A Modified Shuffled Frog Leaping Algorithm with Genetic Mutation for Combinatorial Optimization

Network virtualization provides a promising solution to overcome the ossification of current networks, allowing multiple Virtual Network Requests (VNRs) to be embedded on a common infrastructure. The major challenge in network virtualization is the Virtual Network Embedding (VNE) problem, which is to embed VNRs onto a shared substrate network and known to be $\mathcal {NP}$ -hard. The topological heterogeneity of VNRs is one important factor hampering the performance of the VNE. However, in many specialized applications and infrastructures, VNRs are of some common structural features, e.g., paths and cycles. To achieve better outcomes, it is thus critical to design dedicated algorithms for these applications and infrastructures by taking into accounting topological characteristics. Besides, paths and cycles are two of the most fundamental topologies that all network structures consist of. Exploiting the characteristics of path and cycle embeddings is vital to tackle the general VNE problem. In this paper, we investigate the path and cycle embedding problems. For path embedding, we prove its $\mathcal {NP}$ -hardness and inapproximability. Then, by utilizing Multiple Knapsack Problem (MKP) and Multi-Dimensional Knapsack Problem (MDKP), we propose an efficient and effective MKP-MDKP-based algorithm. For cycle embedding, we propose a Weighted Directed Auxiliary Graph (WDAG) to develop a polynomial-time algorithm to determine the least-resource-consuming embedding. Numerical results show our customized algorithms can boost the acceptance ratio and revenue compared to generic embedding algorithms in the literature.

Binary metaheuristic algorithms for 0–1 knapsack problems: Performance analysis, hybrid variants, and real-world application

In order to improve the premature convergence problem of traditional shuffled frog leaping algorithm (SFLA), this paper proposed a normal cloud mutation shuffled frog leaping algorithm (NCM-SFLA) by mixing the cloud model algorithm (NCM) with SFLA algorithm, NCM is used to overcome the shortage of SFLA which is easy to fall into local optimal solution. The proposed NCM-SFLA has a good parallel characteristic, and the parallel computing can be implemented easily in multi core environment. In case study, this paper takes the Li Xianjiang cascade reservoirs in China as an instance to solve the cascade reservoirs operation optimization problem by the proposed NCM-SFLA. The results show that, compared with the Multi- dimensional Dynamic Programming (MDP), NCM-SFLA has the better global search ability and faster convergence speed, and the corresponding parallel computing can effectively shorten the run-time of NCM-SFLA. Therefore, the feasibility and rationality of the proposed NCM-SFLA and its parallel computing are effectively proved by the case study results.

We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of different classes (colours) need to be placed in bins; the items may have different sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can accommodate. In the class-constrained multiple knapsack (CCMK) problem, our goal is to maximize the total value of packed items, whereas in the class-constrained bin-packing (CCBP), we seek to minimize the number of (identical) bins, needed for packing all the items. We give a polynomial time approximation scheme (PTAS) for CCMK and a dual PTAS for CCBP. We also show that the 0–1 class-constrained knapsack admits a fully polynomial time approximation scheme, even when the number of distinct colours of items depends on the input size. Finally, we introduce the generalized class-constrained packing problem (GCCP), where each item may have more than one colour. We show that GCCP is APX-hard, already for the case of a single knapsack, where all items have the same size and the same value. Our optimization problems have several important applications, including storage management for multimedia systems, production planning, and multiprocessor scheduling. Copyright © 2001 John Wiley & Sons, Ltd.

Knapsack problems are among the most common problems in literature tackled with evolutionary algorithms (EA). Their major advantage lies in the fact that they are relatively simple to implement while they allow generalizations for a wide range of real world problems. The multi-dimensional knapsack problem (MKP), which belongs to the class of NP-complete combinatorial optimization problems, is one of the variations of the knapsack problem. The MKP has a wide range of real world applications such as cargo loading, selecting projects to fund, budget management, cutting stock, etc. The MKP has been studied quite extensively in the EA community. Due to the constrained nature of the problem, constraint handling techniques gain great importance in the performance of the proposed EA approaches. In this study, the applicability of a generational EA that uses a penalty-based constraint handling technique and a gene locus based, asymmetric, adaptive mutation scheme is explored for the MKP. The effects of the parameters of the explored approach is determined through tests. Further experiments, using large MKP instances from commonly used benchmarks available through the Internet are performed. Comparison tables are given for the performance of the explored approach and other good performing EAs found in literature for the MKP. Results show that performance improves greatly when compared with other penalty-based techniques, but the explored approach is still not the best performer among all. However, unlike the explored technique, the EAs using the other constraint handling techniques require a great amount of extra computational effort and need heuristic information specific to the optimization problem. Based on these observations, and the fact that the performance difference between the explored scheme and the better performers is not too high, research on improving the explored approach is still in progress.

