Neural, Genetic, And Neurogenetic Approaches For Solving The 0-1 Multidimensional Knapsack Problem

The multi-dimensional knapsack problem (MDKP) is a well-studied problem in Decision Sciences. The problem’s NP-Hard nature prevents the successful application of exact procedures such as branch and bound, implicit enumeration and dynamic programming for larger problems. As a result, various approximate solution approaches, such as the relaxation approaches, heuristic and metaheuristic approaches have been developed and applied effectively to this problem. In this study, we propose a Neural approach, a Genetic Algorithms approach and a Neurogenetic approach, which is a hybrid of the Neural and the Genetic Algorithms approach. The Neural approach is essentially a problem-space based non-deterministic local-search algorithm. In the Genetic Algorithms approach we propose a new way of generating initial population. In the Neurogenetic approach, we show that the Neural and Genetic iterations, when interleaved appropriately, can complement each other and provide better solutions than either the Neural or the Genetic approach alone. Within the overall search, the Genetic approach provides diversification while the Neural provides intensification. We demonstrate the effectiveness of our proposed approaches through an empirical study performed on several sets of benchmark problems commonly used in the literature

Coevolutionary GA with schema extraction by machine learning techniques and its application to knapsack problems

The authors introduce a novel coevolutionary genetic algorithm with schema extraction by machine learning techniques. Our CGA consists of two GA populations: the first GA (H-GA) searches for the solutions in the given problems and the second GA (P-GA) searches for effective schemata of the H-GA. We aim to improve the search ability of our CGA by extracting more efficiently useful schemata from the H-GA population, and then incorporating those extracted schemata in a natural manner into the P-GA. Several computational simulations on multidimensional knapsack problems confirm the effectiveness of the proposed method</p

Binary artificial algae algorithm for multidimensional knapsack problems

The multidimensional knapsack problem (MKP) is a well-known NP-hard optimization problem. Various meta-heuristic methods are dedicated to solve this problem in literature. Recently a new meta-heuristic algorithm, called artificial algae algorithm (AAA), was presented, which has been successfully applied to solve various continuous optimization problems. However, due to its continuous nature, AAA cannot settle the discrete problem straightforwardly such as MKP. In view of this, this paper proposes a binary artificial algae algorithm (BAAA) to efficiently solve MKP. This algorithm is composed of discrete process, repair operators and elite local search. In discrete process, two logistic functions with different coefficients of curve are studied to achieve good discrete process results. Repair operators are performed to make the solution feasible and increase the efficiency. Finally, elite local search is introduced to improve the quality of solutions. To demonstrate the efficiency of our proposed algorithm, simulations and evaluations are carried out with total of 94 benchmark problems and compared with other bio-inspired state-of-the-art algorithms in the recent years including MBPSO, BPSOTVAC, CBPSOTVAC, GADS, bAFSA, and IbAFSA. The results show the superiority of BAAA to many compared existing algorithms

Incorporating Memory and Learning Mechanisms Into Meta-RaPS

Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics. Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results. The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions. To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature

A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem. We tackle the problem using duality concept, differently from traditional approaches. Our method is based on Lagrangian relaxation. Lagrange multipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the capacity constraints of the problem. Through empirical investigation of Lagrangian space, we can see the potentiality of using a memetic algorithm. So we use a memetic algorithm to find the optimal Lagrange multipliers. We show the efficiency of the proposed method by the experiments on well-known benchmark data

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