A Seed-Based Plant Propagation Algorithm: The Feeding Station Model

The seasonal production of fruit and seeds is akin to opening a feeding station, such as a restaurant. Agents coming to feed on the fruit are like customers attending the restaurant; they arrive at a certain rate and get served at a certain rate following some appropriate processes. The same applies to birds and animals visiting and feeding on ripe fruit produced by plants such as the strawberry plant. This phenomenon underpins the seed dispersion of the plants. Modelling it as a queuing process results in a seed-based search/optimisation algorithm. This variant of the Plant Propagation Algorithm is described, analysed, tested on nontrivial problems, and compared with well established algorithms. The results are included.</jats:p

Restarting from Specific Points to Cure Breakdown in Lanczos-type Algorithms

Breakdown in Lanczos-type algorithms is a common phenomenon which is due to the non-existence of some orthogonal polynomials. It causes the solution process to halt. It is, therefore, important to deal with it to improve the resilience of the algorithms and increase their usability. In this paper, we consider restarting from a number of different approximate solutions that seem to be attractive starting points. They are: (a) the last iterate preceding breakdown, (b) the iterate with minimum residual norm found so far, and (c) the approximate solution whose entries are the median values of entries of all iterates generated by the Lanczos-type algorithm considered. Although it has been shown theoretically in the context of Arnoldi-type algorithms as well as Lanczos-type algorithms that restarting mitigates breakdown and allows the iterative process to continue and converge to good solutions, here we give an alternative theorem to that effect and a proof of it. However, emphasis is on the quality of the restarting points. Numerical results are included

A Switching Approach to Avoid Breakdown in Lanczos-Type Algorithms

Lanczos-type algorithms are well known for their inherent instability. They typically breakdown when relevant orthogonal polynomials do not exist. Current approaches to avoiding breakdown rely on jumping over the non-existent polynomials to resume computation. This jumping strategy may have to be used many times during the solution process. We suggest an alternative to jumping which consists in switching between different algorithms that have been generated using different recurrence relations between orthogonal polynomials. This approach can be implemented as three different strategies: ST1, ST2, and ST3.We shall briefly recall how Lanczos-type algorithms are derived. Four of the most prominent such algorithms namely A4, A12, A5/B10 and A5/B8 will be presented and then deployed in the switching framework. In this paper, only strategy ST2 will be investigated. Numerical results will be presented. © 2014 NSP Natural Sciences Publishing Cor

A Seed-based Plant Propagation Algorithm: The Feeding Station Model

The seasonal production of fruit and seeds resembles opening a feeding station, such as a restaurant agents/ customers will arrive at a certain rate and pick fruit (get served) at a certain rate following some appropriate processes. Therefore, dispersion follows the resource process. Modelling this process results in a search/ optimisation algorithm that used dispersion as an exploration tool that, if well captured, will find the optimum of a function over a given search space. This paper presents such an algorithm and tests it on non-trivial problems

An evolutionary approach to solving a new integrated quay crane assignment and quay crane scheduling mathematical model

This paper puts forward an integrated optimisation model that combines two distinct problems arising in container terminals, namely the Quay Crane Assignment Problem, and the Quay Crane Scheduling Problem. The model is of the mixed-integer programming type with the objective being to minimise the tardiness of vessels. Although exact solutions can be found to the problem using Branch-and-Cut, for instance, they are costly in time when instances are of realistic sizes. To overcome the computational burden of large scale instances, an adapted Genetic Algorithm, is used. Small to medium size instances of the combined model have been solved with both the Genetic Algorithm and the CPLEX implementation of Branch-and-Cut. Larger size instances, however, could only be solved approximately in acceptable times with the Genetic Algorithm. Computational results are included and discussed

An alternative derivation of a new Lanczos-type algorithm for systems of linear equations

Various recurrence relations between formal orthogonal polynomials can be used to derive Lanczos-type algorithms. In this paper, we consider recurrence relation $A_{12}$ for the choice $U_i(x)=P_i(x)$, where $U_i$ is an auxiliary family of polynomials of exact degree $i$. It leads to a Lanczos-type algorithm that shows superior stability when compared to existing Lanczos-type algorithms. The new algorithm is derived and described. It is then computationally compared to the most robust algorithms of this type, namely $A_{12}$, $A_5/B_{10}$ and $A_8/B_{10}$, on the same test problems. Numerical results are included

Enhancing the Stability of Lanczos-type Algorithms by Embedding Interpolation and Extrapolation for the Solution of Systems of Linear Equations

A new method to treat the inherent instability of Lanczos-type algorithms is introduced. It enables us to capture the properties of the sequence of iterates generated by a Lanczos-type algorithm by interpolating on this sequence of points. The interpolation model found is then used to generate a point that is outside the range. It is expected that this new point will link up the rest of the sequence of points generated by the Lanczos-type algorithm if breakdown does not occur. However, because we assume that the interpolation model captures the properties of the Lanczos sequence, the new point belongs to that sequence since it is generated by the model. This paper introduces the so-called Embedded Interpolation and Extrapolation Model in Lanczos-type Algorithms (EIEMLA). The model was implemented in algorithms A13/B6and A13/B13, which are new variants of the Lanczos algorithm. Individually, these algorithms perform badly on high dimensional systems of linear equations (SLEs). However, with the embedded interpolation and extrapolation models, EIEM A13/B6and EIEM A13/B13, a substantial improvement in the performance on SLEs with up to 105variables can be achieved