Constrained Test Functions Research Articles

ALGA: Active Learning-Based Genetic Algorithm for Accelerating Structural Optimization

Optimization of complex structures using standard evolutionary algorithms, like genetic algorithm (GA), is known to be computationally expensive, because a very large number of finite element analysis (FEA) must be conducted for each possible structural design during the optimization. In the literature, different pretrained surrogate models have been used to replace the FEA for improving the computational performance of the structural optimization. However, the optimal solution found by the optimizer often depends on the accuracy of the pretrained surrogate model itself. Moreover, large datasets may be needed for getting the required accuracy of the surrogate model. An adaptive machine learning technique called active learning is used in this paper to accelerate the evolutionary optimization of complex structures. An active learner is a machine-learning-based model that can interactively query the outputs of certain data points, whenever the model would be uncertain about those outputs. In the presented approach, the active learner helps the GA by predicting if the possible design is going to be feasible or infeasible, meaning if it satisfies the required constraints or not. If the active learner is uncertain about the output, an actual FEA is conducted, and it improves its own accuracy for future evaluations. The approach does not need a trained surrogate model before the optimization. The active learner adaptively learns about the structure during the optimization to improve the computational performance. The approach is used to optimize the classic 10-bar truss problem, the Hesse function, curvilinearly stiffened panels under buckling and stress constraints, and some benchmark constrained test functions. The results show that the approach has the potential to reduce the total required constraint evaluations by more than 50%.

Hybrid Stochastic Ranking for Constrained Optimization

Teaching learning based optimization (TLBO) algorithm is a distinguished nature-inspired population-based meta-heuristic, which is basically designed for unconstrained optimization. TLBO mimics teaching learning process through which learners acquire knowledge from their teachers, and improve their results/grades, accordingly. Stochastic ranking (SR) is a constrained handling technique (CHT), which produces greediness among solutions to improve their fitness values and feasibility. Violation constraint handling (VCH) technique produces more feasibility among the existing superiority of feasibility CHTs due to its additional factor of ranking based on the number of constraints violated (NCV). This work brings in a new variant of SR, namely hybrid stochastic ranking (HSR), which combines SR and VCH. For constrained optimization, the integration of some CHT with TLBO is essential. In this paper, HSR is integrated with TLBO and a new constrained version of TLBO called HSR-TLBO is designed. The efficiency of HSR-TLBO is checked on constrained test functions of the suit CEC 2017. The experimental results show that HSR-TLBO got prominent position when compared and ranked with the top four papers and our two newly designed constrained variants of TLBO, MSR-TLBO and MVCH-TLBO, based on the provided budget and ranking criteria of the mentioned suit.

Self-Adaptive Single Objective Hybrid Algorithm for Unconstrained and Constrained Test functions: An Application of Optimization Algorithm

The optimization of continuous space poses a great challenge among the scientific community. When the objective function is nonlinear, the choices of direct search spaces are preferred over the other methods. The use of the hybrid algorithm for these types of optimization is becoming increasingly popular. This study introduced a self-adaptation procedure in a single objective hybrid algorithm and its application for unconstrained and constrained optimization test functions. This single objective hybrid algorithm is based on two popular metaheuristic algorithms, namely the cuckoo search and covariance matrix adaptation evolution strategy. Self-adaptation is a popular way of parameter selection and has a significant place in the computing field. The adaptation is introduced in two significant parameters of this algorithm. Five metaheuristic algorithms, namely cuckoo search, covariance matrix adaptation evolution strategy, particle swarm intelligence, firefly algorithm, and the newly introduced self-adapted single objective hybrid algorithm, were analyzed using unconstrained (unimodal and multimodal) and constrained benchmark test functions. An encouraging performance of this proposed algorithm for unconstrained and constrained test functions was observed.

MOGOA algorithm for constrained and unconstrained multi-objective optimization problems

Grasshopper Optimization Algorithm (GOA) was modified in this paper, to optimize multi-objective problems, and the modified version is called Multi-Objective Grasshopper Optimization Algorithm (MOGOA). An external archive is integrated with the GOA for saving the Pareto optimal solutions. The archive is then employed for defining the social behavior of the GOA in the multi-objective search space. To evaluate and verify the effectiveness of the MOGOA, a set of standard unconstrained and constrained test functions are used. Moreover, the proposed algorithm was compared with three well-known optimization algorithms: Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Ant Lion Optimizer (MOALO), and Non-dominated Sorting Genetic Algorithm version 2 (NSGA-II); and the obtained results show that the MOGOA algorithm is able to provide competitive results and outperform other algorithms.

