Novel Hindu Belief-Inspired Triad Algorithm Balances Complex Engineering Optimization

A pair of researchers, Priteesha Sarangi and Prabhujit Mohapatra, have introduced a novel human-belief-inspired meta-heuristic optimization framework termed the Saraswati-Lakshmi-Ganesha triad algorithm, or SLG algorithm, to address complex global and constrained engineering design problems. Optimization serves as an indispensable tool across modern scientific and technological domains where practitioners must pinpoint the most favorable configuration among an extensive spectrum of potential options. Conventional optimization frameworks, particularly those reliant on mathematical gradients and deterministic formulations, often encounter severe limitations when applied to real-world search landscapes characterized by high dimensionality, non-differentiable formulations, severe non-linearities, and disconnected feasible regions. To bypass the persistent vulnerability of deterministic algorithms becoming trapped within inferior local optima, the researchers formulated an approach grounded in the philosophical and symbolic attributes historically linked to three prominent deities within Hindu traditions.

The conceptual foundation of the SLG algorithm translates traditional symbolic attributes into distinct mathematical mechanisms that manage the critical trade-off between exploratory searching and focused exploitation. In the initial phase, Goddess Saraswati, traditionally recognized for wisdom, learning, and creative thought, represents the generation of constructive knowledge and serves as the conceptual model for populating the search domain. Initial candidate solutions are distributed across the multidimensional bounded space using a uniform random distribution governed by upper and lower problem boundaries. This stage establishes the broad initial diversity necessary to survey the objective space comprehensively before any targeted refinement occurs, ensuring that the population does not artificially cluster near arbitrary coordinates at the onset of execution.

The second operational stage draws from the symbolic role of Goddess Lakshmi, traditionally associated with prosperity, abundance, and the ethical preservation of resources. In the SLG computational framework, prosperity is mapped directly to the retention and directional refinement of high-performing candidate solutions. The formulation establishes that an individual agent’s wealth correlates with its fitness value, using an exponential scaling mechanism for minimization problems where diminishing objective values yield higher accumulated wealth scores. To balance local search behavior, the model defines a pursuit metric that decreases exponentially as the spatial distance between two candidate individuals grows, discouraging agents from chasing excessively distant targets. Total prosperity is evaluated as the arithmetic sum of accumulated wealth and pursuit, which then modulates position updates alongside a spiritual power coefficient ranging between zero and three to guide candidate solutions systematically toward superior positions and the global best solution.

The third functional mechanism reflects the attributes of Lord Ganesha, revered as Vighnahara or the remover of obstacles and impediments. In population-based meta-heuristics, stagnation within sub-optimal regions presents a chronic challenge that can cause premature convergence. Within the SLG framework, this obstacle-removal role is implemented through a systematic abandonment counter governed by a threshold defined as the product of the population size and the maximum iteration count. When candidate solutions fail to exhibit productive improvement and exceed this stagnation threshold, the algorithm classifies them as abandoned and systematically purges them from the population. These stagnant candidates are immediately replaced by newly generated random vectors across the problem bounds, actively injecting fresh diversity into the swarm and granting the algorithm repeated opportunities to escape local traps during extended optimization runs.

To evaluate the structural integrity and individual contributions of these integrated components, the investigators conducted dedicated ablation experiments using benchmark suites such as the Sphere function from the CEC2005 collection. When all three stages functioned in coordination, the SLG algorithm achieved continuous exponential convergence, reaching an optimal objective cost of ten to the power of negative sixty within five hundred iterations. In contrast, removing the Saraswati initialization phase prevented search agents from establishing baseline fitness values or navigating the landscape, causing the trajectory to remain completely flat at an elevated error level across all iterations. Disabling the Lakshmi phase by nullifying the spiritual power coefficient removed directional exploitation capacity, leading to rapid stagnation at an inferior objective value. Similarly, eliminating the Ganesha abandonment mechanism caused the search to freeze into step-like plateaus after roughly one hundred eighty iterations, demonstrating that all three mechanisms are strictly required to avoid premature convergence.

The computational complexity of the SLG algorithm was derived through three constituent phases comprising initialization, objective fitness evaluation, and individual position updates. With a population size of N individuals across D dimensions, the Saraswati initialization phase exhibits a time complexity of O(N multiplied by D). During the Lakshmi phase, evaluating objective functions requires O(N multiplied by the computational cost of evaluating a single solution), while calculating pairwise spatial distances and pursuit values scales as O(N squared) or O(N squared multiplied by D). Across T iterations, the overall simplified asymptotic time complexity resolves to O(T multiplied by N squared multiplied by D). In terms of memory consumption, storing the population matrix demands O(N multiplied by D) space, while auxiliary vectors for fitness values, wealth parameters, and the global best position require O(N plus D) storage, resulting in a total space complexity of O(N multiplied by D).

