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

Evolutionary population dynamics and multi-objective optimisation problems

Griffith Sciences, School of Information and Communication TechnologyFull Tex

Geometric Particle Swarm Optimization for Multi-objective Optimization Using Decomposition

Multi-objective evolutionary algorithms (MOEAs) based on decomposition are aggregation-based algorithms which transform a multi-objective optimization problem (MOP) into several single-objective subproblems. Being effective, efficient, and easy to implement, Particle Swarm Optimization (PSO) has become one of the most popular single-objective optimizers for continuous problems, and recently it has been successfully extended to the multi-objective domain. However, no investigation on the application of PSO within a multi-objective decomposition framework exists in the context of combinatorial optimization. This is precisely the focus of the paper. More specifically, we study the incorporation of Geometric Particle Swarm Optimization (GPSO), a discrete generalization of PSO that has proven successful on a number of single-objective combinatorial problems, into a decomposition approach. We conduct experiments on manyobjective 1/0 knapsack problems i.e. problems with more than three objectives functions, substantially harder than multi-objective problems with fewer objectives. The results indicate that the proposed multi-objective GPSO based on decomposition is able to outperform two version of the wellknow MOEA based on decomposition (MOEA/D) and the most recent version of the non-dominated sorting genetic algorithm (NSGA-III), which are state-of-the-art multi-objective evolutionary approaches based on decomposition

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

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms

A Binary differential search algorithm for the 0-1 multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is known to be NP-hard in operations research and it has a wide range of applications in engineering and management. In this study, we propose a binary differential search method to solve 0-1 MKPs where the stochastic search is guided by a Brownian motion-like random walk. Our proposed method comprises two main operations: discrete solution generation and feasible solution production. Discrete solutions are generated by integrating Brownian motion-like random search with an integer-rounding operation. However, the rounded discrete variables may violate the constraints. Thus, a feasible solution production strategy is used to maintain the feasibility of the rounded discrete variables. To demonstrate the efficiency of our proposed algorithm, we solved various 0-1 MKPs using our proposed algorithm as well as some existing meta-heuristic methods. The numerical results obtained demonstrated that our algorithm performs better than existing meta-heuristic methods. Furthermore, our algorithm has the capacity to solve large-scale 0-1 MKPs