Large amounts of research focus on the balance between Exploration and Exploitation. However, this omits the power of Selection which can turn any metaheuristic into a hill climber by rejecting all exploratory search solutions.
To engage the broader research community in this important discussion, we are organizing a Workshop on Selection to be held at CEC2021 in Krakow, Poland. Please consider participating in our event or on our project page.
https://www.researchgate.net/project/Workshop-on-Selection
Maude Josee Blondin, we're more experimental in our research. We've collected a lot of interesting data which shows when the "balance" is off (for example, stall in PSO -- Conference Paper Particle Swarm Optimization with pbest Perturbations
). We might even be able to produce some measurable metrics. But no proofs!
Dear Maude, the mathematical demonstration of the optimal balance seems to be complicated, but I think it is possible to do the mathematical demonstration of the influence of some operators on the balance sheet. This could allow the operator to be directed towards the search for the desired balance sheet.
One way to observe and control this balance is using the diversity index. It has been observed that the performance of heuristics is so related to this index:
https://www.sciencedirect.com/science/article/abs/pii/S0965997814000970?via%3Dihub
https://link.springer.com/article/10.1007/s11831-021-09546-1
So you can control your optimization tool with the diversity index:
https://arc.aiaa.org/doi/abs/10.2514/1.27020?journalCode=ja
Maybe you can control the algorithm to have a higher diversity index in the beginning and then decrease it gradually.
However, metaheuristics are not good tools for finding optimum and mathematical optimization is always superior.
I think one needs to be leery against regarding "selection" in metaheuristics as an independent attribute from exploitation. If anything, the two really complement one another. History has shown that metahueristics which have a selection property to it invariably have weak explorative capabilities. Prime well-known examples are Artificial Bee Colony algorithm and GAs.
My guess is that the same metrics that we currently use for estimating algorithmic performance (optimized solution, standard deviation, number of functional analysis, diversity index, etc.) can be modified to examine the so-called "selection - exploration" balance for algorithms, since as I said earlier, selection and exploitation are really just two faces of the same coin.
To solve continuous optimization problems, the differential evolution algorithm (DE) offers a simple but efficient structure consisting of a good mutation strategy to create a mutant vector with the difference of vectors and a flexible crossover strategy to vary the effect of the mutant vector by using either a local move of few components or a large (diagonal) move of many components. With a well-designed adaptive control, the DE algorithm can solve a wide range of problems effectively. Balancing local search and global search is not difficult when the algorithm structure is flexible. DE adopts a greedy selection strategy to speed up the convergence. If the selection is too strong, we can add something to control the population diversity. Adapting population sizes or implementing an archive of some solutions to use during the search can give an alternative approach to managing diversity.
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