Comparative analysis of three metaheuristics for short-term open pit block sequencing

This paper presents the application of simulated annealing (SA), Tabu search (TS) and hybrid TS–SA to solve a real-world mining optimisation problem called open pit block sequencing (OPBS). The OPBS seeks the optimum extraction sequences under a variety of geological and technical constraints over short-term horizons. As industry-scale OPBS instances are intractable for standard mixed integer programming (MIP) solvers, SA, TS and hybrid TS–SA are developed to solve the OPBS problem. MIP exact solution is also combined with the proposed metaheuristics to polish solutions in feasible neighbourhood moves. Extensive sensitivity analysis is conducted to analyse the characteristics and determine the optimum sets of values of the proposed metaheuristics algorithms’ parameters. Computational experiments show that the proposed algorithms are satisfactory for solving the OPBS problem. Additionally, this comparative study shows that the hybrid TS–SA is superior to SA or TS in solving the OPBS problem in several aspects.     

Landscape analysis and efficient metaheuristics for solving the n-queens problem

The n-queens problem is a classical combinatorial optimization problem which has been proved to be NP-hard. The goal is to place n non-attacking queens on an n×n chessboard. In this paper, two single-solution-based (Local Search (LS) and Tuned Simulated Annealing (SA)) and two population-based metaheuristics (two versions of Scatter Search (SS)) are presented for solving the problem. Since parameters of heuristic and metaheuristic algorithms have great influence on their performance, a TOPSIS-Taguchi based parameter tuning method is proposed, which not only considers the number of fitness function evaluations, but also aims to minimize the runtime of the presented metaheuristics. The performance of the suggested approaches was investigated through computational analyses, which showed that the Local Search method outperformed the other two algorithms in terms of average runtimes and average number of fitness function evaluations. The LS was also compared to the Cooperative PSO (CPSO) and SA algorithms, which are currently the best algorithms in the literature for finding the first solution to the n-queens problem, and the results showed that the average fitness function evaluation of the LS is approximately 21 and 8 times less than that of SA and CPSO, respectively. Also, a fitness analysis of landscape for the n-queens problem was conducted which indicated that the distribution of local optima is uniformly random and scattered over the search space. The landscape is rugged and there is no significant correlation between fitness and distance of solutions, and so a local search heuristic can search a rugged plain landscape effectively and find a solution quickly. As a result, it was statistically and analytically proved that single-solution-based metaheuristics outperform population-based metaheuristics in finding the first solution of the n-queens problem.     

A robust parameter design for multi-response problems

Most real world search and optimization problems naturally involve multiple responses. In this paper we investigate a multiple response problem within desirability function framework and try to determine values of input variables that achieve a target value for each response through three meta-heuristic algorithms such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Each algorithm has some parameters that need to be accurately calibrated to ensure the best performance. For this purpose, a robust calibration is applied to the parameters by means of Taguchi method. The computational results of these three algorithms are compared against each others. The superior performance of SA over TS and TS over GA is inferred from the obtained results in various situations.     

MONOTONIC ITERATIVE ALGORITHMS FOR A QUASICOMPLEMENTARITY PROBLEM

1. IntroductionConsider the following QCP: find u E Re such thatwhere A, B: R" -+ Re are operators, f E R". The quasivariational inequality which is equivalent to (1) sounds: to find u E Re such that u 2 Ba andIf Ba = c E R" for ally v E R" then QCP(1) reduces into CP. (1) appears in mathematicalprogramming (see, for example, [2] and the references therein), also comes from the discretization of QCP in mathematical physics and control theory (see [1]). For various generalization,see…     

Tabu Search directed by direct search methods for nonlinear global optimization

In recent years, there has been a great deal of interest in metaheuristics in the optimization community. Tabu Search (TS) represents a popular class of metaheuristics. However, compared with other metaheuristics like genetic algorithm and simulated annealing, contributions of TS that deals with continuous problems are still very limited. In this paper, we introduce a continuous TS called Directed Tabu Search (DTS) method. In the DTS method, direct-search-based strategies are used to direct a tabu search. These strategies are based on the well-known Nelder–Mead method and a new pattern search procedure called adaptive pattern search. Moreover, we introduce a new tabu list conception with anti-cycling rules called Tabu Regions and Semi-Tabu Regions. In addition, Diversification and Intensification Search schemes are employed. Numerical results show that the proposed method is promising and produces high quality solutions.     

