A Modified Binary Pigeon-Inspired Algorithm for Solving the Multi-dimensional Knapsack Problem

Binary metaheuristic algorithms for 0–1 knapsack problems: Performance analysis, hybrid variants, and real-world application

PurposeThe purpose of this paper is to propose an improved optimization method for image matching problem, which is based on multi-scale Gaussian mutation pigeon-inspired optimization (MGMPIO) algorithm, with the objective of accomplishing the complicated image matching quickly.Design/methodology/approachThe hybrid model of multi-scale Gaussian mutation (MGM) mechanism and pigeon-inspired optimization (PIO) algorithm is established for image matching problem. The MGM mechanism is a nonlinear model, which can adjust the position of pigeons by mutation operation. In addition, the variable parameter (VP) mechanism is exploited to adjust the map and compass factor of the original PIO. Low-cost quadrotor, a type of electric multiple rotorcraft, is used as a carrier of binocular camera to obtain the images.FindingsThis work improved the PIO algorithm by modifying the search strategy and adding some limits, so that it can have better performance when applied to the image matching problem. Experimental results show that the proposed method demonstrates satisfying performance in convergence speed, robustness and stability.Practical implicationsThe proposed MGMPIO algorithm can be easily applied to solve practical problems and accelerate convergence speed of the original PIO, and thus enhancing the speed of matching process, which will considerably increase the effectiveness of algorithm.Originality/valueA hybrid model of the MGM mechanism and PIO algorithm is proposed for image matching problem. The VP mechanism and low-cost quadrotor is also utilized in image matching problem.

In this paper, a fault recovery strategy for a distribution network based on a pigeon-inspired optimization (PIO) algorithm is proposed to improve the recoverability of the network considering the increased proportion of distributed energy resources. First, an improved Kruskal algorithm-based island partitioning scheme is proposed considering the electrical distance and important load level during the island partitioning process. Secondly, a mathematical model of fault recovery is established with the objectives of reducing active power losses and minimizing the number of switching actions. The conventional PIO algorithm is improved using chaos, reverse strategy, and Cauchy perturbation strategy, and the improved pigeon-inspired optimization (IPIO) algorithm is applied to solve the problem of fault recovery of the distribution network. Finally, simulation analysis is carried out to verify the effectiveness of the proposed PIO algorithm considering a network restauration problem after fault. The results show that compared with traditional algorithms, the proposed PIO algorithm has stronger global search capability, effectively improving the node voltage after restauration and reducing circuit loss.

This paper proposes a novel approach for the multidimensional knapsack problem (MDKP) using differential evolution. Firstly, the principle and the pseudo-code of binary differential evolution with hybrid encoding (HBDE) are presented. On the basis of the existing repair operator 2 (RO2), an improved repair operator 3 (RO3) for handling the infeasible solutions of MDKP is developed. Then, combine HBDE with RO3, an efficient algorithm (HBDE-RO3) for MDKP is proposed. Finally, the experiment results of the 138 well-known MDKP benchmarks show that RO3 is advantageous to deal with the infeasible solutions than RO2, and the proposed algorithm HBDE-RO3 has superior performance for solving MDKP than the state-of-the-art algorithms.

The multi-dimensional knapsack problem (MDKP) is a well-known NP-hard problem in combinatorial optimization. As it has various real-life applications, the MDKP has been intensively studied in the literature. On the other hand, far too little attention has been paid to the multi-objective version of the MDKP. In this chapter, we consider the bi-objective multi-dimensional knapsack problem (BOMDKP). We propose a Binary Genetic Algorithm (BGA) with an external archive for the problem. Our proposed BGA algorithm also employs a binary local search. The non-dominated solution sets are obtained for various bi-objective benchmark instances with 100, 250, 500 and 750 items, by employing the proposed BGA. Then, the performance of the BGA is compared with other multi-objective algorithms from the literature, i.e., MOEA/D and MOFPA. Furthermore, it is observed that the Pareto-optimal solution set provided by Zitzler and Laumans for 500 items and 2 knapsacks includes 30 dominated solutions. Also, the Pareto-optimal solutions for the scenario with 750 items are not reported in Zitzler and Thiele [43]. Hence, the true Pareto-optimal solution sets are found for all benchmark problem instances using Improved Augmented Epsilon Constraint (AUGMECON2) method. The non-dominated solution sets of the BGA, MOEA/D and MOFPA are compared with the Pareto-optimal solution sets for all test instances. The computational results indicate that the proposed BGA is more effective to solve the BOMDKP than the best-performing algorithms from the literature.

