An efficient heuristic for series–parallel redundant reliability problems

This paper presents a novel algorithm for solving a series–parallel redundancy allocation problem with separable constraints. The idea of a heuristic approach design is inspired from the greedy method and the genetic algorithm. The structure of the algorithm includes: (1) randomly generating a specified population size number of minimum workable solutions; (2) assigning components either according to the greedy method or to the random selection method; and (3) improving solutions through an inner-system and inter-system solution revision process. Numerical results for the 33 test problems from previous research are reported and compared. As reported in this paper, the solutions found by our approach are all better than or are in par with the well-known best solutions from the approach taken by previous solutions.     

A boundary integral equation method for axisymmetric elastic contact problems

A numerical method for the solution of axisymmetric contact problems has been developed using the Boundary Integral Equation (BIE) technique. An automatic load incrementation technique is implemented in a BIE axisymmetric computer program using isoparametric quadratic elements. The method is successfully applied to some frictionless contact problems and the results are compared to other numerical and analytical solutions to demonstrate the accuracy of the BIE method.     

Self-adaptive check and repair operator-based particle swarm optimization for the multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is a combinatorial optimization problem belonging to the class of NP-hard problems. This study proposes a novel self-adaptive check and repair operator (SACRO) combined with particle swarm optimization (PSO) to solve the MKP. The traditional check and repair operator (CRO) uses a unique pseudo-utility ratio, whereas SACRO dynamically and automatically changes the alternative pseudo-utility ratio as the PSO algorithm runs. Two existing PSO algorithms are used as the foundation to support the novel SACRO methods, the proposed SACRO-based algorithms were tested using 137 benchmark problems from the OR-Library to validate and demonstrate the efficiency of SACRO idea. The results were compared with those of other population-based algorithms. Simulation and evaluation results show that SACRO is more competitive and robust than the traditional CRO. The proposed SACRO-based algorithms rival other state-of-the-art PSO and other algorithms. Therefore, changing different types of pseudo-utility ratios produces solutions with better results in solving MKP. Moreover, SACRO can be combined with other population-based optimization algorithms to solve constrained optimization problems.     

A constraint-guided method with evolutionary algorithms for economic problems

This paper presents an evolutionary algorithms based constrain-guided method (CGM) that is capable of handling both hard and soft constraints in optimization problems. While searching for constraint-satisfied solutions, the method differentiates candidate solutions by assigning them with different fitness values, enabling favorite solutions to be distinguished more likely and more effectively from unfavored ones.We illustrate the use of CGM in solving two economic problems with optimization involved: (1) searching equilibriums for bargaining problems; (2) reducing the rate of failure in financial prediction problems. The efficacy of the proposed CGM is analyzed and compared with some other computational techniques, including a repair method and a penalty method for the problem (1), a linear classifier and three neural networks for the problem (2), respectively. Our studies here suggest that the evolutionary algorithms based CGM compares favorably against those computational approaches.     

Numerical methods for transient solutions of machine repair problems

This paper reviews and compares two types of numerical methods of computing transient probabilities of finite Markovian queues (particularly the machine repair problem). A brief review of each method is followed by numerical examples of small and moderate size machine repair problems. The results demonstrate the feasibility of applying numerical techniques for obtaining transient solutions to Markovian queueing problems.     

Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.     

Evolutionary computation solutions to the circle packing problem

In this work, we present an evolutionary omputation-based solution to the circle packing problem (ECPP). The circle packing problem consists of placing a set of circles into a larger containing circle without overlaps: a problem known to be NP-hard. Given the impossibility to solve this problem efficiently, traditional and heuristic methods have been proposed to solve it. A naïve representation for chromosomes in a population-based heuristic search leads to high probabilities of violation of the problem constraints, i.e., overlapping. To convert solutions that violate constraints into ones that do not (i.e., feasible solutions), in this paper we propose two repair mechanisms. The first one considers every circle as an elastic ring and overlaps create repulsion forces that lead the circles to positions where the overlaps are resolved. The second one forms a Delaunay triangulation with the circle centers and repairs the circles in each triangle at a time, making sure repaired triangles are not modified later on. Based on the proposed repair heuristics, we present the results of the solution to the CPP problem to a set of unit circle problems (whose exact optimal solutions are known). These benchmark problems are solved using genetic algorithms, evolutionary strategies, particle swarm optimization, and differential evolution. The performance of the solutions is compared to those known solutions based on the packing density. We then perform a series of experiments to determine the performance of ECPP with non-unitary circles. First, we compare ECPP’s results to those of a public competition, which stand as the world record for that particular instance of the non-unitary CPP. On a second set of experiments, we control the variance of the size of the circles. In all experiments, ECPP yields satisfactory near-optimal solutions.     

