A discrete particle swarm optimization for lot-streaming flowshop scheduling problem

We consider an n-job, m-machine lot-streaming problem in a flowshop with equal-size sublots where the objective is to minimize the total weighted earliness and tardiness. To solve this problem, we first propose a so-called net benefit of movement (NBM) algorithm, which is much more efficient than the existing linear programming model for obtaining the optimal starting and completion times of sublots for a given job sequence. A new discrete particle swarm optimization (DPSO) algorithm incorporating the NBM algorithm is then developed to search for the best sequence. The new DPSO improves the existing DPSO by introducing an inheritance scheme, inspired by a genetic algorithm, into particles construction. To verify the proposed DPSO algorithm, comparisons with the existing DPSO algorithm and a hybrid genetic algorithm (HGA) are made. Computational results show that the proposed DPSO algorithm with a two-point inheritance scheme is very competitive for the lot-streaming flowshop scheduling problem.     

A hybrid approach for single-machine tardiness problems with sequence-dependent setup times

Scheduling problems in real systems often require sequence-dependent setup times. The topic of sequence-dependent setup times has not been addressed adequately, and improved competitiveness is thus not achieved. This study proposes a hybrid approach that takes advantage of simulated annealing (SA) and tabu search (TS) to solve single-machine tardiness problems with sequence-dependent setup times. To verify the proposed approach, experiments were conducted on benchmark problem sets that included both the weighted and un-weighted tardiness problems. The results show that the performance of the hybrid approach is superior to that of the SA, genetic algorithm, TS and ant colony optimization approaches, and is comparable with the Tabu-VNS approach. And the proposed approach found new upper bound values for many benchmark problems with an acceptable computational time.     

A hybrid simplex search and particle swarm optimization for unconstrained optimization

This paper proposes the hybrid NM-PSO algorithm based on the Nelder–Mead (NM) simplex search method and particle swarm optimization (PSO) for unconstrained optimization. NM-PSO is very easy to implement in practice since it does not require gradient computation. The modification of both the Nelder–Mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy. In a suite of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid NM-PSO approach outperforms other three relevant search techniques (i.e., the original NM simplex search method, the original PSO and the guaranteed convergence particle swarm optimization (GCPSO)) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the NM-PSO algorithm is compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the NM-PSO algorithm in the performance of accuracy, robustness and function evaluation. As evidenced by the overall assessment based on two kinds of computational experience, the new algorithm has demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for unconstrained optimization.     

A discrete particle swarm optimization method for feature selection in binary classification problems

This paper investigates the feature subset selection problem for the binary classification problem using logistic regression model. We developed a modified discrete particle swarm optimization (PSO) algorithm for the feature subset selection problem. This approach embodies an adaptive feature selection procedure which dynamically accounts for the relevance and dependence of the features included the feature subset. We compare the proposed methodology with the tabu search and scatter search algorithms using publicly available datasets. The results show that the proposed discrete PSO algorithm is competitive in terms of both classification accuracy and computational performance.     

Enhanced speciation in particle swarm optimization for multi-modal problems

In this paper, we present a novel multi-modal optimization algorithm for finding multiple local optima in objective function surfaces. We build from Species-based particle swarm optimization (SPSO) by using deterministic sampling to generate new particles during the optimization process, by implementing proximity-based speciation coupled with speciation of isolated particles, and by including “turbulence regions” around already found solutions to prevent unnecessary function evaluations. Instead of using error threshold values, the new algorithm uses the particle’s experience, geometric mean, and “exclusion factor” to detect local optima and stop the algorithm. The performance of each extension is assessed with leave-it-out tests, and the results are discussed. We use the new algorithm called Isolated-Speciation-based particle swarm optimization (ISPSO) and a benchmark algorithm called Niche particle swarm optimization (NichePSO) to solve a six-dimensional rainfall characterization problem for 192 rain gages across the United States. We show why it is important to find multiple local optima for solving this real-world complex problem by discussing its high multi-modality. Solutions found by both algorithms are compared, and we conclude that ISPSO is more reliable than NichePSO at finding optima with a significantly lower objective function value.     

A multi-objective tabu search for a single-machine scheduling problem with sequence-dependent setup times

An m-objective tabu search algorithm for sequencing of n jobs on a single machine with sequence-dependent setup times is proposed. The algorithm produces a solution set that is reflective of the objectives’ weights and close to the best observed values of the objectives. We also formulate a mixed integer linear program to obtain the optimal solution of a three-objective problem. Numerical examples are used to study the behavior of the proposed m-objective tabu search algorithm and compare its solutions with those of the mixed integer linear program.     