We consider a natural generalization of the knapsack problem and the multiple knapsack problem, which has two phases of packing decisions. In this problem, we have a set of items, several small knapsacks called boxes, and a large knapsack called container. Each item has a size and profit, each box has a size and the container has a capacity. The first phase is to select some items to pack into the boxes, and the second phase is to select the boxes (each includes some packed items) to pack into the container. The total profit of the problem is determined by the items that are selected and packed into the container within some packed box, and the objective is to maximize the total profit. This problem is motivated by various practical applications, e.g., in logistics. It is a generalization of the multiple knapsack problem, and hence is strongly NP-hard. We mainly propose three approximation algorithms for it. Particularly, the first one is a \(\frac{1}{4}\)-approximation algorithm based on its linear programming relaxation; the second one is based on applying the algorithms for the multiple knapsack problem and the knapsack problem, and has an approximation ratio \(\frac{1}{3} - \epsilon \) for any small enough \(\epsilon >0\). We finally provide a polynomial time approximation scheme for this problem.

This paper proposes a novel approach for the multidimensional knapsack problem (MDKP) using differential evolution. Firstly, the principle and the pseudo-code of binary differential evolution with hybrid encoding (HBDE) are presented. On the basis of the existing repair operator 2 (RO2), an improved repair operator 3 (RO3) for handling the infeasible solutions of MDKP is developed. Then, combine HBDE with RO3, an efficient algorithm (HBDE-RO3) for MDKP is proposed. Finally, the experiment results of the 138 well-known MDKP benchmarks show that RO3 is advantageous to deal with the infeasible solutions than RO2, and the proposed algorithm HBDE-RO3 has superior performance for solving MDKP than the state-of-the-art algorithms.

Grid enables resource sharing and dynamic allocation of computational resources. It is a great challenge to make numerous resources available on-demand to guarantee the Quality-of-Service for jobs. This paper presents a two-stage optimization model for resource allocation in grid. Job constraints are classified into mandatory constraints and negotiated constraints. In the first stage, a preprocessing procedure such as resource discovery deals with the mandatory constraints. This has been fulfilled as our previous work. In the second stage, negotiated constraints are treated as Knapsack Problem-based optimization problem. Centralized scheduling and decentralized scheduling have been considered in this paper. This work is fulfilled as part of the Constellation Model for grid resource management. We formulate centralized scheduling as Multi-Constraint Multiple Knapsack Problem (MCMKP). In centralized scheduling, jobs are submitted to a global job queue. A global scheduler assigns each job to a proper grid site according to the scheduling strategy. The scheduling is done periodically (e.g. daily or weekly). We formulate decentralized scheduling as Multi-Dimensional Knapsack Problem (MDKP). In decentralized scheduling, jobs are submitted to local job queues. Allocation decisions are made by local schedulers individually. Jobs that can not be executed immediately are sent to a global waiting queue. When local scheduling is initialized, a local scheduler can select jobs from both the local job queue and the global waiting queue. Objectives of both centralized scheduling and decentralized scheduling are to optimize the utility defined by a grid economy approach. The defined utility makes the trade-offs between user-concerned metrics and system-concerned metrics. Heuristic algorithms such as Very Large-Scale Neighborhood Search proposed by R. K. Ahuja and C. B. Cunha [2005] can be used to solve the combinatorial optimization problem. We implemented a prototype of the Constellation Model. Genetic algorithms for constrained optimization which is proposed by S. Venkatraman and G. G. Yen [2005] have been implemented to solve the above optimization problems. Experimental results show that, performance metrics such as gained utility, response rate, and resource utilization are improved and resources are allocated in an optimal way.

Shuffled Frog Leaping Algorithm (SFLA) is a new meta-heuristic evolutionary algorithm with simple algorithm structure and fast calculation speed. In this paper, a novel algorithm based on SFLA and chaos search is presented. This algorithm uses chaos search to generate neighborhoods of extremum so as to maintain solution diversity and get rid of local optimal solution when the individual stops evolution. The numerical experiments results show it outperforms standard SFLA. Finally, the proposed algorithm is used to solve the problem of mid-long term optimal operation of cascade hydropower stations and is compared with other two algorithms. The operation results show its feasibility and high efficiency.

