In this paper the well-known 0-1 Multiple Knapsack Problem (MKP) is approached by an adaptive Binary Differential Evolution (aBDE) algorithm. The MKP is a NP-hard optimization problem and the aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit. The aBDE self adjusts two parameters, perturbation and mutation rates, using a linear adaptation procedure that changes their probabilities at each generation. Results were obtained using 11 instances of the problem with different degrees of complexity. The results were compared using aBDE, BDE, a standard Genetic Algorithm (GA) and its adaptive version (aGA), and an island-inspired Genetic Algorithm (IGA) and its adaptive version (aIGA). The results show that aBDE obtained better results than the other algorithms. This indicates that the proposed approach is an interesting and a promising strategy to control the parameters and for optimization of complex problems.Index Terms-Adaptive parameter control, binary differential evolution, multiple knapsack problem, evolutionary computation. I. INTRODUCTIONT HE 0-1 Multiple Knapsack Problem (MKP) is a binary NP-hard combinatorial optimization problem that consists in given a set of items and a set of knapsacks, each item with a mass and a value, determine which item to include in which knapsack. The aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit.Different variants of the MKP can be easily adapted to real problems, such as, capital budgeting, cargo loading and others [1]. Hence, the optimization of resource allocation is one major concern in several areas of logistics, transportation and production [2]. In this way, the search for efficient methods to achieve such optimization aims to increase profits and reduce the use of raw materials.According to the size of an instance (number of items and number of knapsacks) of the MKP, the search space can become too large to apply exact methods. Hence, a large number of heuristics and metaheuristics have been applied to the MKP. Some examples are the modified binary Manuscript

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Nature has always been a great source of inspiration for the development of computational approaches for optimization. Two major groups representing this class of biologically inspired algorithms are Swarm Intelligence and Evolutionary Computation. Such algorithms are called metaheuristics and are recognized to be efficient approaches for solving complex problems. Both Swarm Intelligence and Evolutionary Computation share common features such as the use of stochastic components during the optimization process and various parameters for configuration. The setup of parameters of an algorithm has an important role in defining its behavior, guiding the search and biasing the quality of the solutions found. However, adjusting the parameters is not a simple task, becoming an optimization problem within the problem being optimized. In addition, an appropriate setting for the parameters may change during the optimization process making this task even harder. There are two ways to adjust the parameters of an algorithm. The offline control that is performed before running the algorithm and parameter values remains fixed and the online control where parameter values may change during the optimization process. This article focuses on reviewing the online parameter control strategies applied in Evolutionary Computation and Swarm Intelligence. As a result, this review analyzes and points out the key techniques and algorithms used and suggests some directions for future research.

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