# Sum of Three Cubes via Optimisation.

@article{Lazov2020SumOT, title={Sum of Three Cubes via Optimisation.}, author={Boian V. Lazov and T. Vetsov}, journal={arXiv: Number Theory}, year={2020} }

By first solving the equation $x^3+y^3+z^3=k$ with fixed $k$ for $z$ and then considering the distance to the nearest integer function of the result, we turn the sum of three cubes problem into an optimisation one. We then apply three stochastic optimisation algorithms to this function in the case with $k=2$, where there are many known solutions. The goal is to test the effectiveness of the method in searching for integer solutions. The algorithms are a modification of particle swarm…

## Figures and Tables from this paper

## 2 Citations

Exploration and Exploitation Zones in a Minimalist Swarm Optimiser

- BusinessEntropy
- 2021

The aim is to examine the population’s dimensional behaviour in each iteration and each defined exploration-exploitation zone, and to subsequently offer improvements to the working of the optimiser.

Evolutionary Optimisation of Beer Organoleptic Properties: A Simulation Framework

- BusinessFoods
- 2022

Modern computational techniques offer new perspectives for the personalisation of food properties through the optimisation of their production process. This paper addresses the personalisation of…

## References

SHOWING 1-10 OF 23 REFERENCES

Clustering Financial Return Distributions Using the Fisher Information Metric

- Computer ScienceEntropy
- 2019

This work develops a technique to identify the nearest neighbors of a target security in the sense that their best fit model distributions have minimal Fisher distance to the target and develops a hierarchical clustering technique that utilizes the Fisher distance.

The density of zeros of forms for which weak approximation fails

- Mathematics
- 1992

The weak approximation principal fails for the forms x + y + z = kw, when k = 2 or 3. The question therefore arises as to what asymptotic density one should predict for the rational zeros of these…

Dispersive Flies Optimisation

- Business2014 Federated Conference on Computer Science and Information Systems
- 2014

A new metaheuristic - Dispersive Flies Optimisation or DFO - whose inspiration is beckoned from the swarming behaviour of flies over food sources in nature is proposed, which is a potentially suitable candidate for dynamically changing environment.

Particle swarm optimisation based Diophantine equation solver

- Business, MathematicsInt. J. Bio Inspired Comput.
- 2010

The paper introduces particle swarm optimisation as a viable strategy to find numerical solution of Diophantine equation, for which there exists no general method of finding solutions. The proposed…

Fisher information distance: a geometrical reading?

- Computer Science, MathematicsDiscret. Appl. Math.
- 2015

Restarting search algorithms with applications to simulated annealing

- Computer Science
- 2001

It is shown under reasonable conditions that restarting when certain patterns occur yields probabilities that the goal state has not been found by the nth epoch which converge to zero at least geometrically fast in n.

Learning to Optimize ∗

- Economics
- 2008

We consider decision-making by boundedly-rational agents in dynamic stochastic environments. The behavioral primitive is anchored to the shadow price of the state vector. Our agent forecasts the…

Information geometry and its applications

- Mathematics2012 9th European Radar Conference
- 2012

Information geometry is a new mathematical discipline which applies the methodology of differential geometry to statistics. Therefore, families of exponential distributions are considered as embedded…

Waring’s problem for cubes

- Mathematics
- 1996

In his book Meditationes Algebraicae, published in 1770, Edward Waring stated without proof that every nonnegative integer is the sum of four squares, nine cubes, 19 fourth powers, and so on.…

Information and the Accuracy Attainable in the Estimation of Statistical Parameters

- Mathematics
- 1992

The earliest method of estimation of statistical parameters is the method of least squares due to Mark off. A set of observations whose expectations are linear functions of a number of unknown…