Comparison of metaheuristic algorithms for Examination Timetabling Problem

SA, TS, GA and ACS are four of the main algorithms for solving challenging problems of intelligent systems. In this paper we consider Examination Timetabling Problem that is a common problem for all universities and institutions of higher education. There are many methods to solve this problem, In this paper we use Simulated Annealing, Tabu Search, Genetic Algorithm and Ant Colony System in their basic frameworks for solving this problem and compare results of them with each other.     

Combining metaheuristics with mathematical programming, constraint programming and machine learning

During the last years, interest on hybrid metaheuristics has risen considerably in the field of optimization and machine learning. The best results found for many optimization problems in science and industry are obtained by hybrid optimization algorithms. Combinations of optimization tools such as metaheuristics, mathematical programming, constraint programming and machine learning, have provided very efficient optimization algorithms. Four different types of combinations are considered in this paper: (i) Combining metaheuristics with complementary metaheuristics. (ii) Combining metaheuristics with exact methods from mathematical programming approaches which are mostly used in the operations research community. (iii) Combining metaheuristics with constraint programming approaches developed in the artificial intelligence community. (iv) Combining metaheuristics with machine learning and data mining techniques.     

Minimizing crossings in hierarchical digraphs with a hybridized genetic algorithm

Producing clear and intelligible layouts of hierarchical digraphs knows a renewed interest in information visualization. Recent experimental results show that metaheuristics are well-adapted methods for this problem. In this paper, we develop a new Hybridized Genetic Algorithm for arc crossing minimization. It follows the basic scheme of a GA with two major differences: problem-based crossovers adapted from ordering GAs are combined with a local search strategy based on averaging heuristics. Computational testing was performed on a set of 180 random hierarchical digraphs of standard sizes with various structures. Results show that the Hybridized Genetic Algorithm significantly outperforms Tabu Search—which is one of the best known methods for this problem- and also a multi-start descent except for highly connected graphs.     

Hyper-heuristic approaches for the response time variability problem

We propose two classes for the implementation of hyper-heuristic algorithms. The first is based on constructive heuristics, whereas the second uses improvement methods. Within the latter class, a general framework is designed for the use of local search procedures and metaheuristics as low-level heuristics. A dynamic scheme to guide the use of these approaches is also devised. These ideas are tested on an NP-hard scheduling problem known as the response time variability problem (RTVP). An intensive computational experiment shows, especially in the second class where the new best results are found, the effectiveness of the proposed hyper-heuristics.     

Search heuristics for a flowshop scheduling problem in a printed circuit board assembly process

We consider a scheduling problem in a factory producing printed circuit boards (PCBs). The PCB assembly process in this factory can be regarded as a flowshop which has two special characteristics: jobs have sequence dependent setup times and each job consists of a lot (batch) of identical PCBs. Because of the latter characteristic, it is possible to start a job on a following machine before the job is entirely completed on a previous machine, that is, there is time-lag between machines. In this paper, we propose several heuristics, including taboo search (TS) and simulated annealing (SA) methods, for this generalized flowshop scheduling problem with the objective of minimizing mean tardiness. We compare suggested heuristics after series of tests to find appropriate values for parameters needed for the two search algorithms, TS and SA. Results of computational tests on randomly generated test problems are reported.     

Swarm approach based on gravity for optimizing energy savings in grid systems

Execution time optimization is one of the most important objectives to accomplish for experiments launched on grid environments. However, the computing community is becoming more conscious about energy savings, seeking their optimization. In this work, both execution time and energy consumption are optimized through two swarm and multi-objective algorithms based on both physics and biology fields. On the one hand, multi-objective gravitational search algorithm (MOGSA) is inspired by the gravity forces between the planet masses. On the other hand, Multi-Objective Firefly Algorithm is based on the light attraction between the fireflies. These swarm algorithms are compared with the standard multi-objective algorithm non-dominated sorting genetic algorithm II to study their efficiency as multi-objective algorithms. Moreover, the best algorithm proposed, MOGSA, is compared with MOHEFT (a multi-objective version of one of the most-used algorithms in workflow scheduling, HEFT), and also with two real grid schedulers: Workload Management System and deadline budget constraint. Results show the superior performance of MOGSA regarding the others.     

