VIS: An artificial immune network for multi-objective optimization

The aim of this work is to propose and validate a novel multi-objective optimization algorithm based on the emulation of the behaviour of the immune system. The rationale of this work is that the artificial immune system has, in its elementary structure, the main features required by other multi-objective evolutionary algorithms described in the literature, such as diversity preservation, memory, adaptivity, and elitism. The proposed approach is compared with three multi-objective evolutionary algorithms that are representative of the state of the art in multi-objective optimization. Algorithms are tested on six standard problems (both unconstrained and constrained) and comparisons are carried out using three different metrics. Results show that the proposed approach has very good performances and can become a valid alternative to standard algorithms for solving multi-objective optimization problems.     

MOEA/D-SQA: a multi-objective memetic algorithm based on decomposition

A multi-objective memetic algorithm based on decomposition is proposed in this article, in which a simplified quadratic approximation (SQA) is employed as a local search operator for enhancing the performance of a multi-objective evolutionary algorithm based on decomposition (MOEA/D). The SQA is used for a fast local search and the MOEA/D is used as the global optimizer. The multi-objective memetic algorithm based on decomposition, i.e. a hybrid of the MOEA/D with the SQA (MOEA/D-SQA), is designed to balance local versus global search strategies so as to obtain a set of diverse non-dominated solutions as quickly as possible. The emphasis of this article is placed on demonstrating how this local search scheme can improve the performance of MOEA/D for multi-objective optimization. MOEA/D-SQA has been tested on a wide set of benchmark problems with complicated Pareto set shapes. Experimental results indicate that the proposed approach performs better than MOEA/D. In addition, the results obtained are very competitive when comparing MOEA/D-SQA with other state-of-the-art techniques.     

MONSS: A multi-objective nonlinear simplex search approach

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.     

Revolute manipulator workspace optimization using a modified bacteria foraging algorithm: A comparative study

Robotic manipulators with three-revolute (3R) motions to attain desired positional configurations are very common in industrial robots. The capability of these robots depends largely on the workspace of the manipulator in addition to other parameters. In this study, an evolutionary optimization algorithm based on the foraging behaviour of the Escherichia coli bacteria present in the human intestine is utilized to optimize the workspace volume of a 3R manipulator. The new optimization method is modified from the original algorithm for faster convergence. This method is also useful for optimization problems in a highly constrained environment, such as robot workspace optimization. The new approach for workspace optimization of 3R manipulators is tested using three cases. The test results are compared with standard results available using other optimization algorithms, i.e. the differential evolution algorithm, the genetic algorithm and the particle swarm optimization algorithm. The present method is found to be superior to the other methods in terms of computational efficiency.     

Archery Algorithm: A Novel Stochastic Optimization Algorithm for Solving Optimization Problems

Finding a suitable solution to an optimization problem designed in science is a major challenge. Therefore, these must be addressed utilizing proper approaches. Based on a random search space, optimization algorithms can find acceptable solutions to problems. Archery Algorithm (AA) is a new stochastic approach for addressing optimization problems that is discussed in this study. The fundamental idea of developing the suggested AA is to imitate the archer's shooting behavior toward the target panel. The proposed algorithm updates the location of each member of the population in each dimension of the search space by a member randomly marked by the archer. The AA is mathematically described, and its capacity to solve optimization problems is evaluated on twenty-three distinct types of objective functions. Furthermore, the proposed algorithm's performance is compared vs. eight approaches, including teaching-learning based optimization, marine predators algorithm, genetic algorithm, grey wolf optimization, particle swarm optimization, whale optimization algorithm, gravitational search algorithm, and tunicate swarm algorithm. According to the simulation findings, the AA has a good capacity to tackle optimization issues in both unimodal and multimodal scenarios, and it can give adequate quasi-optimal solutions to these problems. The analysis and comparison of competing algorithms’ performance with the proposed algorithm demonstrates the superiority and competitiveness of the AA.     

