Novel approaches based on artificial algae algorithm to solve binary optimization problems

In recent years, many novel algorithms have been proposed for solving optimization problems. These algorithms are usually developed by inspiring from intelligent interactions with each other, behavioral patterns and instinctual movements of living in nature. The proposed algorithms are usually designed to solve problems with a particular type of problem or characteristic. As a consequence of various enhancements and improvements made later on, the method is also able to solve the problems of different characteristics additionally. For instance, an algorithm proposed to solve continuous optimization problems (decision variables that can take all values in a given range) can be developed to solve binary optimization problems (decision variables that can only take values of 0 or 1). In this thesis study, Artificial Algae Algorithm (AAA) that developed for solving continuous optimization problems by inspiring behavior of microalgae that already exists in nature has been improved in order to solve binary optimization problems by establishing novel and unique methods. In this context, 3 (three) novel and unique methods have been developed. In the first proposed method, in order to obtain new candidate solutions, the helical movement phase is re-adapted to work with binary values by initializing algae colonies in the population with binary values. In the helical movement phase, randomly determined three dimension values of selected neighbor solution are copied to the candidate solution and processing logical NOT function by depending on a particular probability. In the developed binAAA method, the adaptation parameter was used to make a decision whether the adaptation process should be operated or not and also to determine the dimensions to be affected in this process. The proposed binAAA method was investigated on Uncapacitated Facility Location Problems (UFLP) and the results were compared with the results of binABC, BPSO, GA, DisABC, IBPSO and ABCbin algorithms. The binAAA method produces equal or better results compared with other methods about solving binary optimization problems. This is because, the binAAA method works in discrete solution space and also it has a capable search strategy on both local and global search. The second proposed method includes two different update mechanisms to produce new candidate solutions. The first of these mechanisms is to produce candidate solutions by using the logical XOR operator, while in the second mechanism, new solutions are produced based on the stigmergic behavior by using the information obtained from the first mechanism. In the proposed SAAA (Stigmergic AAA) method, initial solutions are initialized with binary values, and the adaptation parameter is used to make a decision whether the adaptation process should be operated or not, and also to determine the dimensions to be affected in this process. The performance of the SAAA method was investigated on both UFLPs and numeric benchmark problems. The SAAA method was compared on the UFLP set with 2 different versions of the BAAA method, 3 different versions of the GA method and the BPSO method. For the second comparison, the CEC2015 (bound constrained single-objective computationally expensive numerical optimization problems) test set was used and it is compared with SBHS, HS, BLDE, BHTPSO-QI, GBABC, BQIGSA and SabDE methods in order to evaluate the performance of the proposed method. When all the results are examined in general, the proposed algorithm offers a balanced exploration and exploitation capability for not only low-dimensional problems and also for high-dimensional problems. Furthermore, it is seen that the proposed algorithm is an effective and efficient algorithm for solving the binary optimization problems covered in the research in terms of solution quality, convergence characteristics and robustness. The initialization is been processed with binary values as well in the proposed third method that named PI-AAA (Population Influenced AAA) in the thesis study. A population influence approach was introduced and this approach was integrated into the work of AAA in order to produce new binary candidate solutions. In the PI-AAA method, the randomly selected neighbor solutions from the algae colonies, the current solution and the best solution are used in order to produce candidate solutions. New candidate solutions are produced as a result of the probability calculations made with these solutions. Probability values were defined as peculiar control parameters to PI-AAA algorithm. Due to importance of control parameters' values for the performance of the proposed method, the effects of the parameters are analyzed and it is aimed to determine the most suitable value for these parameters. The adaptation phase in the basic AAA is re-adapted in order to work with binary decision variable values. The proposed PI-AAA method's performance is first compared with the ABC, GA, PSO, EDA algorithms on the UFLP set. The second comparison is performed on the CEC2015 problem set in order to prove the effectiveness of PI-AAA method. The obtained results show that the proposed PI-AAA indicates better or equal performance in comparisons and also those results point out that this proposed approach is a competitive binary optimization algorithm. In conclusion, in this thesis study, 3 (three) novel binary optimization algorithms have been developed with the name of binAAA, SAAA and PI-AAA based on AAA method in order to solve the binary optimization problems. When the results from experimental studies are examined, it is observed that the proposed methods are alternative, competitive and robust for solving binary optimization problems in terms of solution quality, standard deviation and convergence characteristics. In this context, a contribution has been made to the literature in the area of binary optimization with this thesis.