Solving constrained optimization problems with sine-cosine algorithm

Optimization algorithms aim to find the optimum values that give the maximum or minimum result of a function under given circumstance. There are many approaches to solve optimization problems. Stochastic population-based optimization approaches tend to give the best results in a reasonable time. Two of the state-of-art stochastic optimization algorithms are Genetic Algorithms (GA) and Particle Swarm Optimization(PSO). In addition, Sine-Cosine Algorithm is one of the recently developed stochastic population-based optimization algorithms. It is claimed that Sine-Cosine has a higher speed than the counterparts of it. Moreover, Sine-Cosine Algorithm occasionally outperforms other optimization algorithms including GA and PSO. This algorithm is successful because it can balance exploration and exploitation smoothly. In the previous studies, the above-mentioned algorithms were evaluated and compared to each other for the unconstrained optimization test functions. But there is no study on constrained optimization test problems. In this study, we aim to show the performance of Sine-Cosine Algorithm on constrained optimization problems. In order to achieve this, we are going to compare the performances by using well-known constrained test functions

Swarm satellite mission scheduling & planning using Hybrid Dynamic Mutation Genetic Algorithm

Space missions have traditionally been controlled by operators from a mission control center. Given the increasing number of satellites for some space missions, generating a command list for multiple satellites can be time-consuming and inefficient. Developing multi-satellite, onboard mission scheduling & planning techniques is, therefore, a key research field for future space mission operations. In this paper, an improved Genetic Algorithm (GA) using a new mutation strategy is proposed as a mission scheduling algorithm. This new mutation strategy, called Hybrid Dynamic Mutation (HDM), combines the advantages of both dynamic mutation strategy and adaptive mutation strategy, overcoming weaknesses such as early convergence and long computing time, which helps standard GA to be more efficient and accurate in dealing with complex missions. HDM-GA shows excellent performance in solving both unconstrained and constrained test functions. The experiments of using HDM-GA to simulate a multi-satellite, mission scheduling problem demonstrates that both the computation time and success rate mission requirements can be met. The results of a comparative test between HDM-GA and three other mutation strategies also show that HDM has outstanding performance in terms of speed and reliability.

Application of Grasshopper Optimization Algorithm for Constrained and Unconstrained Test Functions

Grasshopper Optimization algorithm is one of the recent algorithm for optimization. This algorithm is swarm based nature inspired algorithm which mimics and mathematically models the behaviour of grasshopper swarm in nature. The proposed algorithm can be used for solving the engineering optimization problems. The GOA is tested for different benchmark test functions to validate and verify the performance of the algorithm. Results obtained from GOA are compared with actual values (results) of the test functions. The results obtained from algorithm show that the algorithm is able to give the accurate results. The unconstrained and constrained test functions solved by using the Grasshopper optimization Algorithm (GOA) and the results can validate that the algorithm gives the trustable results. Constraints handling technique is used to convert the constrained optimization problem into unconstrained optimization problem, so that the problem can be handled by the Grasshopper Optimization Algorithm (GOA). Static penalty method is used as a constraints handling technique in this paper. The algorithm can also apply for different engineering problems in real life.

Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems

This paper proposes a multi-objective version of the recently proposed Ant Lion Optimizer (ALO) called Multi-Objective Ant Lion Optimizer (MOALO). A repository is first employed to store non-dominated Pareto optimal solutions obtained so far. Solutions are then chosen from this repository using a roulette wheel mechanism based on the coverage of solutions as antlions to guide ants towards promising regions of multi-objective search spaces. To prove the effectiveness of the algorithm proposed, a set of standard unconstrained and constrained test functions is employed. Also, the algorithm is applied to a variety of multi-objective engineering design problems: cantilever beam design, brushless dc wheel motor design, disk brake design, 4-bar truss design, safety isolating transformer design, speed reduced design, and welded beam deign. The results are verified by comparing MOALO against NSGA-II and MOPSO. The results of the proposed algorithm on the test functions show that this algorithm benefits from high convergence and coverage. The results of the algorithm on the engineering design problems demonstrate its applicability is solving challenging real-world problems as well.

Design of shell-and-tube heat exchangers for multiple objectives using elitist non-dominated sorting genetic algorithm with termination criteria

In this work, Excel-based multi-objective optimization (EMOO) program, based on the elitist non-dominated sorting genetic algorithm, is improved by implementing two termination criteria: a Chi-squared test-based termination criterion and a novel termination criterion based on steady-state detection. The termination criteria were shown to perform reliably during the MOO of four constrained test functions. Then, the improved EMOO program was applied to the design of several shell-and-tube heat exchangers (STHE) from the literature; these STHE are simulated and then optimized using the EMOO program for two objectives: capital cost and operating cost. It provided better optimal results compared to those in the literature. The termination criteria performed reliably for MOO of STHE design, showing their applicability on industrial MOO problems.