Applying multiple objective tabu search to continuous optimization problems with a simple neighbourhood strategy

One of the first multiple objective versions of the tabu search (TS) algorithm is proposed by the author. The idea of applying TS to multiple objective optimization is inspired from its solution structure. TS works with more than one solution (neighbourhood solutions) at a time and this situation gives the opportunity to evaluate multiple objectives simultaneously in one run. The selection and updating stages are modified to enable the original TS algorithm to work with more than one objective. In this paper, the multiple objective tabu search (MOTS) algorithm is applied to multiple objective non‐linear optimization problems with continuous variables using a simple neighbourhood strategy. The algorithm is applied to four mechanical components design problems. The results are compared with several other solution techniques including multiple objective genetic algorithms. It is observed that MOTS is able to find better and much wider spread of solutions than the reported ones. Copyright © 2005 John Wiley & Sons, Ltd.     

A comparative study of controlled random search algorithms with application to inverse aerofoil design

This article presents a comparative study of some versions of the controlled random search algorithm (CRSA) in global optimization problems. The basic CRSA, originally proposed by Price in 1977 and improved by Ali et al. in 1997, is taken as a starting point. Then, some new modifications are proposed to improve the efficiency and reliability of this global optimization technique. The performance of the algorithms is assessed using traditional benchmark test problems commonly invoked in the literature. This comparative study points out the key features of the modified algorithm. Finally, a comparison is also made in a practical engineering application, namely the inverse aerofoil shape design.     

Hessian approximation algorithms for hybrid optimization methods

This article introduces Hessian approximation algorithms to estimate the search direction of the quasi-Newton methods for solving optimization problems of continuous parameters. The proposed algorithms are quite different from other well-known quasi-Newton methods, such as symmetric rank-one, Davidon–Fletcher–Powell, and Broyden–Fletcher–Goldfarb–Shanno, in that the Hessian matrix is not calculated from the gradient information, rather directly from the function values. The proposed algorithms are designed for a class of hybrid algorithms that combine evolutionary search with the gradient-based methods of quasi-Newton type. The function values calculated for the evolutionary search are used for estimation of the Hessian matrix (or its inverse) as well as the gradient vector. Since the estimation process of the Hessian matrix is independent of that of the gradient vector, more reliable Hessian estimation with a small population is possible compared with the previous methods based upon the classical quasi-Newton methods. Numerical experiments show that the proposed algorithms are very competitive with state-of-the-art evolutionary algorithms for continuous optimization problems.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

DISCRETE MANUFACTURING PROCESS DESIGN OPTIMIZATION USING COMPUTER SIMULATION AND GENERALIZED HILL CLIMBING ALGORITHMS

Discrete manufacturing process designs can be modelled using computer simulation. Determining optimal designs using such models is very difficult, due to the large number of manufacturing process sequences and associated parameter settings that exist. This has forced researchers to develop heuristic strategies to address such design problems. This paper introduces a new general heuristic strategy for discrete manufacturing process design optimization, called generalised hill climbing (GHC) algorithms. GHC algorithms provide a unifying approach for addressing such problems in particular, and intractable discrete optimization problems in general. Heuristic strategies such as simulated annealing, threshold accepting, Monte Carlo search, local search, and tabu search (among others) can all he formulated as GHC algorithms. Computational results are reported with various GHC algorithms applied to computer simulation models of discrete manufacturing process designs under study at the Materials Process Design Branch of Wright Laboratory, Wright Patterson Air Force Base (Dayton, Ohio, USA).     

The inside–outside contact search algorithm for finite element analysis

A new contact search algorithm (Inside–Outside Algorithm) for the sheet forming simulation has been developed and implemented in the dynamic explicit FE code: ‘DYNAMIC’. The inside–outside algorithm is derived based on the feature of the inside–outside status of a nodal ‘mesh normal vector’ in respect to a surface segment for the judgment of the contact of FE nodes with the tool surface. This new algorithm includes local search, local track and penetration calculation processes. Almost no additional CPU time is required for the local search process, because the calculations for both global and local search are combined. Moreover, the problems of conventional contact searching algorithms, such as iterations for local search and the deadzone problem, are resolved. Therefore, the quick, robust contact searching and accurate evaluation of penetration have been achieved. The numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones. © 1997 John Wiley & Sons, Ltd.     

