Abstract
Problem statement: Knapsack problem is a typical NP complete problem. During last few decades, Knapsack problem has been studied through different approaches, according to the theoretical development of combinatorial optimization. Approach: In this study, modified evolutionary algorithm was presented for 0/1 knapsack problem. Results: A new objective_func_evaluation operator was proposed which employed adaptive repair function named as repair and elitism operator to achieve optimal results in place of problem specific knowledge or domain specific operator like penalty operator (which are still being used). Additional features had also been incorporated which allowed the algorithm to perform more consistently on a larger set of problem instances. Conclusion/Recommendations: This study also focused on the change in behavior of outputs generated on varying the crossover and mutation rates. New algorithm exhibited a significant reduction in number of function evaluations required for problems investigated.
Highlights
Knapsack problem is a well known and well studied problem in combinatorial optimization being widely used in areas like network planning, network routing, parallel scheduling and budgeting[1]
Due to space constraint we have shown only 3 instances of the mutation rate i.e., 03, 0.003, 0.70
Experimental results do not show the case when mutation is turned off, because it does not matter much what the crossover rate is when mutation is turned off as mutation is a function which is an integral part of crossover operator and if mutation is off, it yields the same results as when crossover and mutation are set equal to zero
Summary
Knapsack problem is a well known and well studied problem in combinatorial optimization being widely used in areas like network planning, network routing, parallel scheduling and budgeting[1]. The fitness values of the chromosomes in a population are evaluated based on the profits associated with the items. Each generation of the population yields a set of unique items that would result in maximum profit, modifying the solution vector in each step by proceeding towards the best fit solution. ∆: The objective_func_evaluation is a function which evaluates the fitness of chromosomes in the new population. If the total weight of the items in the chromosome generated by the crossover and mutation procedure is greater than the capacity of the knapsack that solution is infeasible and the Repair Operator and the elitism come into play. Objective_func_evaluation operator is basically a combination of Elitism and Repair operator which is simple to implement and provides us with similar results as obtained with other operators which need complex computations.
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