Comparison of evolutionary computation algorithms for solving bi-objective task scheduling problem on heterogeneous distributed computing systems

The task scheduling problem in heterogeneous distributed computing systems is a multiobjective optimization problem (MOP). In heterogeneous distributed computing systems (HDCS), there is a possibility of processor and network failures and this affects the applications running on the HDCS. To reduce the impact of failures on an application running on HDCS, scheduling algorithms must be devised which minimize not only the schedule length (makespan) but also the failure probability of the application (reliability). These objectives are conflicting and it is not possible to minimize both objectives at the same time. Thus, it is needed to develop scheduling algorithms which account both for schedule length and the failure probability. Multiobjective Evolutionary Computation algorithms (MOEAs) are well-suited for Multiobjective task scheduling on heterogeneous environment. The two Multi-Objective Evolutionary Algorithms such as Multiobjective Genetic Algorithm (MOGA) and Multiobjective Evolutionary Programming (MOEP) with non-dominated sorting are developed and compared for the various random task graphs and also for a real-time numerical application graph. The metrics for evaluating the convergence and diversity of the obtained non-dominated solutions by the two algorithms are reported. The simulation results confirm that the proposed algorithms can be used for solving the task scheduling at reduced computational times compared to the weighted-sum based biobjective algorithm in the literature.     

Flower pollination algorithm: A novel approach for multiobjective optimization

Multiobjective design optimization problems require multiobjective optimization techniques to solve, and it is often very challenging to obtain high-quality Pareto fronts accurately. In this article, the recently developed flower pollination algorithm (FPA) is extended to solve multiobjective optimization problems. The proposed method is used to solve a set of multiobjective test functions and two bi-objective design benchmarks, and a comparison of the proposed algorithm with other algorithms has been made, which shows that the FPA is efficient with a good convergence rate. Finally, the importance for further parametric studies and theoretical analysis is highlighted and discussed.     

Efficiency for multiobjective multidisciplinary optimization problems with quasiseparable subproblems

Multidisciplinary optimization (MDO) has proved to be a useful tool for engineering design problems. Multiobjective optimization has been introduced to strengthen MDO techniques and deal with non-comparable and conflicting design objectives. A large majority of papers on multiobjective MDO have been applied in nature. This paper develops theory of multiobjective MDO and examines relationships between efficient solutions of a quasi-separable multiobjective multidisciplinary optimization problem and efficient solutions of its separable counterpart. Equivalence of the original and separable problems in the context of the Kuhn-Tucker constraint qualification and efficiency conditions are proved. Two decomposition approaches are proposed and offer a possibility of finding efficient solutions of the original problem by only finding efficient solutions of the subproblems. The presented results are related to algorithms published in the engineering literature on multiobjective MDO.     

Metamodel-assisted distributed genetic algorithms applied to structural shape optimization problems †

This article is concerned with the development of a general optimization tool based on distributed real genetic algorithms (DRGAs) assisted by metamodel evaluation and applied to structural shape optimization problems of general boundary-element models (BEMs). The evaluation fitness function is performed by a surrogate function based on multidimensional Gaussian random field models (MGRFMs) in order to minimize the computational cost of the evolutionary algorithms. The model boundary of a structural system or a mechanical tool is discretized using the BEM, and selected parts of the boundary are modelled using β-spline curves or surfaces in order to facilitate re-meshing and adaptation of the boundary to the external actions. Then a hypercube topology of populations of these models follows a genetic evolution process to determine the optimum shape of the system. The optimum models have minimum weight and satisfy all imposed constraints. A numerical example is presented and discussed in order to show the efficiency and robustness of the developed computational tool. The number of function evaluations is substantially reduced compared with previous versions of the optimization algorithm without the metamodel evaluation technique.     

An artificial immune network for multiobjective optimization problems

Multiobjective optimization is an important problem of great complexity and evolutionary algorithms have been established as a dominant approach in the field. This article suggests a method for approximating the Pareto front of a given function based on artificial immune networks. The proposed method uses cloning and mutation on a population of antibodies to create local subsets of the Pareto front. Elements of these local fronts are combined, in a way that maximizes diversity, to form the complete Pareto front of the function. The method is tested on a number of well-known benchmark problems, as well as an engineering problem. Its performance is compared against state-of-the-art algorithms, yielding promising results.     