A hybrid cellular automaton–bi-directional evolutionary optimization algorithm for topological optimization of crashworthiness

This article proposes a new algorithm for topological optimization under dynamic loading which combines cellular automata with bi-directional evolutionary structural optimization (BESO). The local rules of cellular automata are used to update the design variables, which avoids the difficulty of obtaining gradient information under nonlinear collision conditions. The intermediate-density design problem of hybrid cellular automata is solved using the BESO concept of 0–1 binary discrete variables. Some improvement strategies are also proposed for the hybrid algorithm to solve certain problems in nonlinear topological optimization, e.g. numerical oscillation. Some typical examples of crashworthiness problems are provided to illustrate the efficiency of the proposed method and its ability to find the final optimal solution. Finally, numerical results obtained using the proposed algorithms are compared with reference examples taken from the literature. The results show that the hybrid method is computationally efficient and stable.     

A new optimization algorithm for solving complex constrained design optimization problems

This article presents the performance of a very recently proposed Jaya algorithm on a class of constrained design optimization problems. The distinct feature of this algorithm is that it does not have any algorithm-specific control parameters and hence the burden of tuning the control parameters is minimized. The performance of the proposed Jaya algorithm is tested on 21 benchmark problems related to constrained design optimization. In addition to the 21 benchmark problems, the performance of the algorithm is investigated on four constrained mechanical design problems, i.e. robot gripper, multiple disc clutch brake, hydrostatic thrust bearing and rolling element bearing. The computational results reveal that the Jaya algorithm is superior to or competitive with other optimization algorithms for the problems considered.     

MDTS: automatic complex materials design using Monte Carlo tree search

Abstract

Complex materials design is often represented as a black-box combinatorial optimization problem. In this paper, we present a novel python library called MDTS (Materials Design using Tree Search). Our algorithm employs a Monte Carlo tree search approach, which has shown exceptional performance in computer Go game. Unlike evolutionary algorithms that require user intervention to set parameters appropriately, MDTS has no tuning parameters and works autonomously in various problems. In comparison to a Bayesian optimization package, our algorithm showed competitive search efficiency and superior scalability. We succeeded in designing large Silicon-Germanium (Si-Ge) alloy structures that Bayesian optimization could not deal with due to excessive computational cost. MDTS is available at https://github.com/tsudalab/MDTS.     

A simulated weed colony system with subregional differential evolution for multimodal optimization

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.     

求解包装生产中复杂问题的布谷鸟算法改进

目的 为了解决在求解复杂的高维函数优化问题时存在的求解精度不够高和易陷入局部最优等问题,提出一种基于莱维飞行发现概率的变步长布谷鸟搜索算法(LFCS).方法 在相同环境下,选取6个不同难度、不同类型的测试函数,将LFCS算法与IPSO,IDE,IABC,CS算法比较,分析算法的收敛速度和收敛精度.结果 相比其他4种算法,LFCS算法迭代次数更少,收敛速度更快,收敛精度更高.结论 无论是低维函数还是高维函数,LFCS算法在收敛速度和收敛精度方面都有所提高,尤其是针对复杂的高维函数优化问题,在取值范围较大的情况下,LFCS算法能够更快、更准地找到最优解.     

