repetitions in sequencing by hybridization.

DNA sequencing by hybridization (SBH) induces errors in the biochemical experiment. Some of them are random and disappear when the experiment is repeated. Others are systematic, involving repetitions in the probes of the target sequence. A good method for solving SBH problems must deal with both types of errors. In this work we propose a new hybrid genetic algorithm for isothermic and standard sequencing that incorporates the concept of structured combinations. The algorithm is then compared with other methods designed for handling errors that arise in standard and isothermic SBH approaches. DNA sequences used for testing are taken from GenBank. The set of instances for testing was divided into two groups. The first group consisted of sequences containing positive and negative errors in the spectrum, at a rate of up to 20%, excluding errors coming from repetitions. The second group consisted of sequences containing repeated oligonucleotides, and containing additional errors up to 5% added into the spectra. Our new method outperforms the best alternative procedures for both data sets. Moreover, the method produces solutions exhibiting extremely high degree of similarity to the target sequences in the cases without repetitions, which is an important outcome for biologists. The spectra prepared from the sequences taken from GenBank are available on our website http://bio.cs.put.poznan.pl/.