Three-bar Truss Design Research Articles

An efficient weighted slime mould algorithm for engineering optimization

In engineering applications, optimal parameter design is crucial. While Slime Mould Algorithm (SMA) excels in parameter discovery under constrained conditions, it faces challenges in achieving global convergence and avoiding local opsecttimal traps in complex tasks. This paper introduces an enhanced variant of SMA, termed CCHSMA, which integrates a Chaotic Local Search (CLS) mechanism to improve initial population diversity and combines Covariance Matrix Adaptation (CMA) and Harris Hawks Optimization (HHO) strategies to enhance global search efficiency. CCHSMA aims to improve search quality and reduce the likelihood of getting trapped in local optima. We evaluated CCHSMA's effectiveness by benchmarking it against the standard SMA and its variants using 30 CEC2017 test functions, and compared its performance with seven notable meta-heuristic algorithms and ten advanced swarm intelligence variants. The experimental results demonstrate that CCHSMA outperforms the other algorithms tested on the benchmark functions. To further validate its practical utility, CCHSMA's performance was also benchmarked against leading algorithms in real-world engineering applications. This paper uses detailed statistical methods, including the Wilcoxon signed-rank test and the Friedman test, to validate the comparative results. Our findings show that CCHSMA outperforms other algorithms in solving complex engineering optimization problems such as tension/compression spring design, pressure vessel design, and three-bar truss design, proving to be a robust tool for complex engineering optimization. Its enhanced initial population diversity and improved global search efficiency are essential for effectively addressing diverse engineering challenges.

Research on Move-to-Escape Enhanced Dung Beetle Optimization and Its Applications.

The dung beetle optimization (DBO) algorithm is acknowledged for its robust optimization capabilities and rapid convergence as an efficient swarm intelligence optimization technique. Nevertheless, DBO, similar to other swarm intelligence algorithms, often gets trapped in local optima during the later stages of optimization. To mitigate this challenge, we propose the Move-to-Escape dung beetle optimization (MEDBO) algorithm in this paper. MEDBO utilizes a good point set strategy for initializing the swarm's initial population, ensuring a more uniform distribution and diminishing the risk of local optima entrapment. Moreover, it incorporates convergence factors and dynamically balances the number of offspring and foraging individuals, prioritizing global exploration initially and local exploration subsequently. This dynamic adjustment not only enhances the search speed but also prevents local optima stagnation. The algorithm's performance was assessed using the CEC2017 benchmark suite, which confirmed MEDBO's significant improvements. Additionally, we applied MEDBO to three engineering problems: pressure vessel design, three-bar truss design, and spring design. MEDBO exhibited an excellent performance in these applications, demonstrating its practicality and efficacy in real-world problem-solving contexts.

Learning cooking algorithm for solving global optimization problems

In recent years, many researchers have made a continuous effort to develop new and efficient meta-heuristic algorithms to address complex problems. Hence, in this study, a novel human-based meta-heuristic algorithm, namely, the learning cooking algorithm (LCA), is proposed that mimics the cooking learning activity of humans in order to solve challenging problems. The LCA strategy is primarily motivated by observing how mothers and children prepare food. The fundamental idea of the LCA strategy is mathematically designed in two phases: (i) children learn from their mothers and (ii) children and mothers learn from a chef. The performance of the proposed LCA algorithm is evaluated on 51 different benchmark functions (which includes the first 23 functions of the CEC 2005 benchmark functions) and the CEC 2019 benchmark functions compared with state-of-the-art meta-heuristic algorithms. The simulation results and statistical analysis such as the t-test, Wilcoxon rank-sum test, and Friedman test reveal that LCA may effectively address optimization problems by maintaining a proper balance between exploitation and exploration. Furthermore, the LCA algorithm has been employed to solve seven real-world engineering problems, such as the tension/compression spring design, pressure vessel design problem, welded beam design problem, speed reducer design problem, gear train design problem, three-bar truss design, and cantilever beam problem. The results demonstrate the LCA’s superiority and capability over other algorithms in solving complex optimization problems.

