Shuffled frog leaping algorithm and its application to 0/1 knapsack problem

With the popularity of complex hydrologic models, the time taken to run these models is increasing substantially. Comparing and evaluating the efficacy of different optimization algorithms for calibrating computationally intensive hydrologic models is becoming a nontrivial issue. In this study, five global optimization algorithms (genetic algorithms, shuffled complex evolution, particle swarm optimization, differential evolution, and artificial immune system) were tested for automatic parameter calibration of a complex hydrologic model, Soil and Water Assessment Tool (SWAT), in four watersheds. The results show that genetic algorithms (GA) outperform the other four algorithms given model evaluation numbers larger than 2000, while particle swarm optimization (PSO) can obtain better parameter solutions than other algorithms given fewer number of model runs (less than 2000). Given limited computational time, the PSO algorithm is preferred, while GA should be chosen given plenty of computational resources. When applying GA and PSO for parameter optimization of SWAT, small population size should be chosen. Copyright © 2008 John Wiley & Sons, Ltd.

Abstract. The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their ability to calibrate the Modified Bartlett-Lewis Model. The list of tested methods consists of: the Downhill Simplex Method, Simplex-Simulated Annealing, Particle Swarm Optimization and Shuffled Complex Evolution. The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the Modified Bartlett-Lewis model. Furthermore, this paper addresses the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights.

The Sacramento model is widely utilized in hydrological forecast, of which the accuracy and performance are primarily determined by the model parameters, indicating the key role of parameter estimation. This paper presents a multi-step parameter estimation method, which divides the parameter estimation of Sacramento model into three steps and realizes optimization step by step. We firstly use the immune clonal selection algorithm (ICSA) to solve the non-liner objective function of parameter estimation, and compare the parameter calibration result of ideal artificial data with Shuffled Complex Evolution (SCE-UA), Parallel Genetic Algorithm (PGA), and Serial Master-slaver Swarms Shuffling Evolution Algorithm Based on Particle Swarms Optimization (SMSE-PSO). The comparison result shows that ICSA has the best convergence, efficiency and precision. Then we apply ICSA to the parameter estimation of single-step and multi-step Sacramento model and simulate 32 floods based on application examples of Dongyang and Tantou river basins for validation. It is clearly shown that the results of multi-step method based on ICSA show higher accuracy and 100% qualified rate, indicating its higher precision and reliability, which has great potential to improve Sacramento model and hydrological forecast.

An important problem in the study of evolutionary algorithms is how to continuously predict promising solutions while simultaneously escaping from local optima. In this paper, we propose an elitist probability schema (EPS) for the first time, to the best of our knowledge. Our schema is an index of binary strings that expresses the similarity of an elitist population at every string position. EPS expresses the accumulative effect of fitness selection with respect to the coding similarity of the population. For each generation, EPS can quantify the coding similarity of the population objectively and quickly. One of our key innovations is that EPS can continuously predict promising solutions while simultaneously escaping from local optima in most cases. To demonstrate the abilities of the EPS, we designed an elitist probability schema genetic algorithm and an elitist probability schema compact genetic algorithm. These algorithms are estimations of distribution algorithms (EDAs). We provided a fair comparison with the persistent elitist compact genetic algorithm (PeCGA), quantum-inspired evolutionary algorithm (QEA), and particle swarm optimization (PSO) for the 0---1 knapsack problem. The proposed algorithms converged quicker than PeCGA, QEA, and PSO, especially for the large knapsack problem. Furthermore, the computation time of the proposed algorithms was less than some EDAs that are based on building explicit probability models, and was approximately the same as QEA and PSO. This is acceptable for evolutionary algorithms, and satisfactory for EDAs. The proposed algorithms are successful with respect to convergence performance and computation time, which implies that EPS is satisfactory.

The multidimensional knapsack problem (MKP), which is a generalization of the 0-1 simple Knapsack problem, is one of the classical NP-hard problems in operations research having a number of engineering applications. Several exact as well as heuristic algorithms are available in literature for its solution. In this paper, we propose a new particle swarm optimization (PSO) algorithm namely socio-cognitive particle swarm optimization (SCPSO) for solving the MKP. Comparing with the basic binary particle swarm optimization (BPSO), this improved algorithm introduces the distance between gbest and pbest as a new velocity update equation which maintains the diversity in the swarm and makes it more effective and efficient in solving MKP. We present computational experiments with various data instances for fine tuning of parameters of SCPSO and to validate our ideas and demonstrate the efficiency of the proposed algorithm.

Knapsack problem is famous NP-complete problem where one has to maximize the benefit of objects in a knapsack without exceeding its capacity. In this paper, a binary bacterial foraging optimization (BBFO) is proposed to find solutions of 0/1 knapsack problems. The original BFO chemotaxis equation is modified to operate in discrete space by using a mapping function, where some new variables and parameter, i.e., binary matrix y, logistic transformation S, and limiting transformation L is built to transform the bacterial position to a binary matrix. By using this schema, the proposed BBFO model can also be easily applied in other discrete problem solving. To further validate the efficiency of the BFO-based approach, an improved version BFO named BFO with linear decreasing chemotaxis step (BFO-LDC) is used to evaluate on six different instances. Comparisons with particle swarm optimization (PSO) and original BFO are presented and discussed.