A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem

In this paper, a particle swarm optimization algorithm (PSO) is presented to solve the permutation flowshop sequencing problem (PFSP) with the objectives of minimizing makespan and the total flowtime of jobs. For this purpose, a heuristic rule called the smallest position value (SPV) borrowed from the random key representation of Bean [J.C. Bean, Genetic algorithm and random keys for sequencing and optimization, ORSA Journal of Computing 6(2) (1994) 154–160] was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems. In addition, a very efficient local search, called variable neighborhood search (VNS), was embedded in the PSO algorithm to solve the well known benchmark suites in the literature. The PSO algorithm was applied to both the 90 benchmark instances provided by Taillard [E. Taillard, Benchmarks for basic scheduling problems, European Journal of Operational Research, 64 (1993) 278–285], and the 14,000 random, narrow random and structured benchmark instances provided by Watson et al. [J.P. Watson, L. Barbulescu, L.D. Whitley, A.E. Howe, Contrasting structured and random permutation flowshop scheduling problems: Search space topology and algorithm performance, ORSA Journal of Computing 14(2) (2002) 98–123]. For makespan criterion, the solution quality was evaluated according to the best known solutions provided either by Taillard, or Watson et al. The total flowtime criterion was evaluated with the best known solutions provided by Liu and Reeves [J. Liu, C.R. Reeves, Constructive and composite heuristic solutions to the P∥∑C_i scheduling problem, European Journal of Operational Research 132 (2001) 439–452], and Rajendran and Ziegler [C. Rajendran, H. Ziegler, Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs, European Journal of Operational Research, 155(2) (2004) 426–438]. For the total flowtime criterion, 57 out of the 90 best known solutions reported by Liu and Reeves, and Rajendran and Ziegler were improved whereas for the makespan criterion, 195 out of the 800 best known solutions for the random and narrow random problems reported by Watson et al. were improved by the VNS version of the PSO algorithm.     

An enhanced dynasearch neighborhood for the single-machine total weighted tardiness scheduling problem

Based on the work by Congram, Potts and Van de Velde, we develop for the single-machine total weighted tardiness scheduling problem an enhanced dynasearch neighborhood obtained by the generalized pairwise interchange (GPI) operators. Despite of the wider neighborhood considered, a fast search procedure using also elimination criteria is developed. The computational results significantly improve over those of Congram, Potts and Van de Velde.     

A multi-start dynasearch algorithm for the time dependent single-machine total weighted tardiness scheduling problem

We extend the dynasearch technique, recently proposed by Congram et al., in the context of time-dependent combinatorial optimization problems. As an application we consider a general time-dependent (idleness) version of the well known single-machine total weighted tardiness scheduling problem, in which the processing time of a job depends on its starting time of execution. We develop a multi-start local search algorithm and present experimental results on several types of instances showing the superiority of the dynasearch neighborhood over the traditional one.     

A dynamic programming algorithm for the single-machine scheduling problem with release dates and deteriorating processing times

We consider a scheduling problem in which the processing time of each job deteriorates, i.e. it increases as time passes after the release date of the job. We present a dynamic programming algorithm coupled with upper bounding and lower bounding techniques to compute exact solutions. We report on problem instances of different size and we analyze the dependence between the ranges to which the data belong and the computing time.     

A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem

We propose a novel cooperative swarm intelligence algorithm to solve multi-objective discrete optimization problems (MODP). Our algorithm combines a firefly algorithm (FA) and a particle swarm optimization (PSO). Basically, we address three main points: the effect of FA and PSO cooperation on the exploration of the search space, the discretization of the two algorithms using a transfer function, and finally, the use of the epsilon dominance relation to manage the size of the external archive and to guarantee the convergence and the diversity of Pareto optimal solutions.We compared the results of our algorithm with the results of five well-known meta-heuristics on nine multi-objective knapsack problem benchmarks. The experiments show clearly the ability of our algorithm to provide a better spread of solutions with a better convergence behavior.     

A rank based particle swarm optimization algorithm with dynamic adaptation

The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. This paper presents a variation on the standard PSO algorithm called the rank based particle swarm optimizer, or PSO_rank, employing cooperative behavior of the particles to significantly improve the performance of the original algorithm. In this method, in order to efficiently control the local search and convergence to global optimum solution, the γ best particles are taken to contribute to the updating of the position of a candidate particle. The contribution of each particle is proportional to its strength. The strength is a function of three parameters: strivness, immediacy and number of contributed particles. All particles are sorted according to their fitness values, and only the γ best particles will be selected. The value of γ decreases linearly as the iteration increases. A time-varying inertia weight decreasing non-linearly is introduced to improve the performance. PSO_rank is tested on a commonly used set of optimization problems and is compared to other variants of the PSO algorithm presented in the literature. As a real application, PSO_rank is used for neural network training. The PSO_rank strategy outperformed all the methods considered in this investigation for most of the functions. Experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness.     

Minimizing total tardiness in parallel machine scheduling with setup times: An adaptive memory-based GRASP approach

This paper deals with the problem of scheduling jobs in uniform parallel machines with sequence-dependent setup times in order to minimize the total tardiness relative to job due dates. We propose GRASP versions that incorporate adaptive memory principles for solving this problem. Long-term memory is used in the construction of an initial solution and in a post-optimization procedure which connects high quality local optima by means of path relinking. Computational tests are carried out on a set of benchmark instances and the proposed GRASP versions are compared with heuristic methods from the literature.     