A Multi-Objective Optimization Problem Solving Method Based on Improved Golden Jackal Optimization Algorithm and Its Application

The traditional golden jackal optimization algorithm (GJO) has slow convergence speed, insufficient accuracy, and weakened optimization ability in the process of finding the optimal solution. At the same time, it is easy to fall into local extremes and other limitations. In this paper, a novel golden jackal optimization algorithm (SCMGJO) combining sine–cosine and Cauchy mutation is proposed. On one hand, tent mapping reverse learning is introduced in population initialization, and sine and cosine strategies are introduced in the update of prey positions, which enhances the global exploration ability of the algorithm. On the other hand, the introduction of Cauchy mutation for perturbation and update of the optimal solution effectively improves the algorithm’s ability to obtain the optimal solution. Through the optimization experiment of 23 benchmark test functions, the results show that the SCMGJO algorithm performs well in convergence speed and accuracy. In addition, the stretching/compression spring design problem, three-bar truss design problem, and unmanned aerial vehicle path planning problem are introduced for verification. The experimental results prove that the SCMGJO algorithm has superior performance compared with other intelligent optimization algorithms and verify its application ability in engineering applications.

A Novel Gaussian Process Surrogate Model with Expected Prediction Error for Optimization under Constraints

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.

Enhanced gorilla troops optimizer powered by marine predator algorithm: global optimization and engineering design

This study presents an advanced metaheuristic approach termed the Enhanced Gorilla Troops Optimizer (EGTO), which builds upon the Marine Predators Algorithm (MPA) to enhance the search capabilities of the Gorilla Troops Optimizer (GTO). Like numerous other metaheuristic algorithms, the GTO encounters difficulties in preserving convergence accuracy and stability, notably when tackling intricate and adaptable optimization problems, especially when compared to more advanced optimization techniques. Addressing these challenges and aiming for improved performance, this paper proposes the EGTO, integrating high and low-velocity ratios inspired by the MPA. The EGTO technique effectively balances exploration and exploitation phases, achieving impressive results by utilizing fewer parameters and operations. Evaluation on a diverse array of benchmark functions, comprising 23 established functions and ten complex ones from the CEC2019 benchmark, highlights its performance. Comparative analysis against established optimization techniques reveals EGTO's superiority, consistently outperforming its counterparts such as tuna swarm optimization, grey wolf optimizer, gradient based optimizer, artificial rabbits optimization algorithm, pelican optimization algorithm, Runge Kutta optimization algorithm (RUN), and original GTO algorithms across various test functions. Furthermore, EGTO's efficacy extends to addressing seven challenging engineering design problems, encompassing three-bar truss design, compression spring design, pressure vessel design, cantilever beam design, welded beam design, speed reducer design, and gear train design. The results showcase EGTO's robust convergence rate, its adeptness in locating local/global optima, and its supremacy over alternative methodologies explored.

Improved honey badger algorithm based on elementary function density factors and mathematical spirals in polar coordinate systema

The Honey Badger Algorithm (HBA) is a new swarm intelligence optimization algorithm by simulating the foraging behavior of honey badgers in nature. To further improve its convergence speed and convergence accuracy, an improved HBA based on the density factors with the elementary functions and the mathematical spirals in the polar coordinate system was proposed. The algorithm proposes six density factors for attenuation states based on elementary functions, and introduces mathematical expressions of the polar diameters and angles of seven mathematical spirals (Fibonacci spiral, Butterfly curve, Rose spiral, Cycloid, Archimedean spiral, Hypotrochoid and Cardioid) in the polar coordinate system based on the density factors with the best synthesized effect to replace the foraging strategy of honey badger digging pattern in HBA. By using 23 benchmark test functions, the above improvements are sequentially compared with the original HBA, and the optimization algorithm with the best improvement, α4CycρHBA, is selected to be compared with SOA, MVO, DOA, CDO, MFO, SCA, BA, GWO and FFA. Finally, four engineering design problems (pressure vessel design, three-bar truss design, cantilever beam design and slotted bulkhead design) were solved. The simulation experiments results show that the proposed improved HBA based on the density factors with the elementary functions and the mathematical spirals of the polar coordinate system has the characteristics of balanced exploration and expiration, fast convergence and high accuracy, and is able to solve the function optimization and engineering optimization problems in a better way.

