Continuous non-revisiting genetic algorithm with random search space re-partitioning and one-gene-flip mutation

Abstract

In continuous non-revisiting genetic algorithm (cNrGA), the solution set with different order leads to different density estimation and hence different mutation step size. As a result, the performance of cNrGA depends on the order of the evaluated solutions. In this paper, we propose to remove this dependence by a search space re-partitioning strategy. At each iteration, the strategy reshuffles the solutions into random order. The reordered sequence is then used to construct a new density tree, which leads to a new space partition sets. Afterwards, instead of randomly picking a mutant within a partition, a new adaptive one-gene-flip mutation is applied. Motivated from the fact that the proposed adaptive mutation concerns only small amount of partitions, we propose a new density tree construction algorithm. This algorithm refuses to partition the sub-regions which do not contain any individual to be mutated, which simplifies the tree topology as well as speeds up the construction time. The new cNrGA integrated with the proposed re-partitioning strategy (cNrGA/RP/OGF) is examined on 19 benchmark functions at dimensions ranging from 2 to 40. The simulation results show that cNrGA/RP/OGF is significantly superior to the original cNrGA at most of the test functions. Its average performance is also better than those of six benchmark EAs.

A dynamic history-driven evolutionary algorithm

“…When the data points are the evaluated solutions of an evolutionary algorithm, the corresponding partitioning scheme represents the distribution of the solutions. [1], [2] use it to control the mutation step size in an adaptive and parameter-less manner. In [4], as the BSP tree stores also the fitness values of the evaluated solutions, it serves as a static fitness landscape estimator.…”

“…In [2], the evaluated solution density provides a good guidance on setting the mutation step size; the corresponding mutation operators are adaptive and applied to handle static optimization problems. While optimizing DOP, the guidance on mutation step size by solution density involves temporal information as well.…”

“…The j th element of s, s j , is replaced by a uniformly distributed random number in the range [l j , u j ]. The individual after element replacement is regarded as the mutant of s. This procedure implements a One-Gene-Flip (OGF) mutation, which is proposed in [2]. Comparing to the adaptive mutation in [1] that randomly selects a point in M, OGF mutation is less disruptive to the schemata structure.…”

“…Originated from the linkage between mutation step size and solution density in [2], we extend it to DOP by simultaneously considering solution density and its reliability. The corresponding history-driven mutation operator adaptively switches the search strategy between exploration and exploitation.…”

On-line Search History-assisted Restart Strategy for Covariance Matrix Adaptation Evolution Strategy

“…The non-revisiting genetic algorithm (NrGA) [7] records the entire on-line search history by a binary space partitioning (BSP) tree, thus, re-evaluation of any solution is completely avoided. The continuous version cNrGA (where 'c' stands for continuous) inherits the BSP tree to store the entire search history [8], [9]. Crossover is used in cNrGA for the first-stage searching, which introduces no new gene into the population, and thus identical solutions (revisits) are prone to be generated by recombinations.…”