A novel modified differential evolution algorithm for constrained optimization problems

A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems.     

On the analysis of creep stability and rupture

The analysis of problems involving creep material failure and creep buckling is considered. Creep buckling analyses are presented for some columns. A finite element creep rupture analysis of a rotating disc is performed and the results are compared with other solutions. Calculations are also reported for titanium notched tensile specimens and the numerical results are compared with experimental creep investigations, in which micrographs have been taken to study the rupture mechanisms.

All numerical solutions have been carried out using ADINA in which a creep-damage material law and the updated-Lagrangian-Jaumann formulation for the thermo-elastic-plastic and creep material model were implemented.     

A branch and bound algorithm for the cyclic job-shop problem with transportation

The cyclic job-shop problem with transportation can be used to describe optimization problems in fully automated manufacturing systems or assembly lines. We study the problem where the machines have no buffers, which rapidly decreases the number of feasible solutions and, therefore, makes it a lot harder to find those feasible solutions. After formulating the problem, we will characterize feasible solutions based on the route of the robot and their properties. With the aim of minimizing the cycle time, we have developed a tree search method to construct feasible solutions and combined it with a bounding procedure. Computational results are reported and compared to those gained by solving the problem with an LP solver.     

Solving constraint-satisfaction problems by a genetic algorithm adopting viral infection

Several approximate algorithms have been reported to solve large constraint-satisfaction problems (CSPs) within a practical time. While those papers discuss techniques to escape from local optima, this paper describes a method that actively performs global searches. The present method improves the rate of search of genetic algorithms by using viral infection instead of mutation. Partial solutions of a CSP are considered to be viruses, and a population of viruses is created, as well as a population of candidate solutions. The search for a solution is conducted by crossover and infection. Infection substitutes the gene of a virus for the locus decided by the virus. Experimental results using randomly generated CSPs prove that the proposed method is faster that usual genetic algorithms at finding a solution when the constraint density of a CSP is low.     

A novel multi-objective optimization algorithm based on Lightning Attachment Procedure Optimization algorithm

In this paper, a novel multi-objective optimization method based on a recently introduced algorithm known as Lightning Attachment Procedure Optimization (LAPO) is presented. The proposed algorithm is based on non-dominated sorting approach where the best solutions chosen from the Pareto Optimal Front (POF), based on crowding distance, are stored in a repository matrix called an Archive matrix. The procedure is performed such that the final best solutions are distributed evenly along the optimal PF. Then, the proposed algorithm is tested by some multi-objective optimization functions and some classical engineering problems also. The results are compared to those of four well-known methods and then discussed. The results are compared using 4 criteria which show how to select a POF close to the true POF, how the results are distributed, and how close the final results approximate all the possible outcomes of true POF. It is shown that the proposed method outperforms the other methods with regards to 3 criteria and yields comparable results regarding the last criteria. Superiority of the proposed method in finding the true POF while covering a wide range of possible optimal results is discussed in the results section. Therefore, it is concluded that the proposed method does an excellent job at solving a wide range of multi-objective optimization problems.     

A new ant colony optimization algorithm for the multidimensional Knapsack problem

The paper proposes a new ant colony optimization (ACO) approach, called binary ant system (BAS), to multidimensional Knapsack problem (MKP). Different from other ACO-based algorithms applied to MKP, BAS uses a pheromone laying method specially designed for the binary solution structure, and allows the generation of infeasible solutions in the solution construction procedure. A problem specific repair operator is incorporated to repair the infeasible solutions generated in every iteration. Pheromone update rule is designed in such a way that pheromone on the paths can be directly regarded as selecting probability. To avoid premature convergence, the pheromone re-initialization and different pheromone intensification strategy depending on the convergence status of the algorithm are incorporated. Experimental results show the advantages of BAS over other ACO-based approaches for the benchmark problems selected from OR library.     