Application of Diversity-Maintaining Adaptive Rafflesia Optimization Algorithm to Engineering Optimisation Problems

The Diversity-Maintained Adaptive Rafflesia Optimization Algorithm represents an enhanced version of the original Rafflesia Optimization Algorithm. The latter draws inspiration from the unique characteristics displayed by the Rafflesia during its growth, simulating the entire lifecycle from blooming to seed dispersion. The incorporation of the Adaptive Weight Adjustment Strategy and the Diversity Maintenance Strategy assists the algorithm in averting premature convergence to local optima, subsequently bolstering its global search capabilities. When tested on the CEC2013 benchmark functions under a dimension of 30, the new algorithm was compared with ten optimization algorithms, including commonly used classical algorithms, such as PSO, DE, CSO, SCA, and the newly introduced ROA. Evaluation metrics included mean and variance, and the new algorithm outperformed on a majority of the test functions. Concurrently, the new algorithm was applied to six real-world engineering problems: tensile/compressive spring design, pressure vessel design, three-bar truss design, welded beam design, reducer design, and gear system design. In these comparative optimizations against other mainstream algorithms, the objective function’s mean value optimized by the new algorithm consistently surpassed that of other algorithms across all six engineering challenges. Such experimental outcomes validate the efficiency and reliability of the Diversity-Maintained Adaptive Rafflesia Optimization Algorithm in tackling optimization challenges. The Diversity- Maintained Adaptive Rafflesia Optimization Algorithm is capable of tuning the parameter values for the optimization of symmetry and asymmetry functions. As part of our future research endeavors, we aim to deploy this algorithm on an even broader array of diverse and distinct optimization problems, such as the arrangement of wireless sensor nodes, further solidifying its widespread applicability and efficacy.

A novel chaotic transient search optimization algorithm for global optimization, real-world engineering problems and feature selection.

Metaheuristic optimization algorithms manage the search process to explore search domains efficiently and are used efficiently in large-scale, complex problems. Transient Search Algorithm (TSO) is a recently proposed physics-based metaheuristic method inspired by the transient behavior of switched electrical circuits containing storage elements such as inductance and capacitance. TSO is still a new metaheuristic method; it tends to get stuck with local optimal solutions and offers solutions with low precision and a sluggish convergence rate. In order to improve the performance of metaheuristic methods, different approaches can be integrated and methods can be hybridized to achieve faster convergence with high accuracy by balancing the exploitation and exploration stages. Chaotic maps are effectively used to improve the performance of metaheuristic methods by escaping the local optimum and increasing the convergence rate. In this study, chaotic maps are included in the TSO search process to improve performance and accelerate global convergence. In order to prevent the slow convergence rate and the classical TSO algorithm from getting stuck in local solutions, 10 different chaotic maps that generate chaotic values instead of random values in TSO processes are proposed for the first time. Thus, ergodicity and non-repeatability are improved, and convergence speed and accuracy are increased. The performance of Chaotic Transient Search Algorithm (CTSO) in global optimization was investigated using the IEEE Congress on Evolutionary Computation (CEC)'17 benchmarking functions. Its performance in real-world engineering problems was investigated for speed reducer, tension compression spring, welded beam design, pressure vessel, and three-bar truss design problems. In addition, the performance of CTSO as a feature selection method was evaluated on 10 different University of California, Irvine (UCI) standard datasets. The results of the simulation showed that Gaussian and Sinusoidal maps in most of the comparison functions, Sinusoidal map in most of the real-world engineering problems, and finally the generally proposed CTSOs in feature selection outperform standard TSO and other competitive metaheuristic methods. Real application results demonstrate that the suggested approach is more effective than standard TSO.

