Empirical Investigation of the Benefits of Partial Lamarckianism

Abstract

Genetic algorithms (GAs) are very efficient at exploring the entire search space; however, they are relatively poor at finding the precise local optimal solution in the region in which the algorithm converges. Hybrid GAs are the combination of improvement procedures, which are good at finding local optima, and GAs. There are two basic strategies for using hybrid GAs. In the first, Lamarckian learning, the genetic representation is updated to match the solution found by the improvement procedure. In the second, Baldwinian learning, improvement procedures are used to change the fitness landscape, but the solution that is found is not encoded back into the genetic string. This paper examines the issue of using partial Lamarckianism (i.e., the updating of the genetic representation for only a percentage of the individuals), as compared to pure Lamarckian and pure Baldwinian learning in hybrid GAs. Multiple instances of five bounded nonlinear problems, the location-allocation problem, and the cell formation problem were used as test problems in an empirical investigation. Neither a pure Lamarckian nor a pure Baldwinian search strategy was found to consistently lead to quicker convergence of the GA to the best known solution for the series of test problems. Based on a minimax criterion (i.e., minimizing the worst case performance across all test problem instances), the 20% and 40% partial Lamarckianism search strategies yielded the best mixture of solution quality and computational efficiency.

A Memetic Approach to Golomb Rulers

“…One of the key points in the experimentation has been analyzing the influence of the local search strategy with respect to the population-based component. To this end, we have experimented with partial Lamarckism [20], that is, applying the local improvement method just on a fraction of the members of the population. To be precise, we have considered a probability p ts for applying LS to each solution.…”

The importance of being structured: A comparative study on multi stage memetic approaches

“…A careful analysis of the dynamic behaviour of the three 5.33e + 00 ± 2.91e + 01 −8.56e + 00 ± 2.49e − 01 -−9.21e + 00 ± 6.35e − 09 -f 6 8.25e + 01 ± 2.83e + 02 4.66e + 01 ± 1.05e + 01 -3.63e + 01 ± 6.31e − 01 -f 7 1.05e + 02 ± 1.23e + 01 1.02e + 02 ± 5.88e + 00 = 1.03e + 02 ± 7.60e + 00 = f 8 1.49e + 02 ± 1.86e − 01 1.52e + 02 ± 2.47e + 00 + 1.51e + 02 ± 2.09e + 00 + f 9 1.25e + 02 ± 1.69e + 00 1.47e + 02 ± 4.28e + 01 + 1.26e + 02 ± 1.10e + 01 + f 10 3.95e + 03 ± 2.63e + 04 6.42e + 03 ± 5.41e + 03 + 2.01e + 02 ± 2.13e + 02 -f 11 1.57e + 02 ± 3.36e + 01 1.01e + 02 ± 9.08e + 00 -1.66e + 02 ± 3.20e + 01 = f 12 −6.12e + 02 ± 1.33e + 01 −2.40e + 02 ± 3.93e + 02 + −6.12e + 02 ± 1.50e + 01 = f 13 4.26e + 01 ± 1.28e + 01 4.62e + 01 ± 1.29e + 01 + 4.28e + 01 ± 1.17e + 01 = f 14 −5.23e + 01 ± 3.05e − 05 −5.23e + 01 ± 2.06e − 03 + −5.23e + 01 ± 6.52e − 05 -f 15 1.10e + 03 ± 6.38e + 01 1.06e + 03 ± 2.23e + 01 -1.06e + 03 ± 2.51e + 01 -f 16 7.97e + 01 ± 4.63e + 00 7.58e + 01 ± 2.03e + 00 -7.67e + 01 ± 3.80e + 00 -f 17 −1.03e + 01 ± 6.57e + 00 −1.51e + 01 ± 9.11e − 01 -−2.32e + 00 ± 1.09e + 01 + f 18 5.80e + 00 ± 2.56e + 01 −1.17e + 01 ± 3.09e + 00 -3.96e + 01 ± 5.28e + 01 + f 19 −9.80e + 01 ± 2.98e + 00 −9.93e + 01 ± 7.62e − 01 -−9.44e + 01 ± 4.24e + 00 + f 20 −5.46e + 02 ± 2.59e − 01 −5.46e + 02 ± 2.17e − 01 -−5.46e + 02 ± 2.44e − 01 -f 21 5.36e + 01 ± 1.34e + 01 4.46e + 01 ± 3.62e + 00 -4.51e + 01 ± 4.16e + 00 -f 22 −9.88e + 02 ± 1.55e + 01 −9.96e + 02 ± 4.73e + 00 -−9.96e + 02 ± 7.80e + 00 -f 23 7.86e + 00 ± 4.95e − 01 7.92e + 00 ± 2.46e − 01 = 7.54e + 00 ± 2.98e − 01 -f 24 1.92e + 02 ± 4.46e + 01 1.56e + 02 ± 1.43e + 01 -1.67e + 02 ± 2.06e + 01 - DIMENSIONS (REFERENCE = 3SOME) 3SOME 3SOME-Powell 3SOME-Rosenbrock f 1 7.95e + 01 ± 2.56e − 14 7.95e + 01 ± 2.89e − 03 + 7.95e + 01 ± 1.99e − 14 = f 2 −2.10e + 02 ± 3.28e − 14 −8.97e + 01 ± 1.09e + 02 + −2.10e + 02 ± 2.07e − 13 + f 3 −4.54e + 02 ± 3.44e + 00 −4.57e + 02 ± 1.51e + 00 -−4.59e + 02 ± 1.86e + 00 -f 4 −4.51e + 02 ± 4.06e + 00 −4.52e + 02 ± 2.64e + 00 -−4.57e + 02 ± 2.56e + 00 -f 5 5.63e + 01 ± 1.78e + 02 −5.43e + 00 ± 7.20e − 01 -−9.21e + 00 ± 6.81e − 12 -f 6 3.59e + 01 ± 9.31e − 07 1.13e + 02 ± 1.04e + 02 + 3.66e + 01 ± 1.07e + 00 + f 7 2.10e + 02 ± 6.39e + 01 2.30e + 02 ± 5.20e + 01 + 2.26e + 02 ± 5.19e + 01 + f 8 1.53e + 02 ± 1.69e + 01 2.31e + 02 ± 3.64e + 01 + 1.83e + 02 ± 3.56e + 01 + f 9 1.25e + 02 ± 1.53e + 00 1.77e + 02 ± 3.46e + 01 + 1.27e + 02 ± 1.54e + 00 + f 10 1.95e + 05 ± 1.40e + 06 2.62e + 04 ± 1.25e + 04 -7.73e + 02 ± 3.58e...…”

“…In particular, related to MAs, several coordination schemes have been proposed in the last two decades. For example, a rather simple strategy to control the activation of local search, called "partial Lamarckianism" [5] consists in randomly applying the local search with some probability. Another possible scheme, proposed in [6] and [7], consists in classifying the solutions processed by the evolutionary framework according to their fitness.…”

A Hybrid GRASP – Evolutionary Algorithm Approach to Golomb Ruler Search

“…Namely, Feeney examined three methods of searching for Golomb Rulers, using genetic algorithms on its own, with local search and Baldwinian learning, and with local search and Lamarckian learning (see e.g. [13][14][15] for more information on Lamarckian and Baldwinian learning). It is known that, combined with EAs, local search techniques often reduces drastically the number of generations to find a nearoptimum solution (see e.g., [16]).…”