Particle swarm optimization and differential evolution for the single machine total weighted tardiness problem

In This work we present a particle swarm optimization algorithm to solve the single machine total weighted tardiness problem. A heuristic rule, the smallest position value (SPV) rule, is developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems, which are NP-hard in the literature. A simple but very efficient local search method is embedded in the particle swarm optimization algorithm. The computational results show that the particle swarm algorithm is able to find the optimal and best-known solutions on all instances of widely used benchmarks from the OR library.

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

A particle swarm optimization algorithm (PSO) has been used to solve the single machine total weighted tardiness problem (SMTWT) with unequal release date. To find the best solutions three different solution approaches have been used. To prepare subhybrid solution system, genetic algorithms (GA) and simulated annealing (SA) have been used. In the subhybrid system (GA and SA), GA obtains a solution in any stage, that solution is taken by SA and used as an initial solution. When SA finds better solution than this solution, it stops working and gives this solution to GA again. After GA finishes working the obtained solution is given to PSO. PSO searches for better solution than this solution. Later it again sends the obtained solution to GA. Three different solution systems worked together. Neurohybrid system uses PSO as the main optimizer and SA and GA have been used as local search tools. For each stage, local optimizers are used to perform exploitation to the best particle. In addition to local search tools, neurodominance rule (NDR) has been used to improve performance of last solution of hybrid-PSO system. NDR checked sequential jobs according to total weighted tardiness factor. All system is named as neurohybrid-PSO solution system.

Particle swarm optimisation (PSO) was developed by Kennedy and Eberhart in 1995 (Kennedy & Eberhart, 1995) inspired by the collective behaviour of natural birds or fish. PSO is a stochastic optimisation technique that uses a behaviour of population composed by many search points called particle. In spite of easy implementation in computer algorithms, it is well known as a powerful numerical optimizer. In the typical PSO algorithms, a set of particles searches the optimal solution in the problem space efficiently, by sharing the common attractor called global best. There are many modified versions of PSO by improving convergence property to a certain problem. While, a standard PSO is defined by Bratton and Kennedy (Bratton & Kennedy, 2007) to give a real standard for PSO studies. PSO seems as one of the evolutionary computations (ECs), and it has been shown that PSO is comparable to a genetic algorithm (Angeline, 1998). Thus, a lot of studies have demonstrated the effectiveness of PSO family in optimizing various continuous and discrete optimization problems. And a plenty of applications of PSO, such as the neural network training, PID controller tuning, electric system optimisation have been studied and achieved well results (Kennedy, 1997). However, PSO is often failed in searching the global optimal solution in the case of the objective function has a large number of dimensions. The reason of this phenomenon is not only existence of the local optimal solutions, the velocities of the particles sometimes lapsed into the degeneracy, so that the successive range is restricted in the sub-plain of the whole search hyper-plain. The sub-plane that is defined by finite number of particle velocities is a partial space in the whole search space. The issue of local optima in PSO has been studied and proposed several modifications on the basic particle driven equation (Parsopoulos et al., 2001; Hendtlass, 2005; Liang et al., 2006). There used a kind of adaptation technique or randomized method (e.g. mutation in evolutionary computations) to keep particles velocities or to accelerate them. Although such improvements work well and have ability to avoid fall in the local optima, the problem of early convergence by the degeneracy of some dimensions is still remaining, even if there are no local optima. Hence the PSO algorithm does not always work well for the high-dimensional function.

Modified particle swarm optimization algorithm for variable selection in MLR and PLS modeling: QSAR studies of antagonism of angiotensin II antagonists.

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

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

Network reconfiguration for loss reduction in a distribution system is a very important way to save the electrical energy. This article proposes a hybrid evolutionary algorithm to solve the distribution feeder reconfiguration problem. The algorithm combines a fuzzy adaptive particle swarm optimization with a differential evolution algorithm, called the fuzzy adaptive particle swarm optimization–differential evolution. The fuzzy adaptive particle swarm optimization includes two parts. The first part is fuzzy adaptive binary particle swarm optimization, which determines the status of tie switches (open or closed), and the second part is fuzzy adaptive discrete particle swarm optimization, which determines the sectionalizing switch number. In the proposed algorithm, due to the results of binary particle swarm optimization and discrete particle swarm optimization algorithms that highly depend on the values of their parameters (such as the inertia weight and learning factors), a fuzzy system is employed to adaptively adjust the parameters during the search process. The differential evolution algorithm is combined with the fuzzy adaptive particle swarm optimization algorithm to improve its performance. The proposed algorithm is tested on two distribution test feeders. The results of simulation show that the proposed method is very powerful and is guaranteed to obtain the global optimization.