Solving the bi-objective multi-dimensional knapsack problem exploiting the concept of core

PurposeAttitude control of unmanned aerial vehicle (UAV) is the purposeful manipulation of controllable external forces to establish a desired attitude, which is inner‐loop of the autonomous flight control system. In the practical applications, classical control methods such as proportional‐integral‐derivative control are usually selected because of simple and high reliability. However, it is usually difficult to select or optimize the control parameters. The purpose of this paper is to investigate an intelligent algorithm based classical controller of UAV.Design/methodology/approachAmong the many intelligent algorithms, shuffled frog leaping algorithm (SFLA) combines the benefits of the genetic‐based memetic algorithm as well as social behavior based particle swarm optimization. SFLA is a population based meta‐heuristic intelligent optimization method inspired by natural memetics. In order to improve the performance of SFLA, a different dividing method of the memeplexes is presented to make their performance balance; moreover, an evolution mechanism of the best frog is introduced to make the algorithm jump out the local optimum. The modified SFLA is applied to the tuning of the proportional coefficients of pitching and rolling channels of UAV flight control system.FindingsSimulation of a UAV control system in which the nonlinear model is obtained by the wind tunnel experiment show the rapid dynamic response and high control precision by using the modified SFLA optimized attitude controller, which is better than that of the original SFLA and particle swarm optimization method.Originality/valueA modification scheme is presented to improve the global searching capability of SFLA. The modified SFLA based intelligent determination method of the UAV flight controller parameters is proposed, in order to improve the attitude control performance of UAV.

We study the multidimensional knapsack problem, present some theoretical and empirical results about its structure, and evaluate different integer linear programming (ILP)-based, metaheuristic, and collaborative approaches for it. We start by considering the distances between optimal solutions to the LP relaxation and the original problem and then introduce a new core concept for the multidimensional knapsack problem (MKP), which we study extensively. The empirical analysis is then used to develop new concepts for solving the MKP using ILP-based and memetic algorithms. Different collaborative combinations of the presented methods are discussed and evaluated. Further computational experiments with longer run times are also performed to compare the solutions of our approaches to the best-known solutions of another so-far leading approach for common MKP benchmark instances. The extensive computational experiments show the effectiveness of the proposed methods, which yield highly competitive results in significantly shorter run times than do previously described approaches.

The pigeon-inspired optimization algorithm is a category of a newly proposed swarm intelligence-based algorithm that belongs to the population-based solution technique. The MKP is a class of complex optimization problems that have many practical applications in the fields of engineering and sciences. Due to the practical applications of MKP, numerous algorithmic-based methods like local search and population-based search algorithms have been proposed to solve the MKP in the past few decades. This paper proposes a modified binary pigeon-inspired optimization algorithm named (Modified-BPIO) for the 0 - 1 multidimensional knapsack problem (MKP). The utilization of the binary pigeon-inspired optimization (BPIO) for solving the multidimensional knapsack problem came with huge success. However, it can be observed that the BPIO converges prematurely due to lost diversity during the search activities. Given the above, the crossover operator is integrated with the landmark component of the BPIO to improve the diversity of the solution space. The MKP benchmarks from the Operations Research (OR) library are utilized to test the performance of the proposed binary method. Experimentally, it is concluded that the proposed Modified-BPIO has a better performance when compared with the BPIO and existing state-of-the-arts that worked on the same MKP benchmarks.

In this paper, we have proposed a novel algorithm based on Ant Colony Optimization (ACO) for finding near-optimal solutions for the Multi-dimensional Multi-choice Knapsack Problem (MMKP). MMKP is a discrete optimization problem, which is a variant of the classical 0-1 Knapsack Problem and is also an NP-hard problem. Due to its high computational complexity, exact solutions of MMKP are not suitable for most real-time decision-making applications e.g. QoS and Admission Control for Adaptive Multimedia Systems, Service Level Agreement (SLA) etc. Although ACO algorithms are known to have scalability and slow convergence issues, here we have augmented the traditional ACO algorithm with a unique random local search, which not only produces near-optimal solutions but also greatly enhances convergence speed. A comparative analysis with other state-of-the-art heuristic algorithms based on public MMKP dataset shows that, in all cases our approaches outperform others. We have also shown that our algorithms find near optimal (within 3% of the optimal value) solutions within milliseconds, which makes our approach very attractive for large scale real time systems.

This study addresses a shuffled frog leaping algorithm for solving the multi-objective reactive power dispatch problem in a power system. Optimal Reactive Power Dispatch (ORPD) is formulated as a nonlinear, multi-modal and mixed-variable problem. The intended technique is based on the minimization of the real power loss, minimization of voltage deviation and maximization of the voltage stability margin. Generator voltages, capacitor banks and tap positions of tap changing transformers are used as optimization variables of this problem. A memetic meta-heuristic named as shuffled frog-leaping algorithm is intended to solve multi-objective optimal reactive power dispatch problems considering voltage stability margin and voltage deviation. The Shuffled Frog-Leaping Algorithm (SFLA) is a population-based cooperative search metaphor inspired by natural memetics. The algorithm contains elements of local search and global information exchange. The most important benefit of this algorithm is higher speed of convergence to a better solution. The intended method is applied to ORPD problem on IEEE 57 bus power systems and compared with two versions of differential evolutionary algorithm. The simulation results show the effectiveness of the intended method.