Expedited surrogate-based quantification of engineering tolerances using a modified polynomial regression

Statistical analysis is frequently used to determine how manufacturing tolerances or operating condition uncertainties affect system performance. Surrogate is one of the accelerating ways in engineering tolerance quantification to analyze uncertainty with an acceptable computational burden rather than costly traditional methods such as Monte Carlo simulation. Compared with more complicated surrogates such as the Gaussian process, or Radial Basis Function (RBF), the Polynomial Regression (PR) provides simpler formulations yet acceptable outcomes. However, PR with the common least-squares method needs to be more accurate and flexible for approximating nonlinear and nonconvex models. In this study, a new approach is proposed to enhance the accuracy and approximation power of PR in dealing with uncertainty quantification in engineering tolerances. For this purpose, first, by computing the differences between training sample points and a reference point (e.g., nominal design), we employ certain linear and exponential basis functions to transform an original variable design into new transformed variables. A second adjustment is made to calculate the bias between the true simulation model and the surrogate’s approximated response. To demonstrate the effectiveness of the proposed PR approach, we provide comparison results between conventional and proposed surrogates employing four practical problems with geometric fabrication tolerances such as three-bar truss design, welded beam design, and trajectory planning of two-link and three-link (two and three degrees of freedom) robot manipulator. The obtained results prove the preference of the proposed approach over conventional PR by improving the approximation accuracy of the model with significantly lower prediction errors.

An Efficient Approach Based on Remora Optimization Algorithm and Levy Flight for Intrusion Detection

With the recent increase in network attacks by threats, malware, and other sources, machine learning techniques have gained special attention for intrusion detection due to their ability to classify hundreds of features into normal system behavior or an attack attempt. However, feature selection is a vital preprocessing stage in machine learning approaches. This paper presents a novel feature selection-based approach, Remora Optimization Algorithm-Levy Flight (ROA-LF), to improve intrusion detection by boosting the ROA performance with LF. The developed ROA-LF is assessed using several evaluation measures on five publicly available datasets for intrusion detection: Knowledge discovery and data mining tools competition, network security laboratory knowledge discovery and data mining, intrusion detection evaluation dataset, block out traffic network, Canadian institute of cybersecurity and three engineering problems: Cantilever beam design, three-bar truss design, and pressure vessel design. A comparative analysis between developed ROA-LF, particle swarm optimization, salp swarm algorithm, snake optimizer, and the original ROA methods is also presented. The results show that the developed ROA-LF is more efficient and superior to other feature selection methods and the three tested engineering problems for intrusion detection.

QL-ADIFA: Hybrid optimization using Q-learning and an adaptive logarithmic spiral-levy firefly algorithm.

Optimization problems are ubiquitous in engineering and scientific research, with a large number of such problems requiring resolution. Meta-heuristics offer a promising approach to solving optimization problems. The firefly algorithm (FA) is a swarm intelligence meta-heuristic that emulates the flickering patterns and behaviour of fireflies. Although FA has been significantly enhanced to improve its performance, it still exhibits certain deficiencies. To overcome these limitations, this study presents the Q-learning based on the adaptive logarithmic spiral-Levy flight firefly algorithm (QL-ADIFA). The Q-learning technique empowers the improved firefly algorithm to leverage the firefly's environmental awareness and memory while in flight, allowing further refinement of the enhanced firefly. Numerical experiments demonstrate that QL-ADIFA outperforms existing methods on 15 benchmark optimization functions and twelve engineering problems: cantilever arm design, pressure vessel design, three-bar truss design problem, and 9 constrained optimization problems in CEC2020.

An opposition learning and spiral modelling based arithmetic optimization algorithm for global continuous optimization problems

In engineering applications, many real-world optimization problems are nonlinear with multiple local optimums. Traditional algorithms that require gradients are not suitable for these problems. Meta-heuristic algorithms are popularly employed to deal with these problems because they can promisingly jump out of local optima and do not need any gradient information. The arithmetic optimization algorithm (AOA), a recently developed meta-heuristic algorithm, uses arithmetic operators (multiplication, division, subtraction, and addition) to solve optimization problems including nonlinear ones. However, the exploration and exploitation of AOA are not effective to handle some complex optimization problems. In this paper, an opposition learning and spiral modelling based AOA, namely OSAOA, is proposed for enhancing the optimization performance. It improves AOA from two perspectives. In the first perspective, the opposition-based learning (OBL) is committed to taking both candidate solutions and their opposite solutions into consideration for improving the global search with a high probability of jumping out of local minima. Then, the spiral modelling is introduced as the second perspective, which is particularly useful in getting the solutions gathering faster and accelerating the convergence speed in the later stage. In addition, OSAOA is compared with other existing advanced meta-heuristic algorithms based on 23 benchmark functions and four engineering problems: the three-bar truss design, the cantilever beam design, the pressure vessel design, and the tubular column design. From our simulations and engineering applications, the proposed OSAOA can provide better optimization results in dealing with these real-world optimization problems.