The performance of the algorithm was validated across sixty-three standard benchmark functions spanning the CEC2005, CEC2017, and CEC2019 test suites, each executed over thirty runs with fifteen thousand function evaluations across thirty search agents on a standard computing setup. The benchmark test suites encompassed unimodal, multimodal, fixed-dimension multimodal, hybrid, and composition functions designed to rigorously test both rapid convergence and complex exploratory escape mechanisms. Sensitivity testing demonstrated that a spiritual power coefficient value of 1.5 offered the most robust baseline across the benchmark collections. In comparative evaluations against established meta-heuristics such as Particle Swarm Optimization, Grey Wolf Optimizer, Gravitational Search Algorithm, and state-of-the-art algorithms including Differential Evolution, Farmland Fertility Algorithm, and LSHADE, the SLG framework demonstrated superior or competitive results across a substantial majority of the test cases, as confirmed by both t-tests and non-parametric Wilcoxon rank-sum evaluations at a five percent significance level.

Beyond abstract mathematical test suites, the research assessed the practical efficacy of the SLG algorithm across four standard constrained mechanical design challenges, employing a penalty function method to handle boundaries, non-linearities, and discrete variable constraints. In the tension and compression spring design problem, the algorithm successfully minimized overall spring weight across three continuous design variables while satisfying four mechanical stress and surge frequency constraints. In the pressure vessel design problem, which incorporates four mixed design variables and four geometric constraints, SLG successfully minimized total manufacturing fabrication costs. Parallel performance advantages were documented in the welded beam design problem, where the algorithm lowered fabrication costs under seven structural stress, deflection, and buckling constraints, as well as in the speed reducer design problem involving seven continuous and discrete mechanical parameters.

The researchers further demonstrated the industrial applicability of the SLG framework by deploying it to resolve complex wind turbine placement challenges across a modeled ten-by-ten grid wind farm containing one hundred potential coordinate locations. Using the Jensen linear wake decay model to compute aerodynamic downstream velocity deficits and wake losses, the optimization sought to maximize total electrical power output while minimizing the overall financial cost per kilowatt. In an experimental case study featuring a constant wind speed of twelve meters per second evaluated across thirty-six directional angles in ten-degree increments, the SLG algorithm achieved a total power output of 17,920 kilowatts utilizing forty turbines at an efficiency of 86.42 percent and a cost per kilowatt of 0.0015340. Under a second scenario assessing variable wind speeds of eight, twelve, and seventeen meters per second across thirty-six wind angles, the algorithm converged on an optimal layout of thirty-nine turbines producing an annual power generation of 32,350.91 kilowatts at an efficiency of 86.67 percent and a cost per kilowatt of 0.00083218, outperforming multiple benchmarked algorithms.

While the empirical results across mathematical functions and structural applications confirm the robustness of the SLG algorithm, the authors noted specific operational boundaries and prospective avenues for future refinement. In its current implementation, the algorithm relies on fixed parameter assignments for the spiritual power coefficient and the abandonment limit, indicating that adaptive or dynamic parameter-control strategies could offer performance improvements across shifting landscapes. Furthermore, because pairwise calculations introduce quadratic computational scaling with respect to population size, large-scale and high-dimensional applications may encounter processing bottlenecks. The researchers suggested that prospective extensions could integrate surrogate-assisted modeling, parallelized computing architectures, and distributed processing environments to alleviate computational overhead in increasingly massive optimization spaces.

Subject of Research: Meta-heuristic optimization algorithms and engineering design benchmarks

Article Title: A novel Saraswati-Lakshmi-Ganesh triad algorithm for global optimization and engineering design problems

Article References: Sarangi, P., & Mohapatra, P. (2026). A novel Saraswati-Lakshmi-Ganesh triad algorithm for global optimization and engineering design problems. Discover Computing, 29(1), Article 778. https://doi.org/10.1007/s10791-026-10725-6

Image Credits: AI Generated

DOI: 10.1007/s10791-026-10725-6

Keywords: optimization algorithms, meta-heuristics, engineering design, global optimization, CEC benchmark functions, computational mechanics, population-based optimization, wind turbine placement, algorithm development, pressure vessel design, tension compression spring, welded beam design, speed reducer design, exploration and exploitation, stochastic search