An optimization design of vehicle axle system based on multiobjective cooperative optimization algorithm

ABSTRACT

To address multiobjective, multi constraint and time-consuming structural optimization problems in a vehicle axle system, a multiobjective cooperative optimization model of a vehicle axle structure is established. In light of the difficulty in the nondominated sorting of the NSGA-II algorithm caused by inconsistent effects of the uniformity objective function and physical objective function, this paper combines a multiobjective genetic algorithm with cooperative optimization and presents a strategy for handling the optimization of a vehicle axle structure. The uniformity objective function of the sub discipline is transformed to its self-constraint. Taking the multiobjective optimization of a vehicle axle system as an example, a multiobjective cooperative optimization design for the system is carried out in ISIGHT. The results show that the multiobjective cooperative optimization strategy can simplify the complexity of optimization problems and that the multiobjective cooperative optimization method based on an approximate model is favorable for accuracy and efficiency, thereby providing a theoretical basis for the optimization of similar complex structures in practical engineering.     

Enhanced Heap-Based Optimizer Algorithm for Solving Team FormationProblem

Team Formation (TF) is considered one of the most significant problems in computer science and optimization. TF is defined as forming the best team of experts in a social network to complete a task with least cost. Many real-world problems, such as task assignment, vehicle routing, nurse scheduling, resource allocation, and airline crew scheduling, are based on the TF problem. TF has been shown to be a Nondeterministic Polynomial time (NP) problem, and high-dimensional problem with several local optima that can be solved using efficient approximation algorithms. This paper proposes two improved swarm-based algorithms for solving team formation problem. The first algorithm, entitled Hybrid Heap-Based Optimizer with Simulated Annealing Algorithm (HBOSA), uses a single crossover operator to improve the performance of a standard heap-based optimizer (HBO) algorithm. It also employs the simulated annealing (SA) approach to improve model convergence and avoid local minima trapping. The second algorithm is the Chaotic Heap-based Optimizer Algorithm (CHBO). CHBO aids in the discovery of new solutions in the search space by directing particles to different regions of the search space. During HBO’s optimization process, a logistic chaotic map is used. The performance of the two proposed algorithms (HBOSA) and (CHBO) is evaluated using thirteen benchmark functions and tested in solving the TF problem with varying number of experts and skills. Furthermore, the proposed algorithms were compared to well-known optimization algorithms such as the Heap-Based Optimizer (HBO), Developed Simulated Annealing (DSA), Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and Genetic Algorithm (GA). Finally, the proposed algorithms were applied to a real-world benchmark dataset known as the Internet Movie Database (IMDB). The simulation results revealed that the proposed algorithms outperformed the compared algorithms in terms of efficiency and performance, with fast convergence to the global minimum.     

Simulated annealing-based multiobjective algorithms and their application for system reliability

The paper presents five simulated annealing based multiobjective algorithms - SMOSA, UMOSA, PSA, PDMOSA and WMOSA. All of these algorithms aim to find a Pareto set of solutions of a system reliability multiobjective optimization problem in a short time. In each algorithm the solution vector explores its neighborhood in a way similar to that of Classical Simulated Annealing. All the algorithms are problem-specific and if the true Pareto-optimal set has few solutions, UMOSA, SMOSA, PSA and WMOSA work better than PDMOSA. In some cases, PSA works the best. The computational cost is least in the case of the WMOSA algorithm since it does not need to use the penalty function approach to handle the constraints, and is the maximum with PDMOSA since it requires two sets of Pareto solutions.     

Multiobjective Optimization of Parallel Cable Layout

We have applied a multiobjective combinatorial optimization (MOCO) based on a vector immune system (VIS) algorithm to determine the optimal sequence of parallel cables in a multiconductor three-phase system. We build the objective function in a way that minimizes the magnetic stray field and the current unbalance of a bunch of rectilinear power cables. Our principal aim is to extend and verify the ability of the VIS algorithm to solve combinatorial problems represented by nonlinear objectives that are not usually solved in MOCO problems.     

