Novel binary differential evolution algorithm based on Taper-shaped transfer functions for binary optimization problems

Tree-seed algorithm (TSA) is a nature-inspired metaheuristic optimization algorithm. TSA is proposed for solving continuous optimization problems. In this work, TSA is modified with transfer functions for solving binary optimization problems. Continuous search space is mapped to binary search space with transfer functions. Four S-shaped and four V-shaped transfer functions are used for discretization. Uncapacitated facility location problem (UFLP) is a pure binary optimization problem. In order to measure the performance, 15 different sized (small, medium, large and extra-large) UFLPs are solved with eight different binary TSA in this work. Experimental results show that S-shaped transfer functions are better than V-shaped transfer functions on these problem sets.

Differential evolution (DE) is one of the most powerful stochastic search methods which was introduced originally for continuous optimization. In this sense, it is of low efficiency in dealing with discrete problems. In this paper we try to cover this deficiency through introducing a new version of DE algorithm, particularly designed for binary optimization. It is well-known that in its original form, DE maintains a differential mutation, a crossover and a selection operator for optimizing non-linear continuous functions. Therefore, developing the new binary version of DE algorithm, calls for introducing operators having the major characteristics of the original ones and being respondent to the structure of binary optimization problems. Using a measure of dissimilarity between binary vectors, we propose a differential mutation operator that works in continuous space while its consequence is used in the construction of the complete solution in binary space. This approach essentially enables us to utilize the structural knowledge of the problem through heuristic procedures, during the construction of the new solution. To verify effectiveness of our approach, we choose the uncapacitated facility location problem (UFLP)--one of the most frequently encountered binary optimization problems--and solve benchmark suites collected from OR-Library. Extensive computational experiments are carried out to find out the behavior of our algorithm under various setting of the control parameters and also to measure how well it competes with other state of the art binary optimization algorithms. Beside UFLP, we also investigate the suitably of our approach for optimizing numerical functions. We select a number of well-known functions on which we compare the performance of our approach with different binary optimization algorithms. Results testify that our approach is very efficient and can be regarded as a promising method for solving wide class of binary optimization problems.

Definitive optimization algorithms are not able to solve high dimensional optimization problems when the search space grows exponentially with the problem size, and an exhaustive search also becomes impractical. To encounter this problem, researchers use approximation algorithms. A category of approximation algorithms is meta-heuristic algorithms which have shown an acceptable degree of efficiency to solve this kind of problems. Social Mimic Optimization (SMO) algorithm is a recently proposed meta-heuristic algorithm which is used to optimize problems with continuous solution space. It is proposed by following the behavior of people in society. SMO can efficiently explore the solution space for obtaining optimal or near-optimal solution by minimizing a given fitness function. Feature selection is a binary optimization problem where the aim is to maximize the classification accuracy of a learning algorithm using minimum the number of features. To convert the continuous search space to a binary one, a proper transfer function is required. The effect a transfer function has on the binary variant of an optimization algorithm is very important since selecting a particular subset of features based on the solution values attained by the algorithm in continuous search space depends on the considered transfer function. To this end, we have proposed a new transfer function, namely X-shaped transfer function, to enhance the exploration and exploitation ability of binary SMO. The proposed X-shaped transfer function utilizes two components and crossover operation to obtain a new solution. Effect of the proposed X-shaped transfer function is compared with the effect of four S-shaped and four V-shaped transfer functions on SMO in terms of achieved classification accuracy, rate of convergence, and number of features selected over 18 standard UCI datasets. The proposed algorithm is also compared with state-of-the-art meta-heuristic feature selection (FS) algorithms. Experimental results confirm the efficiency of the proposed approach in improving the classification accuracy compared to other meta-heuristic algorithms, and the superiority of X-shaped transfer function over commonly used S-shaped and V-shaped transfer functions. The source code of the proposed method along with the datasets used can be found at https://github.com/Rangerix/SocialMimic.

Metaheuristic optimization algorithms are widely used in solving NP-hard continuous optimization problems. Whereas, in the real world, many optimization problems are discrete. The uncapacitated facility location problem (UFLP) is a pure discrete binary optimization problem. Archimedes optimization algorithm (AOA) is a recently develop metaheuristic optimization algorithm and there is no binary variant of AOA. In this work, 17 transfer functions (TF1-TF17) are used for mapping continuous values to binary values. 17 binary variants of AOA (BAOA1- BAOA17) are proposed for solving UFLPs. 16 to 100-dimensional UFLPs were solved with binary variants of AOA. Stationary and non-stationary transfer functions were compared in terms of solution quality. The non-stationary transfer functions were produced better solutions than stationary transfer functions. Peculiar parameter analyzes for binary optimization problems were performed in the best variant (BAOA9) produced with TF9 transfer function.

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

A binary social spider algorithm for uncapacitated facility location problem

In machine learning, searching for the optimal feature subset from the original datasets is a very challenging and prominent task. The metaheuristic algorithms are used in finding out the relevant, important features, that enhance the classification accuracy and save the resource time. Most of the algorithms have shown excellent performance in solving feature selection problems. A recently developed metaheuristic algorithm, gaining-sharing knowledge-based optimization algorithm (GSK), is considered for finding out the optimal feature subset. GSK algorithm was proposed over continuous search space; therefore, a total of eight S-shaped and V-shaped transfer functions are employed to solve the problems into binary search space. Additionally, a population reduction scheme is also employed with the transfer functions to enhance the performance of proposed approaches. It explores the search space efficiently and deletes the worst solutions from the search space, due to the updation of population size in every iteration. The proposed approaches are tested over twenty-one benchmark datasets from UCI repository. The obtained results are compared with state-of-the-art metaheuristic algorithms including binary differential evolution algorithm, binary particle swarm optimization, binary bat algorithm, binary grey wolf optimizer, binary ant lion optimizer, binary dragonfly algorithm, binary salp swarm algorithm. Among eight transfer functions, V4 transfer function with population reduction on binary GSK algorithm outperforms other optimizers in terms of accuracy, fitness values and the minimal number of features. To investigate the results statistically, two non-parametric statistical tests are conducted that concludes the superiority of the proposed approach.

