Slime mould algorithm (SMA): A new method for stochastic optimization

Slime mould algorithm (SMA) is a powerful population-based optimizer based on the oscillation mode of slime mould in nature. In April 2020, the research of SMA was published in the prestigious journal of Future Generation Computer Systems (FGCS).

Without having any brain or neurons, slime moulds, Physarum polycephalum, are extraordinarily intelligent, capable of solving difficult computational problems with extreme efficiency. This single-celled amoeba can remember, make decisions and anticipate change, influencing us to rethink intelligent behaviour. It optimizes the shape of its network over time as it takes in information.

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The SMA has a unique mathematical model and very competitive results along with fast convergence for many problems, especially for real-world cases. The gradient-free SMA method simulates positive and negative feedbacks of the propagation wave of slime mould. It has a dynamic structure with a stable balance between global and local search drifts. Until now, many researchers have applied this method to several real-world problems, and their work is published in leading international journals.

Slime mould can learn and solve problems without any nervous system

Without having any brain or neurons, slime moulds, Physarum polycephalum, are extraordinarily intelligent, capable of solving difficult computational problems with extreme efficiency.

Because of the unique pattern and distinctive, intelligent abilities of slime mould, they can utilize multiple food sources at the same time to construct a venous network for connecting the sources. If there is enough food in the surroundings of the slime, it can even develop and distribute itself to more than 900 square centimetres. Research has confirmed and utilized the slime mould for solving complex mazes, demonstrating that the slime mould is able to detect and develop the optimal path to connect the food in a fairly optimal manner using a combination of positive and negative feedbacks (a sending and signalling way). It is fascinating that the slime mould can dynamically regulate their search patterns according to the quality of food provenance. The venous construction of slime mould produces along with the phase difference of the contraction mode, so there are three correlations between the morphological variations of the venous structure and the contraction mode of slime mould:

1. Thick veins form roughly along the radius when the contraction frequencies vary from outside to inside.
2. When the contraction mode is unbalanced, anisotropy begins to appear.
3. When the contraction pattern of slime mould is no longer ordered with time and space, the venous structure is no longer present.

As a result, the relationship between venous structure and contraction design of slime mould is in line with the shape of naturally designed cells. The thickness of each vein is obtained by the flow feedback of the cytoplasm in the Physarum solver. The rise in the flow of cytoplasm leads to an upsurge in the diameter of veins. As the flow decreases, the veins contract because of the decrease of the diameter. Slime mould can shape a stronger path where food concentration is higher, therefore, ensuring that they get the maximum concentration of nutrients.

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Mathematical model and structure of the SMA optimization

 

Full Text PDF of the original paper

 

 

The following remarks can theoretically help us to understand why the developed SMA can be useful in exploring or exploiting the feature space of a given optimization problem:

• The adaptive weight W enables the SMA to maintain a certain disturbance rate while guaranteeing fast convergence, thus avoiding optimal local trapping during fast convergence.
• The SMA is a swarm-based method with a fast performance, which does not need any info about the problem space. Hence, it can be used for different forms of optimization problems, including single-objective, multi-objective, many objective, fuzzy optimization, robust optimization, and memetic optimization.
• The SMA has several dynamic aspects that help to show a very flexible performance, especially when there is a need to adjust the searching trends towards more stable levels.
• Vibration parameter (vb) allows the individual position of slime mould to contract in a specific way, thus ensuring the efficiency of the early exploration and the accuracy of the later exploitation.
• The adequate utilization of individual fitness values allows SMA to make better decisions based on historical information.
• The location updating decision parameter p and three different location updating methods ensure better adaptability of the SMA in different search phases.
• The SMA code is open source, and FAIR — Findable, Accessible, Interoperable, and Reusable.

Source codes and files of SMA optimization algorithm