Parallelizing simulated annealing algorithms based on high-performance computer

We implemented five conversions of simulated annealing (SA) algorithm from sequential-to-parallel forms on high-performance computers and applied them to a set of standard function optimization problems in order to test their performances. According to the experimental results, we eventually found that the traditional approach to parallelizing simulated annealing, namely, parallelizing moves in sequential SA, difficultly handled very difficult problem instances. Divide-and-conquer decomposition strategy used in a search space sometimes might find the global optimum function value, but it frequently resulted in great time cost if the random search space was considerably expanded. The most effective way we found in identifying the global optimum solution is to introduce genetic algorithm (GA) and build a highly hybrid GA+SA algorithm. In this approach, GA has been applied to each cooling temperature stage. Additionally, the performance analyses of the best algorithm among the five implemented algorithms have been done on the IBM Beowulf PCs Cluster and some comparisons have been made with some recent global optimization algorithms in terms of the number of functional evaluations needed to obtain a global minimum, success rate and solution quality.     

Grey prediction evolution algorithm for global optimization

This article uses the grey prediction theory to structure a new metaheuristic: grey prediction evolution algorithm based on the even grey model. The proposed algorithm considers the population series of evolutionary algorithms as a time series, and uses the even grey model as a reproduction operator to forecast the next population (without employing any mutation and crossover operators). It is theoretically proven that the reproduction operator based on the even grey model is adaptive. Additionally, the algorithmic search mechanism and its differences with other evolutionary algorithms are analyzed. The performance of the proposed algorithm is validated on CEC2005 benchmark functions and a test suite composed of six engineering constrained design problems. The comparison experiments show the effectiveness and superiority of the proposed algorithm.The proposed algorithm can be regarded as the first case of structuring metaheuristics by using the prediction theory. The novel algorithm is anticipated to influence two future works. The first is to propose more metaheuristics inspired by prediction theories (including some statistical algorithms). Another is that the theoretical results of these prediction systems can be used for this novel type of metaheuristics.     

Quadratically convergent algorithms and one-dimensional search schemes

In this paper, the performances of three quadratically convergent algorithms coupled with four one-dimensional search schemes are studied through several nonquadratic examples. The algorithms are the rank-one algorithm (Algorithm I), the projection algorithm (Algorithm II), and the Fletcher-Reeves algorithm (Algorithm III). The search schemes are the exact quadratic search (EQS), the exact cubic search (ECS), the approximate quadratic search (AQS), and the approximate cubic search (ACS). The performances are analyzed in terms of number of iterations and number of equivalent function evaluations for convergence. From the numerical experiments, the following conclusions are found: (a) while the number of iterations generally increases by relaxing the search stopping condition, the number of equivalent function evaluations decreases; therefore, approximate searches should be preferred to exact searches; (b) the numbers of iterations for ACS, ECS, and EQS are about the same; therefore, the use of more sophisticated, higher order search schemes is not called for; the present ACS scheme, modified so that only the function, instead of the gradient, is used in bracketing the minimal point, could prove to be most desirable in terms of the number of equivalent function evaluations; (c) for Algorithm I, ACS and AQS yield almost identical results; it is believed that further improvements in efficiency are possible if one uses a fixed stepsize approach, thus bypassing the one-dimensional search completely; (d) the combination of Algorithm II and ACS exhibits high efficiency in treating functions whose order is higher than two and whose Hessian at the minimal point is singular; and (f) Algorithm III, even with the best search scheme, is inefficient in treating functions with flat bottoms; it is doubtful that the simplicity of its update will compensate for its inefficiency in such pathological cases.This research was supported by the National Science Foundation, Grant No. 32453.     