In this study, the Binary Puma Optimizer (BPO) is introduced as a novel binary metaheuristic. The BPO employs eight Transfer Functions (TFs), consisting of four S-shaped and four V-shaped mappings, to convert the continuous search space of the original Puma Optimizer into binary form. To evaluate its effectiveness, BPO is applied to two well-known combinatorial optimization problems: the 0-1 Knapsack Problems (KPs) and the Uncapacitated Facility Location Problem (UFLP). The solver tailored for KPs is referred to as BPO1, while the solver for the UFLP is denoted as BPO2. In the UFLP experiments, only TFs are integrated into the solutions. Conversely, in the 0-1 KPs experiment, the additional mechanisms are (i) greedy-based population strategies; (ii) a crossover operator; (iii) a penalty algorithm; (iv) a repair algorithm; and (v) an improvement algorithm. Unlike KPs, the UFLP has no infeasible solutions, as facilities are assumed to be uncapacitated. Unlike KPs, the UFLP has no capacity constraints, as facilities are assumed to be uncapacitated. Thus, violations cannot occur, making improvement strategies unnecessary, and the BPO2 depends solely on TFs for binary adaptation. The proposed algorithms are compared with binary optimization algorithms from the literature. The experimental framework demonstrates the versatility and effectiveness of BPO1 and BPO2 in addressing different classes of binary optimization problems.

The present paper introduces a modified flower pollination algorithm (FPA) enhanced by evolutionary operators to solve the uncapacitated facility location problem (UFLP), which is one of the well-known location science problems. The aim in UFLP is to select some locations to open facilities among a certain number of candidate locations so as to minimize the total cost, which is the sum of facility opening costs and transportation costs. Since UFLP is a binary optimization problem, FPA, which is introduced to solve real-valued optimization problems, is redesigned to be able to conduct search in binary domains. This constitutes one of the contributions of the present study. In this context, some evolutionary operators such as crossover and mutation are adopted by the proposed FPA. Next, the mutation operator is further enhanced by making use of an adaptive procedure that introduces greater level of diversity at earlier iterations and encourages intensification toward the end of search. Thus, while premature convergence and local optima problems at earlier iterations are avoided, a more intensified search around the found promising regions is performed. Secondarily, as demonstrated in this study, by making use of the reported evolutionary procedures, FPA is able to run in binary spaces without employing any additional auxiliary procedures such as transfer functions. All available benchmarking instances are solved by the proposed approach. As demonstrated by the comprehensive experimental study that includes statistically verified results, the developed approach is found as a promising algorithm that can be extended to numerous binary optimization problems.

JayaX: Jaya algorithm with xor operator for binary optimization

BE-GWO: Binary extremum-based grey wolf optimizer for discrete optimization problems

DisABC: A new artificial bee colony algorithm for binary optimization

This paper focuses on modification of basic artificial algae algorithm (AAA) for solving binary optimization problems by using a new solution update rule because the agents in AAA work on continuous solution space. The candidate solution generation process of algorithm in the basic version of AAA is replaced with a mechanism that use a neighbor solution randomly selected from the population and three decision variables of this solution. The current solution is taken from the population and randomly selected three dimensions of this solution are changed using the neighbor solution. The agents of AAA work on continuous solution space and this modification for AAA is required for solving a binary optimization problem because a binary optimization problems have decision variables which are element of set {0, 1}. The performance of the proposed algorithm, binAAA for short, is investigated on the uncapacitated facility location problems which are pure binary optimization problem and there is no integer or real valued decision variables in this problem. The results obtained by binAAA are compared with the results of state-of-art algorithms such as artificial bee colony, particle swarm optimization, and genetic algorithms. Experimental results and comparisons show that the binAAA is better than the other algorithm almost all cases in terms of solution quality and robustness based on the mean and standard deviations, respectively.

Binary team game algorithm based on modulo operation for knapsack problem with a single continuous variable

The crow search algorithm (CSA) is a recently proposed population-based optimization algorithm for continuous optimization. Since the original CSA searches for a feasible solution in a continuous search space, it cannot handle binary optimization problems directly. A few binary variants of CSA are presented in the literature. However, these variants search for a new solution in the continuous domain and need transfer functions to adapt the solution to the binary domain. This may cause poor exploration, making some regions in the search space impossible to discover. This paper proposes an effective binary CSA (BinCSA) using bitwise operations that directly searches for a feasible solution in the binary search space. For this purpose, the original update mechanism of the CSA is improved using exclusive-OR and AND logical operators in order to provide a good balance between exploration and exploitation in the binary search space. The effectiveness of the proposed BinCSA is evaluated on the uncapacitated facility location problem (UFLP), one of the most widely investigated pure binary optimization problems. The performance of BinCSA is examined using two different UFLP datasets, ORLIB and M*. The experimental results show that BinCSA obtained the optimal solution for 13 out of 15 instances of ORLIB and 12 out of 20 instances of M*. Moreover, BinCSA exhibits superior performance on ORLIB instances when compared to other methods and is very competitive on M* instances in terms of solution quality and robustness. The source code for BinCSA, as used for the UFLP, is available at https://github.com/3mrullah/BinCSA.