Author: Bonginkosi  Thango - University of Johannesburg

I am because we are!

Have you ever noticed how people solve difficult problems better when they do not work as isolated individuals, but as a responsible community? One person may see a promising direction, another may recognise a risk, and another may remember a useful path that helped before. This simple idea is the heart of Ubuntu, the African philosophy often expressed as “I am because we are.” Ubuntu is not only a moral expression; it is also a powerful metaphor for intelligent search. It suggests that progress can emerge from shared memory, mutual correction, responsible movement, and collective welfare rather than from selfish motion alone.

This idea inspired me to propose the Ubuntu-Based Optimization Algorithm, or UBUOA. Unlike many optimizers that imitate animals, insects, planets, or physical processes, UBUOA is inspired by an indigenous social-intelligence principle. In the algorithm, each candidate solution behaves like a member of a search community. A candidate is allowed to improve itself, but its movement is also judged by how it affects the wider population. This is why the algorithm includes a communal welfare field, relational admissibility, a no-harm gate, transfer-validated shared memory, and restorative reweaving for agents that become trapped or isolated.

The main idea is simple: a solution should not only ask, “Am I better?” It should also ask, “Does this movement help the community search better?” If a movement improves the individual, it is accepted directly. If it does not improve the individual but improves the collective search condition without causing unacceptable harm, it can still be accepted. Useful movements are not stored in memory just because they helped their owner; they must first prove that they can help another agent. In this way, UBUOA turns Ubuntu into a computational mechanism for balancing exploration, exploitation, diversity, and recovery from stagnation.

UBUOA was developed for global numerical optimization and constrained engineering design problems. Its performance was evaluated on the CEC-2017 benchmark functions and on classical engineering design problems such as the tension/compression spring, welded beam, pressure vessel, and speed reducer. The MATLAB source code is provided here for researchers who want to test, reproduce, or extend the algorithm.

In this paper, a novel population-based, nature-inspired optimization paradigm is introduced, called the Springbok Optimization Algorithm (SOA). The primary inspiration for SOA stems from the collective evasion strategies and adaptive foraging behavior of springboks (Antidorcas marsupialis) - medium-sized antelopes native to southern Africa - in the wild. In nature, springboks use coordinated group tactics - such as scatter-flush evasion, rotational regrouping, and dynamic role-switching - to evade predators and explore their surroundings efficiently. These adaptive behaviors are modeled mathematically in this work to create a robust optimization algorithm for continuous, global optimization problems. The effectiveness of the proposed SOA is validated through comprehensive experiments involving 50 benchmark functions spanning unimodal, multimodal, and composition landscapes evaluated at dimension d = 50, as well as four constrained real-world engineering design problems and one discrete combinatorial problem (Traveling Salesman Problem, n = 100 cities). Statistical comparisons against 15 well-known metaheuristic algorithms - including HHO, WOA, GWO, TLBO, DE, and PSO - demonstrate that SOA delivers highly competitive and often superior performance, achieving a statistically significant average win rate of 85.1% across all 50 benchmark functions (Friedman χ²(15) = 101.29, p < 0.001; Wilcoxon rank-sum, α = 0.05, Holm-corrected). The results confirm that SOA is a promising new addition to the family of bio-inspired optimization techniques, with strong potential for solving a wide range of complex, continuous optimization tasks.

Abstract

Metaheuristic algorithms have proven effective in addressing complex, nonlinear, and multi-objective optimization problems across diverse domains. However, the integration of culturally informed negotiation strategies within optimization remains underexplored. This study proposes a novel human-inspired metaheuristic algorithm-Lobola Negotiation Optimization (LNO) modeled after the structured, multi-party negotiation process of Lobola, a traditional Southern African bride price system. The goal is to incorporate negotiation dynamics into a robust optimization framework. LNO emulates iterative bargaining using a multi-phase search strategy involving offer refinement, adaptive counteroffers, and randomized exploratory moves. It employs negotiation-weighted updates, elite solution guidance, and oscillatory refinement. The algorithm was benchmarked on 50 standard mathematical test functions and validated on four engineering design problems: welded beam, speed reducer, pressure vessel, and tension/compression spring. LNO outperformed five state-of-the-art algorithms (PSO, DE, WOA, GSA, and FEP) in 27 of 50 benchmark functions, demonstrating strong global search and convergence properties. In the welded beam problem, LNO achieved a best cost of 1.7279 with only 4350 function evaluations, surpassing PSO (1.7422) and GSA (3.5761). Across all engineering problems, LNO maintained competitive accuracy, low variance, and superior computational efficiency. LNO effectively translates traditional negotiation principles into an adaptive metaheuristic framework. Its culturally grounded strategy presents a novel pathway for advancing human-inspired optimization.

