382,795 research outputs found
Towards large scale continuous EDA: a random matrix theory perspective
Estimation of distribution algorithms (EDA) are a major branch of evolutionary algorithms (EA) with some unique advantages in principle. They are able to take advantage of correlation structure to drive the search more efficiently, and they are able to provide insights about the structure of the search space. However, model building in high dimensions is extremely challenging and as a result existing EDAs lose their strengths in large scale problems.
Large scale continuous global optimisation is key to many real world problems of modern days. Scaling up EAs to large scale problems has become one of the biggest challenges of the field.
This paper pins down some fundamental roots of the problem and makes a start at developing a new and generic framework to yield effective EDA-type algorithms for large scale continuous global optimisation problems. Our concept is to introduce an ensemble of random projections of the set of fittest search points to low dimensions as a basis for developing a new and generic divide-and-conquer methodology. This is rooted in the theory of random projections developed in theoretical computer science, and will exploit recent advances of non-asymptotic random matrix theory
Low-Rank Modifications of Riccati Factorizations for Model Predictive Control
In Model Predictive Control (MPC) the control input is computed by solving a
constrained finite-time optimal control (CFTOC) problem at each sample in the
control loop. The main computational effort is often spent on computing the
search directions, which in MPC corresponds to solving unconstrained
finite-time optimal control (UFTOC) problems. This is commonly performed using
Riccati recursions or generic sparsity exploiting algorithms. In this work the
focus is efficient search direction computations for active-set (AS) type
methods. The system of equations to be solved at each AS iteration is changed
only by a low-rank modification of the previous one, and exploiting this
structured change is important for the performance of AS type solvers. In this
paper, theory for how to exploit these low-rank changes by modifying the
Riccati factorization between AS iterations in a structured way is presented. A
numerical evaluation of the proposed algorithm shows that the computation time
can be significantly reduced by modifying, instead of re-computing, the Riccati
factorization. This speed-up can be important for AS type solvers used for
linear, nonlinear and hybrid MPC
An investigation of messy genetic algorithms
Genetic algorithms (GAs) are search procedures based on the mechanics of natural selection and natural genetics. They combine the use of string codings or artificial chromosomes and populations with the selective and juxtapositional power of reproduction and recombination to motivate a surprisingly powerful search heuristic in many problems. Despite their empirical success, there has been a long standing objection to the use of GAs in arbitrarily difficult problems. A new approach was launched. Results to a 30-bit, order-three-deception problem were obtained using a new type of genetic algorithm called a messy genetic algorithm (mGAs). Messy genetic algorithms combine the use of variable-length strings, a two-phase selection scheme, and messy genetic operators to effect a solution to the fixed-coding problem of standard simple GAs. The results of the study of mGAs in problems with nonuniform subfunction scale and size are presented. The mGA approach is summarized, both its operation and the theory of its use. Experiments on problems of varying scale, varying building-block size, and combined varying scale and size are presented
Smooth heaps and a dual view of self-adjusting data structures
We present a new connection between self-adjusting binary search trees (BSTs)
and heaps, two fundamental, extensively studied, and practically relevant
families of data structures. Roughly speaking, we map an arbitrary heap
algorithm within a natural model, to a corresponding BST algorithm with the
same cost on a dual sequence of operations (i.e. the same sequence with the
roles of time and key-space switched). This is the first general transformation
between the two families of data structures.
There is a rich theory of dynamic optimality for BSTs (i.e. the theory of
competitiveness between BST algorithms). The lack of an analogous theory for
heaps has been noted in the literature. Through our connection, we transfer all
instance-specific lower bounds known for BSTs to a general model of heaps,
initiating a theory of dynamic optimality for heaps.
On the algorithmic side, we obtain a new, simple and efficient heap
algorithm, which we call the smooth heap. We show the smooth heap to be the
heap-counterpart of Greedy, the BST algorithm with the strongest proven and
conjectured properties from the literature, widely believed to be
instance-optimal. Assuming the optimality of Greedy, the smooth heap is also
optimal within our model of heap algorithms. As corollaries of results known
for Greedy, we obtain instance-specific upper bounds for the smooth heap, with
applications in adaptive sorting.
Intriguingly, the smooth heap, although derived from a non-practical BST
algorithm, is simple and easy to implement (e.g. it stores no auxiliary data
besides the keys and tree pointers). It can be seen as a variation on the
popular pairing heap data structure, extending it with a "power-of-two-choices"
type of heuristic.Comment: Presented at STOC 2018, light revision, additional figure
Convergence and Cycling in Walker-type Saddle Search Algorithms
International audienceAlgorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present results for idealized versions of the dimer and gentlest ascent (GAD) saddle search algorithms that show-case the limitations of what is theoretically achievable within the current class of saddle search algorithms: (1) we present an improved estimate on the region of attraction of saddles; and (2) we construct quasi-periodic solutions which indicate that it is impossible to obtain globally convergent variants of dimer and GAD type algorithms
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