A parallel tabu search for the unconstrained binary quadratic programming problem

International audienceAlthough several sequential heuristics have been proposed for dealing with the Unconstrained Binary Quadratic Programming (UBQP), very little effort has been made for designing parallel algorithms for the UBQP. This paper propose a novel decentralized parallel search algorithm, called Parallel Elite Biased Tabu Search (PEBTS). It is based on D2TS, a state-of-the-art sequential UBQP metaheuristic. The key strategies in the PEBTS algorithm include: (i) a lazy distributed cooperation procedure to maintain diversity among different search processes and (ii) finely tuned bit-flip operators which can help the search escape local optima efficiently. Our experiments on the Tianhe-2 supercomputer with up to 24 computing cores show the accuracy of the efficiency of PEBTS compared with a straightforward parallel algorithm running multiple independent and non-cooperating D2TS processes

Construction of a Basket of Diversified Portfolios, via Quantum Annealing, to Aid in Cardinality Constratined Portfolio Optimization

In this project, we propose and investigate a new approach for solving portfolio optimization problems (POP) with cardinality constraints using an evolutionary algorithm based on the distribution of diversified baskets (EADDB).The Diversified basket is the basket of portfolios each of which obtains one of the lowest risks. The distribution of the diversified basket indicates the probability of having each asset in the diversified basket. Finding the diversified basket is an NP-hard problem, and we exploit quantum annealing in order to approximate the diversified basket.In particular, POP is mapped into D-Wave Two™, the first commercially available quantum computer, using one of two methods: discretization, and market graph. Each approach creates several instances of the problem of finding diversified baskets. D-Wave Two’s output is an approximation to this diversified basket, and subsequently the distribution of diversified basket can be determined. Distribution of the diversified basket forms the basis of EADDB. The performance of the proposed EADDB has been evaluated on the Hang-Seng in Hong Kong with 31 assets, one of the benchmark datasets in the OR Library, and has been compared with heuristic algorithms

Metaheuristic approaches to realistic portfolio optimisation

In this thesis we investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs which include a substantial illiquidity premium, and is then applied to a large I 00-stock portfolio. It is shown that genetic algorithms can optimise such portfolios effectively and within reasonable times, without extensive tailoring or fine-tuning of the algorithm. This approach is also flexible in not relying on any assumed or restrictive properties of the model and can easily cope with extensive modifications such as the addition of complex new constraints, discontinuous variables and changes in the objective function. The results indicate that that both floor and ceiling constraints have a substantial negative impact on portfolio performance and their necessity should be examined critically relative to their associated administration and monitoring costs. Another insight is that nonlinear transaction costs which are comparable in magnitude to forecast returns will tend to diversify portfolios; the effect of these costs on portfolio risk is, however, ambiguous, depending on the degree of diversification required for cost reduction. Generally, the number of assets in a portfolio invariably increases as a result of constraints, costs and their combination. The implementation of cardinality constraints is essential for finding the bestperforming portfolio. The ability of the heuristic method to deal with cardinality constraints is one of its most powerful features.Decision SciencesM. Sc. (Operations Research