Competitive genetic algorithms for the open-shop scheduling problem

For more than two machines, and when preemption is forbidden, the computation of minimum makespan schedules for the open-shop problem is NP-hard. Compared to the flow-shop and the job-shop, the open-shop has free job routes which lead to a much larger solution space, to smaller gaps between the optimal makespan and the lower bounds, and to disappointing results for the algorithms based on the disjunctive graph model. For instance, the best existing branch and bound method cannot solve some 7 ×7 hard instances to optimality, and all published metaheuristics (working by reversing some disjunctions already fixed) do not better than some greedy or steepest-descent heuristics which need a much smaller computational effort. In this context, the intrinsic parallelism of genetic algorithms (GAs) seems well adapted, for detecting global optima disseminated among many quasi-optimal schedules. This paper presents several GAs for the open-shop problem. It is shown that even simple and fast versions can compete with the best known heuristics and metaheuristics, thanks to two key-features: a population in which each individual has a distinct makespan, and a special procedure which reorders every new chromosome. Using problem-specific heuristics, it is possible to design more powerful GAs which give excellent results, even on the hardest benchmarks of the literature: for instance, all hard open instances from Taillard are broken, except one for which the best known solution is improved.     

The continuous differential ant-stigmergy algorithm for numerical optimization

Many promising optimization algorithms for solving numerical optimization problems come from population-based metaheuristics. A few of them are based on Swarm-Intelligence Algorithms, which are inspired by the collective behavior of social organisms. One of the most successful of such algorithms is the Differential Ant-Stigmergy Algorithm (DASA), which uses stigmergy, a method of communication in emergent systems where the individual parts (artificial ants) of the system communicate with one another by modifying their local environment (pheromone intensity). The main characteristic of the DASA is its underlying structure (pheromone graph) that uses discrete steps to move through a continuous search space. As a consequence of this the search-space movement is in some way limited and the algorithm’s time/space complexity is increased. In order to overcome the problem an improved algorithm called the Continuous Differential Ant-Stigmergy Algorithm (CDASA) is proposed and then benchmarked on standard benchmark functions. This benchmarking showed that the CDASA performs better than the DASA, especially at lower dimensions, that its time/space complexity is decreased, and that the algorithm code is simplified. As such, the CDASA is more suitable for parallel implementations on General-Purpose Graphic Processing Units. Compared to the Swarm-Intelligence Algorithms presented in this paper, the CDASA is the best-performing algorithm and competitive to the state-of-the-art algorithms belonging to different metaheuristic approaches.     

Theoretical analysis of steady state genetic algorithms

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are given under which the SSGA heuristic converges to the population consisting of copies of the best chromosome.     

Solving a dynamic cell formation problem using metaheuristics

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed by using some traditional metaheuristic methods such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Most of previous researches were done under the static condition. Due to the fact that CF is a NP-hard problem, then solving the model using classical optimization methods needs a long computational time. In this research, a nonlinear integer model of CF is first given and then solved by GA, SA and TS. Then, the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed.     

A novel metaheuristics approach for continuous global optimization

This paper proposes a novel metaheuristics approach to find the global optimum of continuous global optimization problems with box constraints. This approach combines the characteristics of modern metaheuristics such as scatter search (SS), genetic algorithms (GAs), and tabu search (TS) and named as hybrid scatter genetic tabu (HSGT) search. The development of the HSGT search, parameter settings, experimentation, and efficiency of the HSGT search are discussed. The HSGT has been tested against a simulated annealing algorithm, a GA under the name GENOCOP, and a modified version of a hybrid scatter genetic (HSG) search by using 19 well known test functions. Applications to Neural Network training are also examined. From the computational results, the HSGT search proved to be quite effective in identifying the global optimum solution which makes the HSGT search a promising approach to solve the general nonlinear optimization problem.     

A Robust Genetic Algorithm for Resource Allocation in Project Scheduling

Genetic algorithms have been applied to many different optimization problems and they are one of the most promising metaheuristics. However, there are few published studies concerning the design of efficient genetic algorithms for resource allocation in project scheduling. In this work we present a robust genetic algorithm for the single-mode resource constrained project scheduling problem. We propose a new representation for the solutions, based on the standard activity list representation and develop new crossover techniques with good performance in a wide sample of projects. Through an extensive computational experiment, using standard sets of project instances, we evaluate our genetic algorithm and demonstrate that our approach outperforms the best algorithms appearing in the literature.