The 0/1 knapsack problem is weakly NP-hard in that there exist pseudo-polynomial time algorithms based on dynamic programming that can solve it exactly. There are also the core branch and bound algorithms that can solve large randomly generated instances in a very short amount of time. However, as the correlation between the variables is increased, the difficulty of the problem increases. Recently a new class of knapsack problems was introduced by D. Pisinger called the spanner knapsack instances. These instances are unsolvable by the core branch and bound instances; and as the size of the coefficients and the capacity constraint increase, the spanner instances are unsolvable even by dynamic programming based algorithms. In this paper, a genetic algorithm is presented for spanner knapsack instances. Results show that the algorithm is capable of delivering optimum solutions within a reasonable amount of computational duration.
The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show t…
Genetic Algorithm is an evolutionary algorithm and a metaheuristic that was introduced to overcome the failure of gradient based method in solving the optimization and search problems. The purpose of this paper is to evaluate the impact on the convergence of Genetic Algorithm vis-a-vis 0/1 knapsack. By keeping the number of generations and the initial population fixed, different crossover methods like one point crossover and two-point crossover were evaluated and juxtaposed with each other. In addition to this, the impact of different selection methods like rank-selection, roulette wheel and t…
The 0/1 multidimensional knapsack problem is the 0/1 knapsack problem with m constraints which makes it difficult to solve using traditional methods like dynamic programming or branch and bound algorithms. We present a genetic algorithm for the multidimensional knapsack problem with Java and C++ code that is able to solve publicly available instances in a very short computational duration. Our algorithm uses iteratively computed Lagrangian multipliers as constraint weights to augment the greedy algorithm for the multidimensional knapsack problem and uses that information in a greedy crossover …
Cryptanalysis of knapsack cipher is a fascinating problem which has eluded the computing fraternity for decades. However, in most of the cases either the time complexity of the proposed algorithm is colossal or an insufficient number of samples have been taken for verification. The present work proposes a Genetic Algorithm based technique for cryptanalysis of knapsack cipher. The experiments conducted prove the validity of the technique. The results prove that the technique is better than the existing techniques. An extensive review has been carried out in order to find the gaps in the existin…
Multi Expression Programming (MEP) is a Genetic Programming variant that uses linear chromosomes for solution encoding. A unique feature of MEP is its ability of encoding multiple solutions of a problem in a single chromosome. In this paper we use Multi Expression Programming for evolving digital circuits for a well-known NP-Complete problem: the knapsack (subset sum) problem. Numerical experiments show that Multi Expression Programming performs well on the considered test problems.
In this paper the approach to solving several combinatorial optimization problems using the local search and the genetic algorithm techniques is proposed. Initially this approach was developed in purpose to overcome some difficulties inhibiting the application of above mentioned techniques to the problems of the Questionnaire Theory. But when the algorithms were developed it became clear that them could be successfully applied also to the Minimum Set Cover, the 0-1-Knapsack and probably to other combinatorial optimization problems.
In this paper, we propose a method to solve a bi-objective variant of the well-studied Traveling Thief Problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: Traveling Salesman Problem (TSP) and Knapsack Problem (KP). We address the BI-TTP, a bi-objective version of the TTP, where the goal is to minimize the overall traveling time and to maximize the profit of the collected items. Our proposed method is based on a biased-random key genetic algorithm with customizations addressing problem-specific characteristics. We incorporate domain knowledge th…
The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight. The objective is to maximize the total profit of the selected items under the condition that the weight of the selected items only exceeds the given weight bound with a small probability of $α$. In this paper, consider problem-specific single-objective and multi-objective approaches for the problem. We examine the use of heavy-tail mutations and introduce a problem-specific crossover operator to deal with the chance-constrained knap…
Bacteria have been a source of inspiration for the design of evolutionary algorithms. At the beginning of the 20th century synthetic biology was born, a discipline whose goal is the design of biological systems that do not exist in nature, for example, programmable synthetic bacteria. In this paper, we introduce as a novelty the designing of evolutionary algorithms where all the steps are conducted by synthetic bacteria. To this end, we designed a genetic algorithm, which we have named BAGA, illustrating its utility solving simple instances of optimization problems such as function optimizatio…
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently reoptimize linear functions under a dynamic uniform constraint. Motivated by this study, we investigate single- and multi-objective baseline evolutionary algorithms for the classical knapsack problem where the capacity of the knapsack varies over time. We establish different benchmark scenarios where the capacity changes every $τ$ iterations according to a uniform …