The wireless mesh network is a new emerging technology exploiting the advantages of multiple radios and multiple channels. In this paper we have studied the channel assignment problem which is to assign channels to links in the network, and aimed at minimizing the network interference so as to improve the network throughput. The channel assignment problem is proved to be NP-hard. In this paper, we have developed a new approach based on the particle swarm optimization (PSO) algorithm and a heuristic algorithm to solve channel assignment problem in multi-radio multi-channel wireless mesh networks. Meanwhile, the crossover operation is employed in the discrete particle swarm optimization (DPSO) algorithm to handle the discrete channel assignment problem. Experimental results have shown that the rate of interference in the DPSO algorithm descends by 67.67% compared with the Tabu-based algorithm when there are 12 channels and 5 radios. And the heuristic algorithm can also yield good solutions with good quality in both dense and sparse networks.

Neural Network system for SoC is one topic in the world. Recently, SoC began to combine AI technique by Python. When developers consider Intelligent system on SoC, the co-design software and hardware are significant. In this case, small devices and embedded system are target system. For IoT, those techniques will grow up in the world. Those cases, avoiding premature convergence while keeping performance is a challenge in training the neural network, especially in a case of large NNs or a large number of training data. In this case, one problem is a huge memory and processing power. For tiny memory and processing system as SoC, we propose an improved particle swarm optimization (PSO) algorithm called the PSOseed2 algorithm for training NN. The PSOseed2 algorithm solves the premature convergence of the standard PSO (SPSO) algorithm by slightly modifying the velocity update function without adding many computational tasks to the SPSO algorithm. We evaluated this algorithm on field programmable gate array (FPGA)-based NN and software-based NN and trained these NNs with different PSO algorithms that are SPSO, PSOseed, PSOseed2, and dissipative PSO. Experimental results with different datasets confirmed that the NNs trained by the proposed PSOseed2 algorithm had better recognition rates and lower global learning errors than the NN trained by other PSO algorithms. In this talk, I would like to talk those relational research in the world and our results and discussion.

The well-known particle swarm optimization (PSO) proposed by Kennedy and Eberhart has been widely applied to the continuous optimal problems. However, it is still intractable to apply PSO to discrete optimization problems, such as permutation flow shop scheduling problems (PFSSP). In this paper, a new high performing metaheuristic algorithm hybridizing PSO with variable neighborhood search (VNS) is proposed to solve PFSSP with the objective of minimizing makespan. NEH heuristic has been adopted in the first step to generate good solutions in the initial population, and then PSO and VNS are hybridized to search for optimal or near-optimal solutions of the PFSSP. Two effective neighborhood structures concerned with characteristics of PFSSP have been adopted to enhance VNS's performance. Computational experiments have been conducted on benchmarks and comparison results with other existing algorithms show the efficiency of the proposed algorithm.

This paper introduces a new algorithmic nature inspired approach that uses a hybridized Particle Swarm Optimization algorithm with a new neighborhood topology for successfully solving the Feature Selection Problem (FSP). The Feature Selection Problem is an interesting and important topic which is relevant for a variety of database applications. The proposed algorithm for the solution of the FSP, the Particle Swarm Optimization with Expanding Neighborhood Topology (PSOENT), combines a Particle Swarm Optimization (PSO) algorithm and the Variable Neighborhood Search (VNS) strategy. As, in general, the structure of the social network affects strongly a PSO algorithm, the proposed method by using an expanding neighborhood topology manages to increase the performance of the algorithm. As the algorithm starts from a small size neighborhood and by increasing (expanding) the size of the neighborhood, it ends to a neighborhood that includes all the swarm, it manages to take advantage of the exploration capabilities of a global neighborhood structure and of the exploitation abilities of a local neighborhood structure. In order to test the effectiveness and the efficiency of the proposed method we use data sets of different sizes and compare the proposed method with a number of other PSO algorithms and other algorithms from the literature.

Selection of right partners is vital for virtual enterprise (VE) to take the advantage of market opportunity. Partner selection problem belongs to combinatorial optimisation category and known as NP-hard. A modified discrete particle swarm optimisation (PSO) algorithm is proposed, in this work, to select alliances in a VE. The velocity terms, which is commonly used in the standard PSO algorithm, is avoided; rather, the concept of proportional likelihood with modifications, a method used in data mining techniques, is adopted to improve solution quality. A set of experiments have been conducted and results indicate PSO algorithm is an effective and efficient way to solve the partner selection problems with precedence, risk of failure and due date constraints. A design of experiment (DoE) approach is adopted to study statistical significance of various model parameters on solution quality.

Biogeography-based Optimization (BBO) Algorithm for Single Machine Total Weighted Tardiness Problem (SMTWTP)

A kind of discrete Particle Swarm Optimization (PSO) algorithm named NDPSO was proposed for extending the classic PSO model to solve the discrete optimization problems with high effectiveness and stability. The concept of comparison with probability was also introduced based on NDPSO, and then the stochastic repairing operator was constructed for heuristic search to solve the Winner Determination Problem (WDP) in combinatory auction. The experimental results show that NDPSO has great advantages in both success rate and convergence speed compared with other discrete PSO algorithms and genetic algorithm.