Morabaraba Optimization Algorithm (MOA)

A novel socio-game-inspired metaheuristic for global optimization, based on the traditional Southern African board game Morabaraba.

The Morabaraba Optimization Algorithm (MOA) is a novel socio-game-inspired metaheuristic for global optimization, modeled on the traditional Southern African board game Morabaraba (also known as Twelve Men's Morris or Mlabalaba).

Each search agent is a player whose cows (game pieces) progress through the three phases of the game, which map directly onto the exploration-exploitation life cycle of the search:

- PLACING phase: cows are placed on the board (global exploration of the

search space);

- MOVING phase: cows slide along board lines (guided local search);

- FLYING phase: a player reduced to three cows may fly anywhere on the

board (long-range escape from local optima).

The principal mechanism of MOA is mill-formation cooperative selection. When three teammates align their values along a board line (a triplet of decision-variable dimensions) within a relative tolerance, the mill "shoots" a cow off the worst opposing agent and drags that agent's weakest-aligned dimension toward the mill mean. Selection pressure is therefore driven by structural alignment of the population rather than by fitness rank alone. Supporting mechanisms include a cow-count state machine governing phase transitions, a two-team (Black vs White) tournament dynamic, the 24-point Morabaraba board topology as a neighbourhood graph, a mill roster acting as a multi-leader attractor pool, per-agent mood, and a mill-rate stagnation trigger for escaping premature convergence.

HOW TO USE:

Run main.m. Select any benchmark function F1-F50, the population size N, and the maximum iterations T. To solve your own problem, simply define your objective function handle, bounds, and dimension, e.g.:

fobj = @(x) sum(x.^2); lb = -100; ub = 100; dim = 50;

[BestScore, BestPosition, Curve] = MOA(30, 500, lb, ub, dim, fobj);

The package includes a 50-function benchmark library (Get_Functions_details.m) and a ready-to-run demo (main.m). No toolboxes required.

Please cite:

Thango, B.A., "Morabaraba Optimization Algorithm: A novel socio-game-inspired meta-heuristic for global optimization," Mathematics, 2026.