A novel differential evolution algorithm for binary optimization

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.

DisABC: A new artificial bee colony algorithm for binary optimization

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.

JayaX: Jaya algorithm with xor operator for binary optimization

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.

A binary social spider algorithm for uncapacitated facility location problem

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.

The artificial bee colony (ABC) algorithm, which was inspired by the foraging and dance behaviors of real honey bee colonies, was first introduced for solving numerical optimization problems. When the solution space of the optimization problem is binary-structured, the basic ABC algorithm should be modified for solving this class of problems. In this study, we propose XOR-based modification for the solution-updating equation of the ABC algorithm in order to solve binary optimization problems. The proposed method, named binary ABC (binABC), is examined on an uncapacitated facility location problem, which is a pure binary optimization problem, and the results obtained by the binABC are compared with results obtained by binary particle swarm optimization (BPSO), the discrete ABC (DisABC) algorithm, and improved BPSO (IBPSO). The experimental results show that binABC is an alternative tool for solving binary optimization problems and is a competitive algorithm when compared with BPSO, DisABC, and IBPSO in terms of solution quality, robustness, and simplicity.

Artificial bee colony (ABC) algorithm is a swarm intelligence optimization algorithm inspired by the intelligent behavior of honey bees when searching for food sources. The various versions of the ABC algorithm have been widely used to solve continuous and discrete optimization problems in different fields. In this paper a new binary version of the ABC algorithm inspired by quantum computing, called binary quantum-inspired artificial bee colony algorithm (BQIABC), is proposed. The BQIABC combines the main structure of ABC with the concepts and principles of quantum computing such as, quantum bit, quantum superposition state and rotation Q-gates strategy to make an algorithm with more exploration ability. The proposed algorithm due to its higher exploration ability can provide a robust tool to solve binary optimization problems. To evaluate the effectiveness of the proposed algorithm, several experiments are conducted on the 0/1 knapsack problem, Max-Ones and Royal-Road functions. The results produced by BQIABC are compared with those of ten state-of-the-art binary optimization algorithms. Comparisons show that BQIABC presents the better results than or similar to other algorithms. The proposed algorithm can be regarded as a promising algorithm to solve binary optimization problems.

Harmony search (HS) is an optimization technique that uses several operators such as pitch adjustments to provide local improvement to candidate solutions during the optimization process. A standard pitch adjustment operator is known to be inefficient for binary domain optimization problems. A novel adaptive probabilistic harmony search (APHS) algorithm for binary optimization problems is proposed in this paper. APHS combines the power of the standard harmony search with the modelling capability of probabilistic search algorithms, with almost no extra user-tuned parameters. In APHS, the expected value of the search probability distribution is adapted using a sample of “good” vectors among the population to minimize the cross entropy between the actual distribution and the measured one. Moreover, Bernoulli probability distribution was used to enhance the pitch adjustment operator to fit the binary optimization domain. The effectiveness and the robustness of the proposed algorithm are shown by a thorough comparison with state-of-the-art existing techniques in a number of binary space optimization problems with variant complexities and sizes. The set of binary space optimization problems investigated in this paper include: Max-One problem, Order-3 deceptive problem, Bipolar Order-6 deceptive problem, Muehlenbein’s Order-5 problem, Knapsack problem, Multi-Knapsack problem, and finally a real-world problem of the satellite broadcast scheduling. Experimental results show that our proposed algorithm is indeed very effective and outperforms the existing algorithms by finding optimal solutions for almost all tested benchmarks.

A survey on the Artificial Bee Colony algorithm variants for binary, integer and mixed integer programming problems

A new binary grasshopper optimization algorithm for feature selection problem

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.

BinBRO: Binary Battle Royale Optimizer algorithm