A Weight-coded Evolutionary Algorithm for the Multidimensional Knapsack Problem

A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm proposed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.Comment: Submitted to Applied Mathematics and Computation on April 8, 201

Cheating for Problem Solving: A Genetic Algorithm with Social Interactions

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 convergence of the population. We model the social interactions according to Game Theory. The population is, therefore, composed by cooperator and defector individuals whose interactions produce payoffs according to well known game models (prisoner's dilemma, chicken game, and others). Our results on Knapsack problems show, for some game models, a significant performance improvement as compared to a standard genetic algorithm.Comment: 7 pages, 5 Figures, 5 Tables, Proceedings of Genetic and Evolutionary Computation Conference (GECCO 2009), Montreal, Canad

Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

A genetic programming hyper-heuristic for the multidimensional knapsack problem

Purpose: Hyper-heuristics are a class of high-level search techniques which operate on a search space of heuristics rather than directly on a search space of solutions. The purpose of this paper is to investigate the suitability of using genetic programming as a hyper-heuristic methodology to generate constructive heuristics to solve the multidimensional 0-1 knapsack problem. Design/methodology/approach: Early hyper-heuristics focused on selecting and applying a low-level heuristic at each stage of a search. Recent trends in hyper-heuristic research have led to a number of approaches being developed to automatically generate new heuristics from a set of heuristic components. A population of heuristics to rank knapsack items are trained on a subset of test problems and then applied to unseen instances. Findings: The results over a set of standard benchmarks show that genetic programming can be used to generate constructive heuristics which yield human-competitive results. Originality/value: In this work the authors show that genetic programming is suitable as a method to generate reusable constructive heuristics for the multidimensional 0-1 knapsack problem. This is classified as a hyper-heuristic approach as it operates on a search space of heuristics rather than a search space of solutions. To our knowledge, this is the first time in the literature a GP hyper-heuristic has been used to solve the multidimensional 0-1 knapsack problem. The results suggest that using GP to evolve ranking mechanisms merits further future research effort. © Emerald Group Publishing Limited