Encoding transformation-based differential evolution algorithm for solving knapsack problem with single continuous variable

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.

The purpose of this study is to clarify the search performance of differential evolution (DE) and particle swarm optimization (PSO) technologies for instinctively understanding the specificity of the used search methods. Due to achieve the task, here, the several search methods of both, i.e. DE/rand/1, DE/rand/2, DE/best/1, DE/best/2, the PSO, PSOIW, and CPSO, which are implemented in this paper. Therefore, many computer experiments are carried out for handling the given four benchmark problems. Through the analysis of the obtained experimental data, the detail search performance and characteristics of them are observed and compared, respectively. From the obtained results, it is found that the search methods of DE/best/1 and the PSO relatively have better search performance. Based on the findings and know-how, they can provide some important reference and key hint for encouraging development and improvement of both DE and PSO technologies in the near future. And as the applicative examples, the PSO is used to handle typical 2-bit and 3-bit parity problems for pattern classification.

The particle swarm optimization (PSO) method is a population-based optimization technique which searches for solutions by updating simultaneously a number of candidate solutions called particles. Since, in the PSO, the exploration ability is important to find a desirable solution, various kinds of methods have been investigated to improve it. In this paper, we propose a new chaotic dynamical system for PSO having sinusoidal perturbations, in which chaotic particles can be expected to search for solutions around the two tentative solutions by using chaotic sequences. Through computational experiments, by applying them to some global optimization problems, we compare the proposed chaotic PSO with the standard one

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.

The advancements of mobile devices, public networks and the Internet of creature huge amounts of complex data, both construct & unstructured are being captured in trust to allow organizations to produce better business decisions as data is now pivotal for an organizations success. These enormous amounts of data are referred to as Big Data, which enables a competitive advantage over rivals when processed and analyzed appropriately. However Big Data Analytics has a few concerns including Management of Data, Privacy & Security, getting optimal path for transport data, and Data Representation. However, the structure of network does not completely match transportation demand, i.e., there still exist a few bottlenecks in the network. This paper presents a new approach to get the optimal path of valuable data movement through a given network based on the knapsack problem. This paper will give value for each piece of data, it depends on the importance of this data (each piece of data defined by two arguments size and value), and the approach tries to find the optimal path from source to destination, a mathematical models are developed to adjust data flows between their shortest paths based on the 0 - 1 knapsack problem. We also take out computational experience using the commercial software Gurobi and a greedy algorithm (GA), respectively. The outcome indicates that the suggest models are active and workable. This paper introduced two different algorithms to study the shortest path problems: the first algorithm studies the shortest path problems when stochastic activates and activities does not depend on weights. The second algorithm studies the shortest path problems depends on weights.

Metaheuristics are a fundament pillar of Industry 4.0, as they allow for complex optimization problems to be solved by finding good solutions in a reasonable amount of computational time. One category of important problems in modern industry is that of binary problems, where decision variables can take values of zero or one. In this work, we propose a binary version of the Pufferfish optimization algorithm (BPOA), which was originally created to solve continuous problems. The binary mapping follows a two-step technique, first transforming using transfer functions and then discretizing using binarization rules. We study representative pairings of transfer functions and binarization rules, comparing our algorithm with Particle Swarm Optimization, Secretary Bird Optimization Algorithm, and Arithmetic Optimization Algorithm with identical computational budgets. To validate its correct functioning, we solved binary problems present in industry, such as the Set Covering Problem together with its Unicost variant, as well as the Knapsack Problem. The results we achieved with regard to these problems were promising and statistically validated. The tests performed on the executions indicate that many pair differences are not statistically significant when both methods are already close to the optimal level, and significance arises precisely where the descriptive gaps widen, underscoring that transfer-rule pairing is the main performance factor. BPOA is a competitive and flexible framework whose effectiveness is mainly governed by the discretization design.

It has been reported for multi-objective knapsack problems that the recombination of similar parents often improves the performance of evolutionary multi-objective optimization (EMO) algorithms. Recently performance improvement was also reported by exchanging only a small number of genes between two parents (i.e., crossover with a very small gene exchange probability) without choosing similar parents. In this paper, we examine these performance improvement schemes through computational experiments where NSGA-II is applied to 500-item knapsack problems with 2-10 objectives. We measure the parent-parent distance and the parent-offspring distance in computational experiments. Clear performance improvement is observed when the parent-offspring distance is small. To further examine this observation, we implement a distance-based crossover operator where the parent-offspring distance is specified as a user-defined parameter. Performance of NSGA-II is examined for various parameter values. Experimental results show that an appropriate parameter value (parent-offspring distance) is surprisingly small. It is also shown that a very small parameter value is beneficial for diversity maintenance.

Keeping networks security has never been such an imperative task as today. In this paper, by combining particle swarm optimization and clustering algorithm, a new detection method, Intrusion Detection based on Unsupervised Clustering and PSO algorithm (IDCPSO), is proposed. Particle swarm optimization algorithm is used to optimize the clustering results and obtain the optimal detection result. IDCPSO needs unlabeled data for training and automatically establish clusters and detect intruders by labeling normal and abnormal groups. Computer experiment results with KDD cup show that this algorithm is effective for intrusion detection.