How to maintain relative high diversity is important to avoid premature convergence in population-based optimization methods. Island model is widely considered as a major approach to achieve this because of its flexibility and high efficiency. The model maintains a group of sub-populations on different islands and allows sub-populations to interact with each other via predefined migration policies. However, current island model has some drawbacks. One is that after a certain number of generations, different islands may retain quite similar, converged sub-populations thereby losing diversity an…
Quality diversity (QD) algorithms have been shown to be very successful when dealing with problems in areas such as robotics, games and combinatorial optimization. They aim to maximize the quality of solutions for different regions of the so-called behavioural space of the underlying problem. In this paper, we apply the QD paradigm to simulate dynamic programming behaviours on knapsack problem, and provide a first runtime analysis of QD algorithms. We show that they are able to compute an optimal solution within expected pseudo-polynomial time, and reveal parameter settings that lead to a full…
Complutense University of Madrid（马德里康普顿斯大学）；University of Nottingham（诺丁汉大学）
We propose a variation of the standard genetic algorithm that incorporates social interaction between the individuals in the population. Our goal is to understand the evolutionary role of social systems and its possible application as a non-genetic new step in evolutionary algorithms. In biological populations, ie animals, even human beings and microorganisms, social interactions often affect the fitness of individuals. It is conceivable that the perturbation of the fitness via social interactions is an evolutionary strategy to avoid trapping into local optimum, thus avoiding a fast convergenc…
An algorithm is described that adaptively learns a non-linear mutation distribution. It works by training a denoising autoencoder (DA) online at each generation of a genetic algorithm to reconstruct a slowly decaying memory of the best genotypes so far. A compressed hidden layer forces the autoencoder to learn hidden features in the training set that can be used to accelerate search on novel problems with similar structure. Its output neurons define a probability distribution that we sample from to produce offspring solutions. The algorithm outperforms a canonical genetic algorithm on several …
The multidimensional knapsack problem is a well-known constrained optimization problem with many real-world engineering applications. In order to solve this NP-hard problem, a new modified Imperialist Competitive Algorithm with Constrained Assimilation (ICAwICA) is presented. The proposed algorithm introduces the concept of colony independence, a free will to choose between classical ICA assimilation to empires imperialist or any other imperialist in the population. Furthermore, a constrained assimilation process has been implemented that combines classical ICA assimilation and revolution oper…
Multi-Objective Evolutionary Optimization of Chance-Constrained Multiple-Choice Knapsack Problems with Implicit Probability Distributions
Southern University of Science and Technology（南方科技大学）；Central China Normal University（华中师范大学）；Institute of High Performance Computing, Agency for Science Technology and Research（新加坡科技研究局高性能计算研究所）；Nanyang Technological University（南洋理工大学）
Using a Genetic Algorithm and Decision Tree Classifier, the features of the NSL-KDD dataset are reduced using combinatorial optimization to determine the minimum features required to accurately classify Denial of Service attacks within the NSL-KDD dataset.
Traceless Genetic Programming (TGP) is a new Genetic Programming (GP) that may be used for solving difficult real-world problems. The main difference between TGP and other GP techniques is that TGP does not explicitly store the evolved computer programs. In this paper, TGP is used for solving real-world classification problems taken from PROBEN1. Numerical experiments show that TGP performs similar and sometimes even better than other GP techniques for the considered test problems.
An approach to the acceleration of parametric weak classifier boosting is proposed. Weak classifier is called parametric if it has fixed number of parameters and, so, can be represented as a point into multidimensional space. Genetic algorithm is used instead of exhaustive search to learn parameters of such classifier. Proposed approach also takes cases when effective algorithm for learning some of the classifier parameters exists into account. Experiments confirm that such an approach can dramatically decrease classifier training time while keeping both training and test errors small.
Universidade Federal de Ouro Preto（奥罗普雷托联邦大学）；Universidade Federal de Viçosa（维索萨联邦大学）；The University of Adelaide（阿德莱德大学）
We tackle the Thief Orienteering Problem (ThOP), an academic multi-component problem that combines two classical combinatorial problems, namely the Knapsack Problem and the Orienteering Problem. In the ThOP, a thief has a time limit to steal items that distributed in a given set of cities. While traveling, the thief collects items by storing them in their knapsack, which in turn reduces the travel speed. The thief has as the objective to maximize the total profit of the stolen items. In this article, we present an approach that combines swarm-intelligence with a randomized packing heuristic. O…