A method for simulation based optimization using radial basis functions

We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.     

SSABA: Search Step Adjustment Based Algorithm

Finding the suitable solution to optimization problems is a fundamental challenge in various sciences. Optimization algorithms are one of the effective stochastic methods in solving optimization problems. In this paper, a new stochastic optimization algorithm called Search Step Adjustment Based Algorithm (SSABA) is presented to provide quasi-optimal solutions to various optimization problems. In the initial iterations of the algorithm, the step index is set to the highest value for a comprehensive search of the search space. Then, with increasing repetitions in order to focus the search of the algorithm in achieving the optimal solution closer to the global optimal, the step index is reduced to reach the minimum value at the end of the algorithm implementation. SSABA is mathematically modeled and its performance in optimization is evaluated on twenty-three different standard objective functions of unimodal and multimodal types. The results of optimization of unimodal functions show that the proposed algorithm SSABA has high exploitation power and the results of optimization of multimodal functions show the appropriate exploration power of the proposed algorithm. In addition, the performance of the proposed SSABA is compared with the performance of eight well-known algorithms, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Teaching-Learning Based Optimization (TLBO), Gravitational Search Algorithm (GSA), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Marine Predators Algorithm (MPA), and Tunicate Swarm Algorithm (TSA). The simulation results show that the proposed SSABA is better and more competitive than the eight compared algorithms with better performance.     

MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM

This paper presents an evolutionary algorithm for generic multiobjective design optimization problems. The algorithm is based on nondominance of solutions in the objective and constraint space and uses effective mating strategies to improve solutions that are weak in either. Since the methodology is based on nondominance, scaling and aggregation affecting conventional penalty function methods for constraint handling does not arise. The algorithm incorporates intelligent partner selection for cooperative mating. The diversification strategy is based on niching which results in a wide spread of solutions in the parametric space. Results of the algorithm for the design examples clearly illustrate the efficiency of the algorithm in solving multidisciplinary design optimization problems.     

Intelligent interactive multiobjective optimization method and its application to reliability optimization

In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designer's preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designer's preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five different value functions simulating the designer in the solution evaluation process. The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems.     

Skill Optimization Algorithm: A New Human-Based Metaheuristic Technique

Metaheuristic algorithms are widely used in solving optimization problems. In this paper, a new metaheuristic algorithm called Skill Optimization Algorithm (SOA) is proposed to solve optimization problems. The fundamental inspiration in designing SOA is human efforts to acquire and improve skills. Various stages of SOA are mathematically modeled in two phases, including: (i) exploration, skill acquisition from experts and (ii) exploitation, skill improvement based on practice and individual effort. The efficiency of SOA in optimization applications is analyzed through testing this algorithm on a set of twenty-three standard benchmark functions of a variety of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types. The optimization results show that SOA, by balancing exploration and exploitation, is able to provide good performance and appropriate solutions for optimization problems. In addition, the performance of SOA in optimization is compared with ten metaheuristic algorithms to evaluate the quality of the results obtained by the proposed approach. Analysis and comparison of the obtained simulation results show that the proposed SOA has a superior performance over the considered algorithms and achieves much more competitive results.     

A Swarm Metaphor for Multiobjective Design Optimization

This paper presents a new optimization algorithm to solve multiobjective design optimization problems based on behavioral concepts similar to that of a real swarm. The individuals of a swarm update their flying direction through communication with their neighboring leaders with an aim to collectively attain a common goal. The success of the swarm is attributed to three fundamental processes: identification of a set of leaders, selection of a leader for information acquisition, and finally a meaningful information transfer scheme. The proposed algorithm mimics the above behavioral processes of a real swarm. The algorithm employs a multilevel sieve to generate a set of leaders, a probabilistic crowding radius-based strategy for leader selection and a simple generational operator for information transfer. Two test problems, one with a discontinuous Pareto front and the other with a multi-modal Pareto front is solved to illustrate the capabilities of the algorithm in handling mathematically complex problems. Three well-studied engineering design optimization problems (unconstrained and constrained problems with continuous and discrete variables) are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. The results clearly indicate that the swarm algorithm is capable of generating an extended Pareto front, consisting of well spread Pareto points with significantly fewer function evaluations when compared to the nondominated sorting genetic algorithm (NSGA).     

