A Clustering Based Niching Method for Effectively Solving the 0-1 Knapsack Problem

Clustering is an unsupervised learning algorithm. k-Means algorithm is one of the well-known and promising clustering algorithms that can converge to a local optimum in few iterative. In our work, we will be hybridizing k-Means algorithm with Genetic Algorithms to look for the solution in the global search space in order to converge to a global optima. The problem for clustering is that when the number of clusters increases up to the same number of total records in the dataset, it leads to a scenario in which a cluster only contains a single record, and thus the cluster purity is maximized to the maximum value, 1. However, it will be useless since the common regularities among records will not be seen. Therefore, choosing the best number of clusters is trivial. Instead of choosing an inappropriate number of clusters and risking the main purpose of the clustering process, a Genetic Algorithm based k-Means ensemble is proposed in order to find the consensus result of several runs of clustering task using different number of clusters, k.

Niching ethods are useful extension of evolutionary algorithm that can permit population to search many peaks in parallel in multimodal domains. Traditional niching methods that can effectively be used to solve function optimization problems (FOPs) are not suitable for solving combinatorial optimization problems (COPs). We propose a new genetic algorithm (GA) for forming niches that can be efficiently applied to COPs. For this, we propose four requirements that are needed for an ideal method of forming niches for COPs. We then discuss a niching method we designed that satisfies these requirements. The proposed GA was applied to job shop scheduling problems (JSP) to demonstrate its effectiveness.

This is a research project on using Genetic Algorithm to solve 0-1 Knapsack Problem. Knapsack problem is a combinational optimization problem. Given a set of items, each with a weight & value, it determine the number of each item to include in a collection so that the total weight is less than a given limit & the total value is as large as possible. The paper consists of three parts. In the first section we give brief description of Genetic Algorithms and some of its basic elements. Next, we describe the Knapsack Problem and Implementation of Knapsack problem using Genetic Algorithm. The main purpose of this paper is to implement Knapsack problem by an algorithm that is based on Genetic Algorithm. In this paper I have used Roulette-Wheel, Tournament Selection and Stochastic selection as a selection function and the succeeding populations are analyzed for the fitness value with hope to achieve the correct solution and expected results were observed.

This paper presents a new binary optimization technique for solving the 0–1 knapsack problem. This algorithm is based on converting the continuous search space of the recently proposed quadratic interpolation optimization (QIO) into discrete search space using various V-shaped and S-shaped transfer functions; this algorithm is abbreviated as BQIO. To further improve its performance, it is effectively integrated with a uniform crossover operator and a swap operator to explore the discrete binary search space more effectively. This improved variant is called BIQIO. Both BQIO and BIQIO are assessed using 20 well-known knapsack instances and compared to four recently published metaheuristic algorithms to reveal their effectiveness. The comparison among algorithms is based on three performance metrics: the mean fitness value, Friedman mean rank and computational cost. The first two metrics are used to observe the accuracy of the results, while the last metric is employed to show the efficiency of each algorithm. The results of this comparison reveal the superiority of BIQIO over the classical BQIO and four rival optimizers.

We present two novel contributions for achieving and assessing quantum advantage in solving difficult optimisation problems, both in theory and foreseeable practice. (1) We introduce the “Quantum Tree Generator” to generate in superposition all feasible solutions of a given 0-1 knapsack instance; combined with amplitude amplification, this identifies optimal solutions. Assuming fully connected logical qubits and comparable quantum clock speed, QTG offers perspectives for runtimes competitive to classical state-of-the-art knapsack solvers for instances with only 100 variables. (2) By introducing a new technique that exploits logging data from a classical solver, we can predict the runtime of our method way beyond the range of existing quantum platforms and simulators, for benchmark instances with up to 600 variables. Under the given assumptions, we demonstrate the QTG’s potential practical quantum advantage for such instances, indicating the promise of an effective approach for hard combinatorial optimisation problems.

Particle Swarm Optimization (PSO) is a stochastic optimization approach that originated from early attempts to simulate the behavior of birds looking for food. Estimation of distributions algorithms (EDAs) are a class of evolutionary algorithms that build and maintain a probabilistic model capturing the search space characteristics and continuously use this model to generate new individuals. In this work, we propose a new PSO and EDA hybrid algorithm that uses the particles' distribution in the search space in order to adjust the search space bounds, hence, restricting the particles movement as well as their allowable maximum velocity. The algorithms is augmented with a mechanism to overcome premature convergence and escape local minima. The algorithm is compared to the standard PSO algorithm using a suite of well-known benchmark optimization functions. Experimental results show that the proposed algorithm has a promising performance.

This paper looks at the processing of skyline queries on peer-to-peer (P2P) networks. We propose Skyframe, a framework for efficient skyline query processing in P2P systems, which addresses the challenges of quick response time, low network communication cost and query load balancing among peers. Skyframe consists of two querying methods: one is optimized for network communication while the other focuses on query response time. These methods are different in the way in which the query search space is defined. In particular, the first method uses a high dominating point that has a large dominating region to prune the search space to achieve a low cost in network communication. On the other hand, the second method relaxes the search space in order to allow parallel query processing to speed up query response. Skyframe achieves query load balancing by both query load conscious data space splitting/merging during the join/departure of nodes and dynamic load migration. We further show how to apply Skyframe to both the P2P systems supporting multi-dimensional indexing and the P2P systems supporting single-dimensional indexing. Finally, we have conducted extensive experiments on both real and synthetic data sets over two existing P2P systems: CAN (Ratnasamy in A scalable content-addressable network. In: Proceedings of SIGCOMM Conference, pp. 161---172, 2001) and BATON (Jagadish et al. in A balanced tree structure for peer-to-peer networks. In: Proceedings of VLDB Conference, pp. 661---672, 2005) to evaluate the effectiveness and scalability of Skyframe.

