An efficient binary differential evolution algorithm for the multidimensional knapsack problem

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

A binary differential evolution algorithm learning from explored solutions

The pigeon-inspired optimization algorithm is a category of a newly proposed swarm intelligence-based algorithm that belongs to the population-based solution technique. The MKP is a class of complex optimization problems that have many practical applications in the fields of engineering and sciences. Due to the practical applications of MKP, numerous algorithmic-based methods like local search and population-based search algorithms have been proposed to solve the MKP in the past few decades. This paper proposes a modified binary pigeon-inspired optimization algorithm named (Modified-BPIO) for the 0 - 1 multidimensional knapsack problem (MKP). The utilization of the binary pigeon-inspired optimization (BPIO) for solving the multidimensional knapsack problem came with huge success. However, it can be observed that the BPIO converges prematurely due to lost diversity during the search activities. Given the above, the crossover operator is integrated with the landmark component of the BPIO to improve the diversity of the solution space. The MKP benchmarks from the Operations Research (OR) library are utilized to test the performance of the proposed binary method. Experimentally, it is concluded that the proposed Modified-BPIO has a better performance when compared with the BPIO and existing state-of-the-arts that worked on the same MKP benchmarks.

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.

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.

Many real-world optimization problems are dynamic in nature. The interest in the Evolutionary Algorithms (EAs) community in applying EA variants to dynamic optimization problems has increased greatly. Differential Evolution (DE) belongs to the group of evolutionary algorithms which operate in continuous search spaces. DE has been successfully applied to many stationary problem domains. Recently there has been some research into applying DE to dynamic optimization problems too. Many real-world problems consist of decision variables which require the optimization algorithm to work with binary parameters. This makes it impossible to apply DE in its basic form. For this purpose, binary differential evolution (BDE) approaches have been introduced. The main focus of this paper is to perform a series of experiments to test the behavior of a simple BDE under different change conditions. A simple bit-matching problem is chosen as the test environment. The results of this preliminary study show that further study is needed to make BDEs suitable to work in dynamic environments.

This paper proposed an improved binary differential evolution (BDE) algorithm based on a Taguchi approach (Taguchi-BDE) for optimization problems. An estimation operator with efficient probability was adopted to preserve the diversity of populations and enhance the global search ability in Taguchi-BDE, and the Taguchi approach was used to optimize solutions after the crossover operations in Taguchi-BDE The performance of the Taguchi-BDE algorithm was evaluated on a set of ten numerical benchmarks, and the results showed that our algorithm achieved better mean values over 40 repeated tests than did the other BDE-based algorithms. Taguchi-BDE was also applied to a real-world problem in statistical data mining, namely identification of interactions between single nucleotide polymorphisms. A total of 1,500 data sets under different settings were used to evaluate the efficiency of Taguchi-BDE, and the results showed that the proposed algorithm can achieve a 92.07% success rate. In conclusion, Taguchi-BDE revealed efficient convergence toward promising search regions, and achieved satisfactory search results.

In this paper, a new modified version of the flower pollination algorithm based on the crossover for solving the multidimensional knapsack problems called (MFPA) is proposed. MFPA uses the sigmoid function as a discretization method to deal with the discrete search space. The penalty function is added to the evaluation function to recognize the infeasible solutions and assess them. A two-stage procedure is called FRIO is used to treat the infeasible solutions. MFPA uses an elimination procedure to decrease any duplication in the population in order to increase the diversity. The proposed algorithm is verified on a set of benchmark instances, and a comparison with other algorithms available in literature is shown. Several statistical and descriptive analysis was done such as recoding the results of the best, mean, worst, standard deviation, success rate, and time to prove the effectiveness and robustness of MFPA. The empirical results show that the proposed algorithm can be an effective algorithm as human-centric decision-making model for solving the multidimensional knapsack problems.

In this work, we propose modified versions of shuffled frog leaping algorithm (SFLA) to solve multiple knapsack problems (MKP). The proposed algorithm includes two important operations: repair operator and genetic mutation with a small probability. The former is utilizing the pseudo-utility to repair infeasible solutions, and the later can effectively prevent the algorithm from trapping into the local optimal solution. Computational experiments with a large set of instances show that the proposed algorithm can be an efficient alternative for solving 0/1 multidimensional knapsack problem.

We develop and test a new approach for generating initial populations for the application of genetic algorithms (GA) to problems in combinatorial optimisation, specifically the multidimensional knapsack problem. We focus the empirical study of our approach on a set of two dimensional knapsack problems (2KP) used in a past study of 2KP algorithm performance. Our proposed approach for initial population generation focuses on generating populations that are stronger in terms of solution quality, solution diversity and in terms of solutions hovering near the border of feasible and infeasible solutions within the problem solution space. We report the results of a Monte Carlo experiment comparing our approach with the traditional initial population generation approach and report the results of computational tests involving 1120 2KP instances that cover a range of problem constraint characteristics. The collective of these computational results show that our proposed approach provides an initial population of sufficient quality and diversity to produce improved convergence to near optimal solutions which can equate to reduced computational burden in applications involving complex computations.

Lifetime requirements and coverage demands are emphasized in wireless sensor networks. An area coverage algorithm based on differential evolution is developed in this study to obtain a given coverage ratio [Formula: see text]. The proposed algorithm maximizes the lifetime of wireless sensor networks to monitor the area of interest. To this end, we translate continuous area coverage into classical discrete point coverage, so that the optimization process can be realized by wireless sensor networks. Based on maintaining the ε-coverage performance, area coverage algorithm based on differential evolution takes the minimal energy as optimization objective. In area coverage algorithm based on differential evolution, binary differential evolution is redeveloped to search for an improved node subset and thus meet the coverage demand. Taking into account that the results of binary differential evolution are depended on the initial value, the resulting individual is not an absolutely perfect node subset. A compensation strategy is provided to avoid unbalanced energy consumption for the obtained node subset by introducing the positive and negative utility ratios. Under the helps of those ratios and compensation strategy, the resulting node subset can be added additional nodes to remedy insufficient coverage, and redundancy active nodes can be pushed into sleep state. Furthermore, balance and residual energy are considered in area coverage algorithm based on differential evolution, which can expand the scope of population exploration and accelerate convergence. Experimental results show that area coverage algorithm based on differential evolution possesses high energy and computation efficiencies and provides 90% network coverage.

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

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