Knapsack problems are among the most common problems in literature tackled with evolutionary algorithms (EA). Their major advantage lies in the fact that they are relatively simple to implement while they allow generalizations for a wide range of real world problems. The multi-dimensional knapsack problem (MKP), which belongs to the class of NP-complete combinatorial optimization problems, is one of the variations of the knapsack problem. The MKP has a wide range of real world applications such as cargo loading, selecting projects to fund, budget management, cutting stock, etc. The MKP has been studied quite extensively in the EA community. Due to the constrained nature of the problem, constraint handling techniques gain great importance in the performance of the proposed EA approaches. In this study, the applicability of a generational EA that uses a penalty-based constraint handling technique and a gene locus based, asymmetric, adaptive mutation scheme is explored for the MKP. The effects of the parameters of the explored approach is determined through tests. Further experiments, using large MKP instances from commonly used benchmarks available through the Internet are performed. Comparison tables are given for the performance of the explored approach and other good performing EAs found in literature for the MKP. Results show that performance improves greatly when compared with other penalty-based techniques, but the explored approach is still not the best performer among all. However, unlike the explored technique, the EAs using the other constraint handling techniques require a great amount of extra computational effort and need heuristic information specific to the optimization problem. Based on these observations, and the fact that the performance difference between the explored scheme and the better performers is not too high, research on improving the explored approach is still in progress.

Three pseudo-utility ratio-inspired particle swarm optimization with local search for multidimensional knapsack problem

A two-phase tabu-evolutionary algorithm for the 0–1 multidimensional knapsack problem

Solving the bi-objective multi-dimensional knapsack problem exploiting the concept of core

This paper introduces solutions to deal with the Multidimensional Knapsack Problem (MKP), which is a NP-hard combinatorial optimisation problem. Two hybrid heuristics based on Genetic Algorithms (GA) are proposed: the Memetic Search Algorithm (MSA) and the Genetic Algorithm Guided by Pretreatment information (GAGP). MSA combines sequentially GA with the Stochastic Local Search-Simulated Annealing algorithm (SLSA). GAGP is composed of two steps, in the first, a ratio-based greedy algorithm extracts useful information and the core concept is utilised to decompose items according to their ratios; In the second, these information are integrated to the operators of a GA allowing to reach the best solutions faster. An operator is added to the GA to dynamically update the ratio values of the items. Two groups of data were used to examine the proposed approaches. A group of simple instances of MKP has been used to examine MSA and a group of complex MKP has been used to examine GAGP. The obtained results indicate that MSA and GAGP have the capability to give solutions of high quality.

Local and global lifted cover inequalities for the 0–1 multidimensional knapsack problem

Trajectory Design of Re-entry Vehicles using combined Pigeon Inspired Optimization and Orthogonal Collocation method

We study the multidimensional knapsack problem, present some theoretical and empirical results about its structure, and evaluate different integer linear programming (ILP)-based, metaheuristic, and collaborative approaches for it. We start by considering the distances between optimal solutions to the LP relaxation and the original problem and then introduce a new core concept for the multidimensional knapsack problem (MKP), which we study extensively. The empirical analysis is then used to develop new concepts for solving the MKP using ILP-based and memetic algorithms. Different collaborative combinations of the presented methods are discussed and evaluated. Further computational experiments with longer run times are also performed to compare the solutions of our approaches to the best-known solutions of another so-far leading approach for common MKP benchmark instances. The extensive computational experiments show the effectiveness of the proposed methods, which yield highly competitive results in significantly shorter run times than do previously described approaches.

An adaptation of hybrid binary optimization algorithms for medical image feature selection in neural network for classification of breast cancer

The multidimensional knapsack problem (MKP), which is a generalization of the 0-1 simple Knapsack problem, is one of the classical NP-hard problems in operations research having a number of engineering applications. Several exact as well as heuristic algorithms are available in literature for its solution. In this paper, we propose a new particle swarm optimization (PSO) algorithm namely socio-cognitive particle swarm optimization (SCPSO) for solving the MKP. Comparing with the basic binary particle swarm optimization (BPSO), this improved algorithm introduces the distance between gbest and pbest as a new velocity update equation which maintains the diversity in the swarm and makes it more effective and efficient in solving MKP. We present computational experiments with various data instances for fine tuning of parameters of SCPSO and to validate our ideas and demonstrate the efficiency of the proposed algorithm.