Optimization of Reliability–Redundancy Allocation Problems: A Review of the Evolutionary Algorithms

The study of optimization methods for reliability–redundancy allocation problems is a constantly changing field. New algorithms are continually being designed on the basis of observations of nature, wildlife, and humanity. In this paper, we review eight major evolutionary algorithms that emulate the behavior of civilization, ants, bees, fishes, and birds (i.e., genetic algorithms, bee colony optimization, simulated annealing, particle swarm optimization, biogeography-based optimization, artificial immune system optimization, cuckoo algorithm and imperialist competitive algorithm). We evaluate the mathematical formulations and pseudo-codes of each algorithm and discuss how these apply to reliability–redundancy allocation problems. Results from a literature survey show the best results found for series, series–parallel, bridge, and applied case problems (e.g., overspeeding gas turbine benchmark). Review of literature from recent years indicates an extensive improvement in the algorithm reliability performance. However, this improvement has been difficult to achieve for high-reliability applications. Insights and future challenges in reliability–redundancy allocation problems optimization are also discussed in this paper.     

Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method

In many engineering optimization problems, the number of function evaluations is often very limited because of the computational cost to run one high-fidelity numerical simulation. Using a classic optimization algorithm, such as a derivative-based algorithm or an evolutionary algorithm, directly on a computational model is not suitable in this case. A common approach to addressing this challenge is to use black-box surrogate modelling techniques. The most popular surrogate-based optimization algorithm is the efficient global optimization (EGO) algorithm, which is an iterative sampling algorithm that adds one (or many) point(s) per iteration. This algorithm is often based on an infill sampling criterion, called expected improvement, which represents a trade-off between promising and uncertain areas. Many studies have shown the efficiency of EGO, particularly when the number of input variables is relatively low. However, its performance on high-dimensional problems is still poor since the Kriging models used are time-consuming to build. To deal with this issue, this article introduces a surrogate-based optimization method that is suited to high-dimensional problems. The method first uses the ‘locating the regional extreme’ criterion, which incorporates minimizing the surrogate model while also maximizing the expected improvement criterion. Then, it replaces the Kriging models by the KPLS(+K) models (Kriging combined with the partial least squares method), which are more suitable for high-dimensional problems. Finally, the proposed approach is validated by a comparison with alternative methods existing in the literature on some analytical functions and on 12-dimensional and 50-dimensional instances of the benchmark automotive problem ‘MOPTA08’.     

Heuristics for permutation flow shop scheduling with batch setup times

In this paper we consider permutation flow shop scheduling problems with batch setup times. Each job has to be processed on each machine once and the technological routes are identical for all jobs. The set of jobs is divided into groups. There are given processing timest _ij of jobi on machinej and setup timess _rj on machinej when a job of ther-th group is processed after a job of another group. It is assumed that the same job order has to be chosen on each machine. We consider both the problems of minimizing the makespan and of minimizing the sum of completion times, where batch or item availability of the jobs is assumed. For these problems we give various constructive and iterative algorithms. The constructive algorithms are based on insertion techniques combined with beam search. We introduce suitable neighbourhood structures for such problems with batch setup times and describe iterative algorithms that are based on local search and reinsertion techniques. The developed algorithms have been tested on a large collection of problems with up to 80 jobs.Supported by Deutsche Forschungsgemeinschaft (Project ScheMA) and by the International Association for the Promotion of Cooperation with Scientists from the Independent States of the Former Soviet Union (Project INTAS-93-257)     

An enhanced preference-inspired co-evolutionary algorithm using orthogonal design and an ε-dominance archiving strategy

The concept of co-evolution of preferences and candidate solutions has proven effective for many-objective optimization. One realization of this concept, namely preference-inspired co-evolutionary algorithms using goal vectors (PICEA-g), is found to outperform many state-of-the-art multi-objective evolutionary algorithms for many-objective problems. However, PICEA-g is susceptible to unevenness in the solution distribution. This study seeks to tackle this issue and to improve the performance of PICEA-g further. Two established strategies are incorporated into PICEA-g: (i) an adaptive ε-dominance archiving strategy which is applied to obtain a set of well spread solutions online; and (ii) the orthogonal design method which is used to initialize candidate solutions. The improved algorithm, denoted as aε-ODPICEA-g, shows a better performance than PICEA-g on both 2- and 7-objective benchmark problems as well as a real-world problem.