An Improved Particle Swarm Optimization Algorithm for Constrained Chemical Engineering Optimization

An improved particle swarm optimization (IPSO) is proposed for solving constrained numerical and engineering optimization problems in this paper. In proposed algorithm, an initialization strategy based on the opposition learning is applied to diversity the initial particles in the search space. Self-adaptive inertia weight is introduced to balance the ability of exploration and exploitation. Diversity mutation strategy is employed for best of particles to introduce diversity in the swarm space. Simulation results and comparisons with other algorithms using two benchmark constrained test functions and chemical engineering optimization problem are provided.

An effective hybrid cuckoo search algorithm for constrained global optimization

As a novel evolutionary computation, cuckoo search (CS) algorithm has attracted much attention and wide applications, owing to its easy implementation. CS as most population-based algorithm is good at identifying promising area of the search space, but less good at fine-tuning the approximation to the minimization. To the best of our knowledge, the hybridization of augmented Lagrangian method, cuckoo search and Solis and Wets local search has not been attempted yet. In this paper, an effective hybrid cuckoo search algorithm based on Solis and Wets local search technique is proposed for constrained global optimization that relies on an augmented Lagrangian function for constraint-handling. Numerical results and comparisons with other state-of-the-art stochastic algorithms using a set of benchmark constrained test functions and engineering design optimization problems are provided.

A comparative study of a teaching–learning-based optimization algorithm on multi-objective unconstrained and constrained functions

Multi-objective optimization is the process of simultaneously optimizing two or more conflicting objectives subject to certain constraints. Real-life engineering designs often contain more than one conflicting objective function, which requires a multi-objective approach. In a single-objective optimization problem, the optimal solution is clearly defined, while a set of trade-offs that gives rise to numerous solutions exists in multi-objective optimization problems. Each solution represents a particular performance trade-off between the objectives and can be considered optimal. In this paper, the performance of a recently developed teaching–learning-based optimization (TLBO) algorithm is evaluated against the other optimization algorithms over a set of multi-objective unconstrained and constrained test functions and the results are compared. The TLBO algorithm was observed to outperform the other optimization algorithms for the multi-objective unconstrained and constrained benchmark problems.

A multi-objective improved teaching-learning based optimization algorithm for unconstrained and constrained optimization problems

Article history: Received July 2 2013 Received in revised format September 7 2013 Accepted September 15 2013 Available online September 23 2013 The present work proposes a multi-objective improved teaching-learning based optimization (MO-ITLBO) algorithm for unconstrained and constrained multi-objective function optimization. The MO-ITLBO algorithm is the improved version of basic teaching-learning based optimization (TLBO) algorithm adapted for multi-objective problems. The basic TLBO algorithm is improved to enhance its exploration and exploitation capacities by introducing the concept of number of teachers, adaptive teaching factor, tutorial training and self-motivated learning. The MO-ITLBO algorithm uses a grid-based approach to adaptively assess the non-dominated solutions (i.e. Pareto front) maintained in an external archive. The performance of the MO-ITLBO algorithm is assessed by implementing it on unconstrained and constrained test problems proposed for the Congress on Evolutionary Computation 2009 (CEC 2009) competition. The performance assessment is done by using the inverted generational distance (IGD) measure. The IGD measures obtained by using the MO-ITLBO algorithm are compared with the IGD measures of the other state-of-the-art algorithms available in the literature. Finally, Lexicographic ordering is used to assess the overall performance of competitive algorithms. Results have shown that the proposed MO-ITLBO algorithm has obtained the 1st rank in the optimization of unconstrained test functions and the 3rd rank in the optimization of constrained test functions. © 2013 Growing Science Ltd. All rights reserved

Symbolic Interval Inference Approach for Subdivision Direction Selection in Interval Partitioning Algorithms

In bound constrained global optimization problems, partitioning methods utilizing Interval Arithmetic are powerful techniques that produce reliable results. Subdivision direction selection is a major component of partitioning algorithms and it plays an important role in convergence speed. Here, we propose a new subdivision direction selection scheme that uses symbolic computing in interpreting interval arithmetic operations. We call this approach symbolic interval inference approach (SIIA). SIIA targets the reduction of interval bounds of pending boxes directly by identifying the major impact variables and re-partitioning them in the next iteration. This approach speeds up the interval partitioning algorithm (IPA) because it targets the pending status of sibling boxes produced. The proposed SIIA enables multi-section of two major impact variables at a time. The efficiency of SIIA is illustrated on well-known bound constrained test functions and compared with established subdivision direction selection methods from the literature.