A novel nondominated sorting simplified swarm optimization for multi-stage capacitated facility location problems with multiple quantitative and qualitative objectives

Capacitated facility location problems (CFLPs) arise in the practical application of many supply chain networks that select a set of suppliers, plants, distribution centers, and customers. In general, the goal of CFLPs is to consider multiple critical performances that involve quantitative and qualitative factors, such as cost, transportation time, inventory, profit, and customer satisfaction, to obtain various perspectives from decision makers in most real-world applications. CFLP becomes increasingly complex and challenging when decision makers simultaneously consider both factors; however, offering comprehensive decisions is important. In this study, a novel solution based on simplified swarm optimization (SSO) and a nondominated sorting technique is proposed to provide Pareto-optimal solutions for enhancing search efficiency and solution quality. To yield feasible solutions, three repairer mechanisms, namely, random repair, cost-based, and utility-based mechanisms, are proposed to enhance the search efficiency and diversity of each population. A fuzzy analytic hierarchy process is used to calculate the weight of qualitative objectives. To evaluate the efficiency and effectiveness of the proposed algorithm, extensive experiments are conducted on benchmark and newly generated instances of the four stages of CFLPs. Then, results are compared with those of the nondominated sorting genetic algorithm-II, multi-objective SSO, and multi-objective particle swarm optimization reported from the literature. The computational results demonstrate that the proposed algorithm is highly competitive and performs well in terms of solution quality and computational time. The Pareto set in the investigated type of facility location problems leads to solutions that may better support decision-making.     

Bat algorithm for constrained optimization tasks

In this study, we use a new metaheuristic optimization algorithm, called bat algorithm (BA), to solve constraint optimization tasks. BA is verified using several classical benchmark constraint problems. For further validation, BA is applied to three benchmark constraint engineering problems reported in the specialized literature. The performance of the bat algorithm is compared with various existing algorithms. The optimal solutions obtained by BA are found to be better than the best solutions provided by the existing methods. Finally, the unique search features used in BA are analyzed, and their implications for future research are discussed in detail.     

Numerical simulation of blow-up solutions for the generalized Davey–Stewartson system

Blow-up solutions for the generalized Davey–Stewartson system are studied numerically by using a split-step Fourier method. The numerical method has spectral-order accuracy in space and first-order accuracy in time. To evaluate the ability of the split-step Fourier method to detect blow-up, numerical simulations are conducted for several test problems, and the numerical results are compared with the analytical results available in the literature. Good agreement between the numerical and analytical results is observed.     

Surface loading of a thin-walled toroidal shell

Series solutions for elastostatic shell problems can provide results for particular loading cases economically, and give a basis of comparison with finite element method (FEM) solutions. For toroidal shells series solutions have been given by several authors, using mainly a stress approach. In the present study a displacement-based solution is given using the linear Sanders shell theory. This theory is considered to be one of the most accurate first-order theories. The governing equations are first developed in toroidal coordinates. The loading case of a pad of normal pressure on the shell surface is then considered in detail, and series expansions are written for the load, displacement and stress terms. Results are computed using the shell theory for a sample problem, and these results are compared with results obtained using the FEM. The results given provide practical information of interest to designers and furthermore give information about the shell theory and FEM solution characteristics.     

A modified particle swarm optimization for economic dispatch with non-smooth cost functions

This paper presents a new approach to economic dispatch (ED) problems with non-smooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have non-smooth cost functions with equality and inequality constraints, which makes the problem of finding the global optimum difficult when using any mathematical approaches. Since, standard PSO may converge at the early stage, in this paper, a modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. To validate the results obtained by MPSO, standard particle swarm optimization (PSO) and guaranteed convergence particle swarm optimization (GCPSO) are applied for comparison. Also, the results obtained by MPSO, PSO and GCPSO are compared with the previous approaches reported in the literature. The results show that the MPSO produces optimal or nearly optimal solutions for the study systems.     

Adomian decomposition method by Gegenbauer and Jacobi polynomials

In this paper, orthogonal polynomials on [–1,1] interval are used to modify the Adomian decomposition method (ADM). Gegenbauer and Jacobi polynomials are employed to improve the ADM and compared with the method of using Chebyshev and Legendre polynomials. To show the efficiency of the developed method, some linear and nonlinear examples are solved by the proposed method, results are compared with other modifications of the ADM and the exact solutions of the problems.