Speedup in Quantum Adiabatic Evolution Algorithm

Quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving instances of NP-complete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential to examine the minimum energy gap between the ground level and the next one through the evolution. In this letter, we show a way of speedup in quantum adiabatic evolution algorithm, using the extended Hamiltonian. We present the exact relation between the energy gap and the elements of the extended Hamiltonian, which provides the new point of view to reduce the running time.Comment: 5 pages, Late

An inflationary differential evolution algorithm for space trajectory optimization

In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points towards which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard Differential Evolution on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance, reducing the probability of stagnation in deceptive local minima.Comment: IEEE Transactions on Evolutionary Computation 2011. ISSN 1089-778

Dynamics of quantum adiabatic evolution algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size $n$. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxilary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap, $g_{\rm min}={\cal O}(n 2^{-n/2})$, corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simulteneous fipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimenssional quantum diffusion in the energy space. This effect provides a general limitation on the power of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.Comment: 32 pages, 5 figures, 3 Appendices; List of additions compare to v.3: (i) numerical solution of the stationary Schroedinger equation for the adiabatic eigenstates and eigenvalues; (ii) connection between the scaling law of the minimum gap with the problem size and the shape of the coarse-grained distribution of the adiabatic eigenvalues at the avoided-crossing poin

An Improved Differential Evolution Algorithm for Maritime Collision Avoidance Route Planning

High accuracy navigation and surveillance systems are pivotal to ensure efficient ship route planning and marine safety. Based on existing ship navigation and maritime collision prevention rules, an improved approach for collision avoidance route planning using a differential evolution algorithm was developed. Simulation results show that the algorithm is capable of significantly enhancing the optimized route over current methods. It has the potential to be used as a tool to generate optimal vessel routing in the presence of conflicts

Fuzzy Differential Evolution Algorithm

The Differential Evolution (DE) algorithm is a powerful search technique for solving global optimization problems over continuous space. The search initialization for this algorithm does not adequately capture vague preliminary knowledge from the problem domain. This thesis proposes a novel Fuzzy Differential Evolution (FDE) algorithm, as an alternative approach, where the vague information of the search space can be represented and used to deliver a more efficient search. The proposed FDE algorithm utilizes fuzzy set theory concepts to modify the traditional DE algorithm search initialization and mutation components. FDE, alongside other key DE features, is implemented in a convenient decision support system software package. Four benchmark functions are used to demonstrate performance of the new FDE and its practical utility. Additionally, the application of the algorithm is illustrated through a water management case study problem. The new algorithm shows faster convergence for most of the benchmark functions

How Powerful is Adiabatic Quantum Computation?

We analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'.Comment: 12 pages, LaTeX2e, requires fullpage, times, amssymb, and amsmath packages. This article appeared in the proceedings of FOCS'01; original submission date: April 27, 200