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

A Heuristic Algorithm for Resource Allocation/Reallocation Problem

This paper presents a 1-opt heuristic approach to solve resource allocation/reallocation problem which is known as 0/1 multichoice multidimensional knapsack problem (MMKP). The intercept matrix of the constraints is employed to find optimal or near-optimal solution of the MMKP. This heuristic approach is tested for 33 benchmark problems taken from OR library of sizes upto 7000, and the results have been compared with optimum solutions. Computational complexity is proved to be (2) of solving heuristically MMKP using this approach. The performance of our heuristic is compared with the best state-of-art heuristic algorithms with respect to the quality of the solutions found. The encouraging results especially for relatively large-size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems

A comparison of crossover control mechanisms within single-point selection hyper-heuristics using HyFlex

Hyper-heuristics are search methodologies which operate at a higher level of abstraction than traditional search and optimisation techniques. Rather than operating on a search space of solutions directly, a hyper-heuristic searches a space of low-level heuristics or heuristic components. An iterative selection hyper-heuristic operates on a single solution, selecting and applying a low-level heuristic at each step before deciding whether to accept the resulting solution. Crossover low-level heuristics are often included in modern selection hyper-heuristic frameworks, however as they require multiple solutions to operate, a strategy is required to manage potential solutions to use as input. In this paper we investigate the use of crossover control schemes within two existing selection hyper-heuristics and observe the difference in performance when the method for managing potential solutions for crossover is modified. Firstly, we use the crossover control scheme of AdapHH, the winner of an international competition in heuristic search, in a Modified Choice Function - All Moves selection hyper-heuristic. Secondly, we replace the crossover control scheme within AdapHH with another method taken from the literature. We observe that the performance of selection hyper-heuristics using crossover low level heuristics is not independent of the choice of strategy for managing input solutions to these operators

Application of Pigeon Inspired Optimization for Multidimensional Knapsack Problem

The multidimensional knapsack problem (MKP) is a generalization of the classical knapsack problem, a problem for allocating a resource by selecting a subset of objects that seek for the highest profit while satisfying the capacity of knapsack constraint. The MKP have many practical applications in different areas and classified as a NP-hard problem. An exact method like branch and bound and dynamic programming can solve the problem, but its time computation increases exponentially with the size of the problem. Whereas some approximation method has been developed to produce a near-optimal solution within reasonable computational times. In this paper a pigeon inspired optimization (PIO) is proposed for solving MKP. PIO is one of the metaheuristic algorithms that is classified in population-based swarm intelligent that is developed based on the behavior of the pigeon to find its home although it had gone far away from it home. In this paper, PIO implementation to solve MKP is applied to two different characteristic cases in total 10 cases. The result of the implementation of the two-best combination of parameter values for 10 cases compared to particle swarm optimization, intelligent water drop algorithm and the genetic algorithm gives satisfactory results

A modified choice function hyper-heuristic controlling unary and binary operators

Hyper-heuristics are a class of high-level search methodologies which operate on a search space of low-level heuristics or components, rather than on solutions directly. Traditional iterative selection hyper-heuristics rely on two key components, a heuristic selection method and a move acceptance criterion. Choice Function heuristic selection scores heuristics based on a combination of three measures, selecting the heuristic with the highest score. Modified Choice Function heuristic selection is a variant of the Choice Function which emphasises intensification over diversification within the heuristic search process. Previous work has shown that improved results are possible in some problem domains when using Modified Choice Function heuristic selection over the classic Choice Function, however in most of these cases crossover low-level heuristics (operators) are omitted. In this paper, we introduce crossover low-level heuristics into a Modified Choice Function selection hyper-heuristic and present results over six problem domains. It is observed that although on average there is an increase in performance when using crossover low-level heuristics, the benefit of using crossover can vary on a per-domain or per-instance basis

Improved binary artificial fish swarm algorithm for the 0–1 multidimensional knapsack problems

The 0–1 multidimensional knapsack problem (MKP) arises in many fields of optimization and is NP-hard. Several exact as well as heuristic methods exist. Recently, an artificial fish swarm algorithm has been developed in continuous global optimization. The algorithm uses a population of points in space to represent the position of fish in the school. In this paper, a binary version of the artificial fish swarm algorithm is proposed for solving the 0–1 MKP. In the proposed method, a point is represented by a binary string of 0/1 bits. Each bit of a trial point is generated by copying the corresponding bit from the current point or from some other specified point, with equal probability. Occasionally, some randomly chosen bits of a selected point are changed from 0 to 1, or 1 to 0, with an user defined probability. The infeasible solutions are made feasible by a decoding algorithm. A simple heuristic add_item is implemented to each feasible point aiming to improve the quality of that solution. A periodic reinitialization of the population greatly improves the quality of the solutions obtained by the algorithm. The proposed method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method gives a competitive performance when solving this kind of problems.Fundação para a Ciência e a Tecnologia (FCT