Minimizing the sum of maximum earliness and maximum tardiness in the single-machine scheduling problem with sequence-dependent setup time

This paper considers the problem of scheduling a given number of jobs on a single machine to minimize the sum of maximum earliness and maximum tardiness when sequence-dependent setup times exist (1∣ST _sd ∣ET_max). In this paper, an optimal branch-and-bound algorithm is developed that involves the implementation of lower and upper bounding procedures as well as three dominance rules. For solving problems containing large numbers of jobs, a polynomial time-bounded heuristic algorithm is also proposed. Computational experiments demonstrate the effectiveness of the bounding and dominance rules in achieving optimal solutions in more than 97% of the instances.     

Memetic particle swarm optimization

We propose a new Memetic Particle Swarm Optimization scheme that incorporates local search techniques in the standard Particle Swarm Optimization algorithm, resulting in an efficient and effective optimization method, which is analyzed theoretically. The proposed algorithm is applied to different unconstrained, constrained, minimax and integer programming problems and the obtained results are compared to that of the global and local variants of Particle Swarm Optimization, justifying the superiority of the memetic approach.     

Precedence theorems and dynamic programming for the single-machine weighted tardiness problem

We tackle precedence-constrained sequencing on a single machine in order to minimize total weighted tardiness. Classic dynamic programming (DP) methods for this problem are limited in performance due to excessive memory requirements, particularly when the precedence network is not sufficiently dense. Over the last decades, a number of precedence theorems have been proposed, which distinguish dominant precedence constraints for a job pool that is initially without precedence relation. In this paper, we connect and extend the findings of the foregoing two strands of literature. We develop a framework for applying the precedence theorems to the precedence-constrained problem to tighten the search space, and we propose an exact DP algorithm that utilizes a new efficient memory management technique. Our procedure outperforms the state-of-the-art algorithm for instances with medium to high network density. We also empirically verify the computational gain of using different sets of precedence theorems.     

A novel hybrid differential evolution and particle swarm optimization algorithm for unconstrained optimization

An algorithm called DE-PSO is proposed which incorporates concepts from DE and PSO, updating particles not only by DE operators but also by mechanisms of PSO. The proposed algorithm is tested on several benchmark functions. Numerical comparisons with different hybrid meta-heuristics demonstrate its effectiveness and efficiency.     

Balancing and scheduling tasks in assembly lines with sequence-dependent setup times

The classical Simple Assembly Line Balancing Problem (SALBP) has been widely enriched over the past few years with many realistic approaches and much effort has been made to reduce the distance between the academic theory and the industrial reality. Despite this effort, the scheduling of the execution of tasks assigned to every workstation following the balancing of the assembly line has been scarcely reported in the scientific literature. This is supposed to be an operational concern that the worker should solve himself, but in several real environments, setups between tasks exist and optimal or near-optimal tasks schedules should be provided inside each workstation. The problem presented in this paper adds sequence-dependent setup time considerations to the classical SALBP in the following way: whenever a task is assigned next to another at the same workstation, a setup time must be added to compute the global workstation time. After formulating a mathematical model for this innovative problem and showing the high combinatorial nature of the problem, eight different heuristic rules and a GRASP algorithm are designed and tested for solving the problem in reasonable computational time.     

A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design

Multi-objective particle swarm optimization (MOPSO) is an optimization technique inspired by bird flocking, which has been steadily gaining attention from the research community because of its high convergence speed. On the other hand, in the face of increasing complexity and dimensionality of today’s application coupled with its tendency of premature convergence due to the high convergence speeds, there is a need to improve the efficiency and effectiveness of MOPSO. In this paper a competitive and cooperative co-evolutionary approach is adapted for multi-objective particle swarm optimization algorithm design, which appears to have considerable potential for solving complex optimization problems by explicitly modeling the co-evolution of competing and cooperating species. The competitive and cooperative co-evolution model helps to produce the reasonable problem decompositions by exploiting any correlation, interdependency between components of the problem. The proposed competitive and cooperative co-evolutionary multi-objective particle swarm optimization algorithm (CCPSO) is validated through comparisons with existing state-of-the-art multi-objective algorithms using established benchmarks and metrics. Simulation results demonstrated that CCPSO shows competitive, if not better, performance as compared to the other algorithms.     

Balanced fuzzy particle swarm optimization

In the present study an extension of particle swarm optimization (PSO) algorithm which is in conformity with actual nature is introduced for solving combinatorial optimization problems. Development of this algorithm is essentially based on balanced fuzzy sets theory. The classical fuzzy sets theory cannot distinguish differences between positive and negative information of membership functions, while in the new method both kinds of information “positive and negative” about membership function are equally important. The balanced fuzzy particle swarm optimization algorithm is used for fundamental optimization problem entitled traveling salesman problem (TSP). For convergence inspecting of new algorithm, method was used for TSP problems. Convergence curves were represented fast convergence in restricted and low iterations for balanced fuzzy particle swarm optimization algorithm (BF-PSO) comparison with fuzzy particle swarm optimization algorithm (F-PSO).