Lévy flight and chaos theory-based gravitational search algorithm for mechanical and structural engineering design optimization

Abstract The main aim of this article is to explore the real-life problem-solving potential of the proposed Lévy flight-based chaotic gravitational search algorithm (LCGSA) for the minimization of engineering design variables of speed reducer design (SRD), three bar truss design (TBTD), and hydrodynamic thrust bearing design (HTBD) problems. In LCGSA, the diversification of the search space is carried out by Lévy flight distribution. Simultaneously, chaotic maps have been utilized for the intensification of the candidate solutions towards the global optimum. Moreover, the penalty function method has been used to deal with the non-linear and fractional design constraints. The investigation of experimental outcomes has been performed through various performance metrics like statistical measures, run time analysis, convergence rate, and box plot analysis. Moreover, statistical verification of experimental results is carried out using a signed Wilcoxon rank-sum test. Furthermore, eleven heuristic algorithms were employed for comparative analysis of the simulation results. The simulation outcomes clearly show that LCGSA provides better values for TBTD and HTBD benchmarks than standard GSA and most of the competing algorithms. Besides, all the participating algorithms, including LCGSA, have the same results for the SRD problem. On the qualitative side, LCGSA has successfully resolved entrapment in local minima and convergence issues of standard GSA.

Agent State Flipping Based Hybridization of Heuristic Optimization Algorithms: A Case of Bat Algorithm and Krill Herd Hybrid Algorithm

This paper describes a unique meta-heuristic technique for hybridizing bio-inspired heuristic algorithms. The technique is based on altering the state of agents using a logistic probability function that is dependent on an agent’s fitness rank. An evaluation using two bio-inspired algorithms (bat algorithm (BA) and krill herd (KH)) and 12 optimization problems (cross-in-tray, rotated hyper-ellipsoid (RHE), sphere, sum of squares, sum of different powers, McCormick, Zakharov, Rosenbrock, De Jong No. 5, Easom, Branin, and Styblinski–Tang) is presented. Furthermore, an experimental evaluation of the proposed scheme using the industrial three-bar truss design problem is presented. The experimental results demonstrate that the hybrid scheme outperformed the baseline algorithms (mean rank for the hybrid BA-KH algorithm is 1.279 vs. 1.958 for KH and 2.763 for BA).

Hybridization of Chaotic Maps and Gravitational Search Algorithm for Constrained Mechanical and Civil Engineering Design Frameworks

The Chaotic Gravitational Search Algorithm (CGSA) is a physics-based heuristic algorithm inspired by Newton's law of universal gravitation. It uses 10 chaotic maps for optimal global search and fast convergence rate. The advantages of CGSA has been incorporated in various Mechanical and Civil engineering design frameworks which include Speed Reducer Design (SRD), Gear Train Design (GTD), Three Bar Truss Design (TBTD), Stepped Cantilever Beam Design (SCBD), Multiple Disc Clutch Brake Design (MDCBD), and Hydrodynamic Thrust Bearing Design (HTBD). The CGSA has been compared with eleven state of the art stochastic algorithms. In addition, a non-parametric statistical test namely the Signed Wilcoxon Rank-Sum test has been carried out at a 5% significance level to statistically validate the results. The simulation results indicate that CGSA shows efficient performance in terms of high convergence speed and minimization of the design parameter values as compared to other heuristic algorithms. The source codes are publicly available on Github i.e. https://github.com/SajadAHMAD1.