Ant algorithm for single and multiobjective reliability optimization problems

The paper illustrates the application of the ant colony optimization algorithm to solve both continuous function and combinatorial optimization problems in reliability engineering. The ant algorithm is combined with the strength Pareto fitness assignment procedure to handle multiobjective problems. Further, a clustering procedure has been applied to prune the Pareto set and to maintain diversity. Benchmark case examples show the superiority of the ant algorithm to such problems. Copyright © 2002 John Wiley & Sons, Ltd.     

Multiobjective robust optimization method for drawbead design in sheet metal forming

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality.     

On the effect of numerical noise in approximate optimization of forming processes using numerical simulations

The coupling of Finite Element (FE) simulations with approximate optimization techniques is becoming increasingly popular in forming industry. By doing so, it is implicitly assumed that the optimization objective and possible constraints are smooth functions of the design variables and, in case of robust optimization, design and noise variables. However, non-linear FE simulations are known to introduce numerical noise caused by the discrete nature of the simulation algorithms, e.g. errors caused by re-meshing, time-step adjustments or contact algorithms. The subsequent usage of metamodels based on such noisy data reduces the prediction quality of the optimization routine and is known to even magnify the numerical errors. This work provides an approach to handle noisy numerical data in approximate optimization of forming processes, covering several fundamental research questions in dealing with numerical noise. First, the deteriorating effect of numerical noise on the prediction quality of several well-known metamodeling techniques is demonstrated using an analytical test function. Next, numerical noise is quantified and its effect is minimized by the application of local approximation and regularization techniques. A general approximate optimization strategy is subsequently presented and coupling with a sequential update algorithm is proposed. The strategy is demonstrated by the sequential deterministic and robust optimization of 2 industrial metal forming processes i.e. a V-bending application and a cup-stretching application. Although numerical noise is often neglected in practice, both applications in this work show that the general awareness of its presence is highly important to increase the overall accuracy of optimization results.     

A new Kriging–Bat Algorithm for solving computationally expensive black-box global optimization problems

Many global optimization (GO) algorithms have been introduced in recent decades to deal with the Computationally Expensive Black-Box (CEBB) optimization problems. The high number of objective function evaluations, required by conventional GO methods, is prohibitive or at least inconvenient for practical design applications. In this work, a new Kriging–Bat algorithm (K–BA) is introduced for solving CEBB problems with further improved search efficiency and robustness. A Kriging surrogate model (SM) is integrated with the Bat Algorithm (BA) to find the global optimum using substantially reduced number of evaluations of the computationally expensive objective function. The new K–BA algorithm is tested and compared with other well-known GO algorithms, using a set of standard benchmark problems with 2 to 16 design variables, as well as a real-life engineering optimization application, to determine its search capability, efficiency and robustness. Results of the comprehensive tests demonstrated the suitability and superior capability of the new K–BA.     

Optimization of a pipe end upsetting process

A method is proposed for the optimization, by finite element analysis, of design variables of sheet metal forming processes. The method is useful when the non-controllable process parameters (e.g. the coefficient of friction or the material properties) can be modelled as random variables, introducing a degree of uncertainty into any process solution. The method is suited for problems with large FEM computational times and small process window. The problem is formulated as the minimization of a cost function, subject to a reliability constraint. The cost function is indirectly optimized through a “metamodel”, built by “Kriging” interpolation. The reliability, i.e. the failure probability, is assessed by a binary logistic regression analysis of the simulation results. The method is applied to the u-channel forming and springback problem presented in Numisheet 1993, modified by handling the blankholder force as a time-dependent variable.