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:
- What is have
- What is happen
- What you want
- 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).