ABSTRACT
Recent work attempted to demonstrate the global best minimum in complex problems. This paper proposes a population and direct-based swarm optimization algorithm called as HPO algorithm. The HPO algorithm is designed by inspired of personal behaviorand demonstrated in the 30 and 100 dimensionson benchmark functions. The model have four concepts: what you want?, what you have?, what others have?, what is happened?. These concepts take into account the balancing between exploration and exploitation operator and demonstrate its efficiency, robustness and stability insynthetic and real problems.In experiment, we consider 15 benchmark functions include unimodal and multimodal characteristic of functions.For compression, our algorithm and some well-known algorithms with 30 times run and applied on the benchmark functions and compared with statistical value and Wilcoxon signed-rank test. As a consequence, the performance and convenient ofour work aredemonstratedbetter than the others.
1- INTRUDOCTION
Many real-world applications include the complexity problem that should be optimize and then applied on the real work. The purpose of optimization is the minimization or maximization of fitness function for real problem such as energy consumption, designing, routing, transportation et al. The performance, efficiency and sustainability of optimization algorithms are important in solving complex problem.
In many case, optimization problem is highly complex and nonlinear function, whom scientist attempts to solve the problem by using popular methods of soft computing. In recent years, metaheuristic algorithms have been used and applied on the real problems in engineering field [1-5]. The advantage of metaheuristic algorithm rather than the deterministic algorithm is scape of trap from local minimum state. There are two popular methodology such as Evolutionary Algorithms (EA) and Swarm Intelligence (SI), which have new landscape for the complex problem in the metaheuristics optimization algorithm. The advantages of them are the power of based-population solution and providea new solutionby considering the balance of exploration and exploitation.Thepoint of view of efficiency and balancing of them should be se the best solution by escaping from many local minimum.By inspired of Darwin’s theory the Evolutionary Optimization techniques are presented and used in real problems. The principle of mechanism includes selection, mutation and crossover operation. Genetic algorithm is one of EA which is popular in metaheuristic algorithm (GA) and have rigorous mathematical analyses [6-7].And some works with based on this paradigm is tabu search [9], simulated annealing [10], forest optimization algorithm [11], biogeography-based optimizer (BBO) [12], Evolutionary Programing (EP) [13], Evolution Strategy (ES) [14].Beni and Wang in 1993 presented concept of swarm intelligence, which include simulation of behavior of living creature [15]. Scientist attempt to find local rule between creatures and then convert to aalgorithm for using in soft computing.The other algorithmsare computational method, which based on directed best agent. The framework of them are repeatedlytrying to improve a solution in relation toa given measure of quality fitness.Examples of SI-based approaches are particle swarm optimization [16], Glowworm algorithm [17] Intelligent water drops [18], Cat Swarm Optimization [19],artificial bee colony(ABC) [20], Gravitational search algorithm [21] and selfish herdoptimizer (SHO) [22], Dolphin Echolocation (DE) [23].Some algorithms inspired by the phenomenon of physics are proposed and surveyed for example Central Force Optimization CFO[24], Artificial Physics Optimization APO[25], Gravitational Search Algorithm GSA[26], Gravitational Interactions Optimization GIO[27]. The No Free Lunch (NFL) theorem logically proved that there is no metaheuristic algorithms capable to solve the general problem.In order to improve the flexible of optimization algorithm for solving more problems scientist attempt to present novel algorithm or improve the old version of algorithms, which are able to solve general problems [28]. There are many algorithms proposed which have advantages and disadvantages. In this study,mathematical analyzing, demonstratingthe convergenceof ,large-scale problems and tuning parameters are considered and provided a novel method for solving optimization problems.
The restof the paper is organized as follows. Section 2 provides the detail of HPO algorithm and discusses about the concept of exploration and exploitation.The experimental results and evaluation are shown in Section 3. Section 4 provides the performance of HPO on a real problem. Section 5 states some concluding remarks and suggests some directions for future.
2- HAPPINESS OPTIMIZER
As discussed in book[29]general equation is that “Happiness equals Reality minus Shifting Expectations,” and indicate that happiness is always on the move and difficult to find, whilethe expectations follow reality. To preserve happiness in the mind, one needs to achieve control on the expectations and assure reality is one-steppast. As a result, when the reality of Human beings’ life is better than they had expected, theywould be happiness in their life. Otherwise reality to be worse than the expectations, they would be unhappiness. The other words, when you think about high expectation you will be face with negative realization slit, which means more exposed to unhappiness in the future. Therefore, we can take general equation and which is discussed about it in [30-31].In this study, a new population-based algorithmcalled as Happiness Optimizer (HPO)isproposed,that inspired by the theory ofHappiness in social science field. Four main concepts of the Happiness theory (what you want, what is happen, what you have, and what others have) are mathematically modelled to build the HPO.As mentioned before the formula is Eq (1).
Happiness=Reality minus Expectation (1)
Based on the Equation 1 there arefour effective component one is for reality and remain is for the expectation such as:
  1. What is have
  2. What is happen
  3. What you want
  4. What others have
As mentioned above, our expectation are infinitive. They are function of outdoor event, “what you want” in short and long time and “what others have” in neighbors(such as workplace, neighbors and etc).“What is happen ”is related to a thing that happens in neighbors or the world which are important for you (see Fig 1).