The Knapsack Problem belongs to the best-studied classical problems in combinatorial optimization. The Multiple-choice Knapsack Problem (MCKP) represents a generalization of the problem, with various application fields such as industry, transportation, telecommunication, national defense, bioinformatics, finance, and life. We found a lack of survey papers on MCKP. This paper overviews MCKP and presents its variants, solution methods, and applications. Traditional operational research methods solving the knapsack problem, such as dynamic programming, greedy heuristics, and branch-and-bound algorithms, can be adapted to MCKP. Only a few algorithms appear to have solved the problem in recent years. We found various related problems during the literature study and explored the broad spectrum of application areas. We intend to inspire research into MCKP algorithms and motivate experts from different domains to apply MCKP.

This paper considers the locally and globally optimal solutions of the global optimisation problem whose objective function is a max‐plus vector‐valued function and constraint function is a real affine function. The formulas about global optimisation in the existing work are further explained and simplified. The necessary and sufficient conditions for the existence and uniqueness of locally optimal solutions of a single objective are established, which are then used to deduce these of globally optimal solutions. Furthermore, the general formulas of locally and globally optimal solutions are presented, respectively. The local optimisation is then applied to solve the load distribution problem of distributed systems with no globally optimal solution, and the optimal allocation scheme is proposed to complete the overall task at the earliest time. The proposed method is constructive, and the obtained results are illustrated by the numerical examples.

Knapsack problem is a combinatorial optimisation problem which is concerned with finding a solution where an exhaustive search is difficult or even impractical to do. Approximate algorithms, also called heuristics are therefore applied in solving Knapsack problems. The goal of this study was to solve the Knapsack model using three heuristics viz: greedy, dynamic programming, and branch-and-bound strategies. The ultimate objective of our study was to evaluate the time complexities of these heuristics as input sizes become larger. In the bid to get that done, a Knapsack problem was solved using the approximate algorithms, employing the same programming environment, with varying input sizes. The problem was simulated using different input data sizes. A synthesis of the results obtained, that is, the various time complexities, was then carried out and a comparative study of the three algorithms was done. The coefficients of the variables used in the Knapsack model for simulation were generated using random numbers generating algorithm. Our results showed that the greedy algorithm was the most efficient computationally. The second best efficient was the dynamic progranmming algorithm while the least in terms of time complexity is branch-and-bound strategy. It is considered a worthwhile effort to study more metrics of complexity measurement. This is recommended as good enough for further research attention. However, our present study has shown in pragmatic form the computational complexity of the greedy, dynamic programming, and branch-and-bound algorithms.

Approximation algorithms for fractional knapsack problems

Though Knapsack Problem appears to be simple, it is a NP-hard problem that is not solved in polynomial time as combinational optimization problems. To solve this problem, GA(Genetic Algorithms) was used in the past. However, there were difficulties in real experiments because the conventional method didn`t reflect the precise characteristics of DNA. In this paper we proposed ACO (Algorithm for Code Optimization) that applies DNA coding method to DNA computing to solve problems of Knapsack Problem. ACO was applied to (0,1) Knapsack Problem; as a result, it reduced experimental errors as compared with conventional methods, and found accurate solutions more rapidly.

This paper proposes a new function for the Ad Hoc On-Demand Distance Vector (AODV) algorithm using the connectivity concept to decide between source and local repair when a link break occurs. Besides, we used a Computational Intelligence algorithm, called Particle Swarm Optimization (PSO), which enables to find candidate solutions in all considered search space in order to reduce average data packet delivery delay sent over the network. The performance of the original AODV protocol, according to its Request for Comments (RFC), is compared with this new implemented approach, called here as AODVPSO. Three metrics were used to evaluate the performance of the algorithm: throughput (as data packet delivery fraction), routing overhead and average data packet delivery delay. We observed that the AODV-PSO outperformed the original AODV protocol in the scenarios studied in this paper.

Various real-life datasets can be viewed as a set of records consisting of attributes explaining the records and set of measures evaluating the records. In this paper, we address the problem of automatically discovering interesting subsets from such a dataset, such that the discovered interesting subsets have significantly different characteristics of performance than the rest of the dataset. We present an algorithm to discover such interesting subsets. The proposed algorithm uses a generic domain-independent definition of interestingness and uses various heuristics to intelligently prune the search space in order to build a solution scalable to large size datasets. This paper presents application of the interesting subset discovery algorithm on four real-world case-studies and demonstrates the effectiveness of the interesting subset discovery algorithm in extracting insights in order to identify problem areas and provide improvement recommendations to wide variety of systems.

This work investigates the use of the Moth-Flame Optimisation (MFO) algorithm in solving the Permutation Flow Shop Scheduling Problem and proposes further optimisations. MFO is a population-based approach that simulates the behaviour of real moths by exploiting the search space randomly without employing any local searches that may stick in local optima. Therefore, we propose a Hybrid Moth Optimisation Algorithm (HMOA) that is embedded within a local search to better exploit the search space. HMOA entails employing three search procedures to intensify and diversify the search space in order to prevent the algorithm's becoming trapped in local optima. Furthermore, HMOA adaptively selects the search procedure based on improvement ranks. In order to evaluate the performances of MFO and HMOA, we perform a comparison against other approaches drawn from the literature. Experimental results demonstrate that HMOA is able to produce better-quality solutions and outperforms many other approaches on the Taillard benchmark.