Informatica

The field of Quantum Genetic Algorithm (QGA) has seen extensive efforts to develop reasonable algorithmic designs mainly due to its potential as well as the intrinsic difficulty to reproduce the necessary processes with the limited amount of quantum resources available, although it still remains one of rather theoretical concepts of approach to achieving quantum optimization. In this paper, we propose a dynamic encoding scheme that combines quantum adaptive search with iterative approximation of the search region. The method reuses the same quantum index register while updating the classical coordinate mapping associated with its basis states, thereby increasing local coordinate resolution without globally refining the entire continuous domain. Through noiseless statevector simulations on benchmark functions, we compare the proposed method with selected QGA variants in terms of final optimization accuracy and simulated qubit usage. The results show improved optimization performance under similar maximum qubit constraints, establishing a simulation-level resource advantage.

This paper reviews the interplay between global optimization and probability models, concentrating on a class of deterministic optimization algorithms that are motivated by probability models for the objective function. Some complexity results are described for the univariate and multivariate cases.

In this paper, we consider the so-called structured low rank approximation (SLRA) problem as a problem of optimization on the set of either matrices or vectors. Briefly, SLRA is defined as follows. Given an initial matrix with a certain structure (for example, Hankel), the aim is to find a matrix of specified lower rank that approximates this initial matrix, whilst maintaining the initial structure. We demonstrate that the optimization problem arising is typically very difficult; in particular, the objective function is multiextremal even in simple cases. We also look at different methods of solving the SLRA problem. We show that some traditional methods do not even converge to a locally optimal matrix.

We consider a stochastic algorithm of optimization in the presented paper. We deal here with the average results of a “mixture” of the deterministics heuristics algorithm and uniform random search. We define the optimal “mixture”.

We consider finite population slotted ALOHA where each of n terminals has its own transmission probability pi. Given the overall traffic load λ, the probabilities pi are determined in such a way as to maximize throughput. This is achieved by solving a constrained optimization problem. The results of Abramson (1970) are obtained as a special case. Our recent results are improved (Mathar and Žilinskas, 1993).