Heuristic algorithm for 1D and 2D unfolding

A very simple heuristic approach to the unfolding problem will be described. An iterative algorithm starts with an empty histogram and every iteration aims to add one entry to this histogram. The entry to be added is selected according to a criteria which includes a $\chi^2$ test and a regularization. After a relatively small number of iterations (500 - 1000) the growing reconstructed distribution converges to the true distribution

Quantum heuristic algorithm for traveling salesman problem

We propose a quantum heuristic algorithm to solve a traveling salesman problem by generalizing Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with extremal costs, reaching almost to unity and they are shown characterized by statistical properties of tour costs. In particular for a Gaussian distribution of the tours along the cost we show that the quantum algorithm exhibits the quadratic speedup of its classical counterpart, similarly to Grover search.Comment: Published versio

Testing systems of identical components

We consider the problem of testing sequentially the components of a multi-component reliability system in order to figure out the state of the system via costly tests. In particular, systems with identical components are considered. The notion of lexicographically large binary decision trees is introduced and a heuristic algorithm based on that notion is proposed. The performance of the heuristic algorithm is demonstrated by computational results, for various classes of functions. In particular, in all 200 random cases where the underlying function is a threshold function, the proposed heuristic produces optimal solutions

A honeybees-inspired heuristic algorithm for numerical optimisation

© 2019, The Author(s). Swarm intelligence is all about developing collective behaviours to solve complex, ill-structured and large-scale problems. Efficiency in collective behaviours depends on how to harmonise the individual contributors so that a complementary collective effort can be achieved to offer a useful solution. The main points in organising the harmony remain as managing the diversification and intensification actions appropriately, where the efficiency of collective behaviours depends on blending these two actions appropriately. In this paper, a hybrid bee algorithm is presented, which harmonises bee operators of two mainstream well-known swarm intelligence algorithms inspired of natural honeybee colonies. The parent algorithms have been overviewed with many respects, strengths and weaknesses are identified, first, and the hybrid version has been proposed, next. The efficiency of the hybrid algorithm is demonstrated in comparison with the parent algorithms in solving two types of numerical optimisation problems; (1) a set of well-known functional optimisation benchmark problems and (2) optimising the weights of a set of artificial neural network models trained for medical classification benchmark problems. The experimental results demonstrate the outperforming success of the proposed hybrid algorithm in comparison with two original/parent bee algorithms in solving both types of numerical optimisation benchmarks

Robust Portfolio Optimization with a Hybrid Heuristic Algorithm

Estimation errors in both the expected returns and the covariance matrix hamper the constructing of reliable portfolios within the Markowitz framework. Robust techniques that incorporate the uncertainty about the unknown parameters are suggested in the literature. We propose a modification as well as an extension of such a technique and compare both with another robust approach. In order to eliminate oversimplifications of Markowitz’ portfolio theory, we generalize the optimization framework to better emulate a more realistic investment environment. Because the adjusted optimization problem is no longer solvable with standard algorithms, we employ a hybrid heuristic to tackle this problem. Our empirical analysis is conducted with a moving time window for returns of the German stock index DAX100. The results of all three robust approaches yield more stable portfolio compositions than those of the original Markowitz framework. Moreover, the out-of-sample risk of the robust approaches is lower and less volatile while their returns are not necessarily smaller.Hybrid heuristic algorithm, Markowitz, Robust optimization, Uncertainty sets.