Simulated annealing: theory and applications
Simulated annealing: theory and applications
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Solving k-shortest and constrained shortest path problems efficiently
Annals of Operations Research
Randomized algorithms and pseudorandom numbers
Journal of the ACM (JACM)
Simulated annealing: past, present, and future
WSC '95 Proceedings of the 27th conference on Winter simulation
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
How to solve it: modern heuristics
How to solve it: modern heuristics
Algorithm 247: Radical-inverse quasi-random point sequence
Communications of the ACM
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Software for uniform random number generation: distinguishing the good and the bad
Proceedings of the 33nd conference on Winter simulation
On Random Numbers And The Performance Of Genetic Algorithms
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Genetic algorithms using low-discrepancy sequences
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Random number generators: mc integration and tsp-solving by simulated annealing, genetic, and ant system approaches
Golden ratio in science, as random sequence source, its computation and beyond
Computers & Mathematics with Applications
The traveling salesman: computational solutions for TSP applications
The traveling salesman: computational solutions for TSP applications
Numerical results on some generalized random Fibonacci sequences
Computers & Mathematics with Applications
Best k-digit rational bounds for irrational numbers: Pre- and super-computer era
Mathematical and Computer Modelling: An International Journal
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The algebraic irrational number golden ratio @f=(1+5)/2 = one of the two roots of the algebraic equation x^2-x-1=0 and the transcendental number @p=2sin^-^1(1) = the ratio of the circumference and the diameter of any circle both have infinite number of digits with no apparent pattern. We discuss here the relative merits of these numbers as possible random sequence sources. The quality of these sequences is not judged directly based on the outcome of all known tests for the randomness of a sequence. Instead, it is determined implicitly by the accuracy of the Monte Carlo integration in a statistical sense. Since our main motive of using a random sequence is to solve real-world problems, it is more desirable if we compare the quality of the sequences based on their performances for these problems in terms of quality/accuracy of the output. We also compare these sources against those generated by a popular pseudo-random generator, viz., the Matlab rand and the quasi-random generator halton both in terms of error and time complexity. Our study demonstrates that consecutive blocks of digits of each of these numbers produce a good random sequence source. It is observed that randomly chosen blocks of digits do not have any remarkable advantage over consecutive blocks for the accuracy of the Monte Carlo integration. Also, it reveals that @p is a better source of a random sequence than @f when the accuracy of the integration is concerned.