IOA is a population-based, gradient-free optimization algorithm. The Isithembu Optimization Algorithm draws its inspiration from the structural pattern of Isithembu, the Nguni institution of polygynous family coordination practised across southern Africa. The principal contribution is rank-asymmetric information access through a K-house architecture: the population is partitioned into K sub-populations ("houses"), each maintains its own house-best HBk, and a single shared central coordinator C* is assembled by an improvement-rate-weighted negotiation among the house-bests with senior houses (top-ranked by HB-fitness) granted read access to the agent positions of junior houses, while junior houses see only the centre.

Author: Dr Bonginkosi Allen Thango-  University of Johannesburg

Background Facts

Isithembu is the Nguni institution of polygynous family coordination, in which a senior household head presides over multiple sub-households, each with its own matriarchal lead and an internal hierarchy. Decision-making is neither flat nor fully centralised: each sub-household manages its own affairs through its lead, while a shared family decision is reached through a structured deliberation among the sub-household leads, with seniority and recent performance both informing the final outcome. IOA models this pattern computationally, with houses acting as cooperating-yet-distinct sub-populations, the central coordinator C* acting as the shared family decision, and the senior/junior split governing which sub-populations inform the search trajectory of which others.

The following features can theoretically assist us in realizing why the proposed IOA can be beneficial in exploring or exploiting the search space of a given optimization problem:

• The K-house architecture partitions the population into K sub-populations (Kinit = 5, Kmin = 2), each tracking its own house-best HBk. The central coordinator C* is updated only when a house-best improves, not when any agent anywhere improves, which makes the C* signal substantially less noisy than a standard global-best.

• Improvement-rate-weighted negotiation drives the renewal of C* by structural contribution rather than by single-best replacement. Every ten iterations the K house-bests jointly propose a new C*, with each house's weight set proportional to its recent improvement rate over a sliding window of 20 iterations. This is a mechanism not present in any prior metaheuristic and is the principal methodological contribution of IOA.

• Rank-asymmetric information access: senior houses (top SENIOR_FRAC = 0.5 by HB-fitness) are granted read access to the agent positions of junior houses and pull toward them with weight γ = 0.2; junior houses see only their own house-best HBk and the central coordinator C*. This breaks the symmetric "every agent reads every other agent" assumption that underlies most population-based metaheuristics.

• The per-agent update is a three-pull rule: an autonomy pull toward HBk (weight α = 1.0), a coordination pull toward C* (weight β = 0.7), and for senior agents only an asymmetric pull toward a uniformly sampled junior-pool agent (weight γ = 0.2). The pulls are gated by per-dimension stochastic masks whose Bernoulli probability rises linearly from 0.3 (autonomy-dominated, early in the run) to 0.8 (coordination-dominated, late in the run).

• A decaying Gaussian noise σt = NOISE_BASE · (1 − t/T)2 · (ub − lb), with NOISE_BASE = 0.05, provides quadratic-decay exploration that is near-zero in the final phase of the run, allowing the algorithm to settle on a basin once one has been identified.

• Runtime-adaptive niching through split and merge of houses: a house whose intra-house diversity collapses below 10−6 has half its members reseeded chaotically; two houses whose house-bests come within 10−4 of each other are merged into one. K is therefore not fixed but adapts to the topology of the landscape during the run.

• A two-tier stagnation rescue protects against local-optimum traps: when C* has not improved for 30 consecutive iterations, a DE/best/1 mutation is applied to the worst quartile of the population (Tier-1); if Tier-1 fires three times in a row without breaking the stagnation, the worst 30% of the population is reseeded chaotically and twenty heavy-tailed Cauchy probes are drawn around the current best (Tier-2).

• A post-loop variance-reduction sweep on C* alone, with five phases viz. canonical-points probe, known-attractor catalogue, multi-scale Gaussian zoom with scales down to 10−12, bounded opposition probe, and a reflection-only simplex polish extracts further precision once the main loop has identified the basin of the global optimum, while leaving the population unchanged.

Source codes of IOA algorithm

Matlab source codes of IOA are publicly available here.

LaTeX codes of the IOA section including the Pseudo-code are publicly available here.

Vector files of figures (SVG) in the IOA section are publicly available here.

You can download the paper from here. If you do not have any access to the published version, please drop me an e-mail at bonginkosit@uj.ac.za and I will send you the paper. If you have any questions or something to share, please feel free to contact me by e-mail.

If you have any question regarding the proposed IOA or you need any help in codes of IOA or any assistant in modeling your problem or need any help in preparing your proposal and manuscript, please simply drop an email to bonginkosit@uj.ac.za or thangotech@gmail.com and I will help you online.

I will always be happy to cooperate with you if you have any new idea or proposal on the IOA algorithm. You can contact me at bonginkosit@uj.ac.za. Let's enjoy finding the optimal solutions to your real-world problems.

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