Feasibility-Guided Constraint-Handling Techniques for Engineering Optimization Problems

The particle swarm optimization (PSO) algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and fish. PSO is essentially an unconstrained algorithm and requires constraint handling techniques (CHTs) to solve constrained optimization problems (COPs). For this purpose, we integrate two CHTs, the superiority of feasibility (SF) and the violation constraint-handling (VCH), with a PSO. These CHTs distinguish feasible solutions from infeasible ones. Moreover, in SF, the selection of infeasible solutions is based on their degree of constraint violations, whereas in VCH, the number of constraint violations by an infeasible solution is of more importance. Therefore, a PSO is adapted for constrained optimization, yielding two constrained variants, denoted SF-PSO and VCH-PSO. Both SF-PSO and VCH-PSO are evaluated with respect to five engineering problems: the Himmelblau’s nonlinear optimization, the welded beam design, the spring design, the pressure vessel design, and the three-bar truss design. The simulation results show that both algorithms are consistent in terms of their solutions to these problems, including their different available versions. Comparison of the SF-PSO and the VCH-PSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used. We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.

Hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism for global optimization problems

The butterfly optimization algorithm (BOA) is a new metaheuristic algorithm that is inspired from food foraging behavior of the butterflies. Because of its simplicity and effectiveness, the algorithm has been proved to be effective in solving global optimization problems and applied to practical problems. However, BOA is prone to local optimality and may lose its diversity, thus suffering losses of premature convergence. In this work, a hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism called MBFPA was proposed. Firstly, the flower pollination algorithm has good exploration ability and the hybrid butterfly optimization algorithm and the flower pollination algorithms greatly improve the exploration ability of the algorithm; secondly, the symbiosis organisms search has a strong exploitation capability in the mutualism phase. By introducing the mutualism phase, the algorithm's exploitation capability is effectively increased and the algorithm's convergence speed is accelerated. Finally, the adaptive switching probability is increased to increase the algorithm's balance in exploration and exploitation capabilities. In order to evaluate the effectiveness of the algorithm, in the 49 standard test functions, the proposed algorithm was compared with six basic metaheuristic algorithms and five hybrid metaheuristic algorithms. MBFPA has also been used to solve five classic engineering problems (three-bar truss design problem; multi-plate disc clutch brake design; welded beam design; pressure vessel design problem; and speed reducer design). The results show that the proposed method is feasible and has good application prospect and competitiveness.

Improving exploration and exploitation via a Hyperbolic Gravitational Search Algorithm

Finding the best compromise between exploration and exploitation phases of a search algorithm is a hard task. The Gravitational Search Algorithm (GSA) is an evolutionary algorithm based on the Newton’s universal law of gravitation. Many studies show that GSA suffers from slow exploitation which generates premature convergence. This paper proposes a Hyperbolic Gravitational Search Algorithm (HGSA) able to find an optimal balance between exploration and exploitation. The main contributions of this work are: the definition of suitable hyperbolic acceleration coefficients, the dynamic regulation of the gravitational constant coefficient through hyperbolic function and the definition of a decreasing hyperbolic function for the best agents which attract the other agents. The proposed algorithm is compared with well-known search algorithms on classical benchmark functions, CEC-06 2019 benchmark functions and three-bar truss design problem. The results show that HGSA is better than other algorithms in terms of optimization and convergence performances.

Poor and rich optimization algorithm: A new human-based and multi populations algorithm

This paper presents a new optimization algorithm called poor and rich optimization (PRO). This algorithm is inspired by the efforts of the two groups of the poor and the rich to achieve wealth and improve their economic situation. The rich always try to increase their class gap with the poor by gaining wealth from different ways. The rich are always trying to increase their class gap with the poor by acquiring wealth from different ways. On the other hand, the poor try to gain wealth and reduce their class gap with the rich. On the other hand, the poor try to gain wealth and reduce their class gap by modeling the rich. This struggle is always going on and should be mention that the poor may get rich and vice versa. The proposed algorithm is evaluated using 33 test functions and the simulation results are compared with a number of new and well-known optimization algorithms. The evaluation domain includes uni-modal, multi-modal, fixed dimension, hybrid and large scale functions. In addition, for more precise evaluation, Tension/compression spring design, pressure vessel design, Gear drain design, and three-bar truss design problems are solved by PRO algorithm. PRO algorithm has had better performance in these four problems by finding optimal values of parameters as compared to other algorithms. Finally, PRO algorithm was used to estimate software effort by UCP for more accurate evaluation. The obtained results confirmed the superiority of PRO in exploration, exploitation and convergence aspects, compared to other algorithms.