Towards the right amount of randomness in quantum-inspired evolutionary algorithms

Abstract

Quantum-inspired evolutionary algorithms (QIEAs) combine the advantages of quantum-inspired bit (Q-bit), representation and operators with evolutionary algorithms for better performance. Using quantum-inspired representation the complete binary search space can be generated by collapsing a single Q-bit string repeatedly. Thus, even a population size of 1 can be taken in a QIEA implementation resulting in enormous saving in computation. Although this is correct in theory, QIEA implementations run into trouble in exploring large search spaces with this approach. The Q-bit string has to be initialized to produce each possible binary string with equal probability and then altered slowly to probabilistically favor generation of strings with better fitness values. This process is unacceptably slow when the search spaces are very large. Many ideas have been reported with EAs/QIEAs for speeding up convergence while ensuring that the algorithm does not get stuck in local optima. In this paper, the possible features are identified and systematically introduced and tested in the QIEA framework in various combinations. Some of these features increase the randomness in the search process for better exploration and the others compensate by local search for better exploitation together enabling a judicious combination tailored for particular problem being solved. This is referred to as “right-sizing the randomness” in the QIEA search. Benchmark instances of the well-known and well-studied Quadratic Knapsack Problem are used to demonstrate how effective these features are—individually and collectively. The new framework, dubbed QIEA-QKP, is shown to be much more effective than canonical QIEA. The framework can be utilized with profit on other problems and is being attempted.