Enhancing Hyperheuristics for the Knapsack Problem through Fuzzy Logic

Abstract

Hyperheuristics rise as powerful techniques that get good results in less computational time than exact methods like dynamic programming or branch and bound. These exact methods promise the global best solution, but with a high computational time. In this matter, hyperheuristics do not promise the global best solution, but they promise a good solution in a lot less computational time. On the contrary, fuzzy logic provides the tools to model complex problems in a more natural way. With this in mind, this paper proposes a fuzzy hyperheuristic approach, which is a combination of a fuzzy inference system with a selection hyperheuristic. The fuzzy system needs the optimization of its fuzzy rules due to the lack of expert knowledge; indeed, traditional hyperheuristics also need an optimization of their rules. The fuzzy rules are optimized by genetic algorithms, and for the rules of the traditional methods, we use particle swarm optimization. The genetic algorithm will also reduce the number of fuzzy rules, in order to find the best minimal fuzzy rules, whereas traditional methods already use very few rules. Experimental results show the advantage of using our approach instead of a traditional selection hyperheuristic in 3200 instances of the 0/1 knapsack problem.

Knapsack problem in fuzzy nature: Different models based on credibility ranking method

“…Olivas et al [24] 2021 -Fuzzy hyperheuristic approach Singh and Chakrabor [30] 2019 Profit and weights Two-stage decisionmaking approach Singh [29] 2019 Weights and profit…”

“…To solve the knapsack problem using fuzzy programming, Abboud et al modeled the multi-objective knapsack problem as a fuzzy linear programming problem (FLP) and used genetic algorithms to solve it [2]. A fuzzy hyperheuristic approach, which is a combination of a fuzzy inference system with a selection hyperheuristic is proposed in [24]. An integrated fuzzy TOPSIS-knapsack problem model for order selection in a bakery is presented in [10].…”

Hybrid Metaheuristics Using Rough Sets for QoS-Aware Service Composition

“…One of the primary goals of combinatorial optimization is to devise efficient algorithms for solving problems that arise in everyday life. In general, combinatorial optimization problems are renowned as traveling salesman [95], The vehicular routing problem [96], task scheduling [97], and knapsack problem [98].…”

Improved discrete particle swarm optimization using Bee Algorithm and multi-parent crossover method (Case study: Allocation problem and benchmark functions)

“…Even for a small problem, traditional optimization methods take much time to nd an accurate solution (Olivas et al, 2021). Moreover, nding the optimal solution becomes more complicated as the search space expands (Kosarwal et al, 2020).…”