Gravitational Search Algorithm (GSA) is an optimization method inspired by the theory of Newtonian gravity in physics. Till now, many variants of GSA have been introduced, most of them are motivated by gravity-related theories such as relativity and astronomy. On the one hand, to solve different kinds of optimization problems, modified versions of GSA have been presented such as continuous (real), binary, discrete, multimodal, constraint, single-objective, and multi-objective GSA. On the other hand, to tackle the difficulties in real-world problems, the efficiency of GSA has been improved using specialized operators, hybridization, local search, and designing the self-adaptive algorithms. Researchers have utilized GSA to solve various engineering optimization problems in diverse fields of applications ranging from electrical engineering to bioinformatics. Here, we discussed a comprehensive investigation of GSA and a brief review of GSA developments in solving different engineering problems to build up a global picture and to open the mind to explore possible applications. We also made a number of suggestions that can be undertaken to help move the area forward.

A comprehensive survey on gravitational search algorithm

How to improve the global search ability without significantly impairing the convergence speed is still a big challenge for most of the meta-heuristic optimization algorithms. In this paper, a concept for the optimization of continuous nonlinear functions applying crisscross optimization algorithm is introduced. The crisscross optimization algorithm is a new search algorithm inspired by Confucian doctrine of gold mean and the crossover operation in genetic algorithm, which has distinct advantages in solution accuracy as well as convergence rate compared to other complex optimization algorithms. The procedures and related concepts of the proposed algorithm are presented. On this basis, we discuss the behavior of the main search operators such as horizontal crossover and vertical crossover. It is just because of the perfect combination of both, leading to a magical effect on improving the convergence speed and solution accuracy when addressing complex optimization problems. Twelve benchmark functions, including unimodal, multimodal, shifted and rotated functions, are used to test the feasibility and efficiency of the proposed algorithm. The experimental results show that the crisscross optimization algorithm has an excellent performance on most of the test functions, compared to other heuristic algorithms. At the end, the crisscross optimization algorithm is successfully applied to the optimization of a large-scale economic dispatch problem in electric power system. It is concluded that the crisscross optimization algorithm is not only robust in solving continuous nonlinear functions, but also suitable for addressing the complex real-world engineering optimization problems.

Crisscross optimization algorithm and its application

The gravitational search algorithm (GSA) is a meta-heuristic algorithm based on the theory of Newtonian gravity. This algorithm uses the gravitational forces among individuals to move their positions in order to find a solution to optimization problems. Many studies indicate that the GSA is an effective algorithm, but in some cases, it still suffers from low search performance and premature convergence. To alleviate these issues of the GSA, an aggregative learning GSA called the ALGSA is proposed with a self-adaptive gravitational constant in which each individual possesses its own gravitational constant to improve the search performance. The proposed algorithm is compared with some existing variants of the GSA on the IEEE CEC2017 benchmark test functions to validate its search performance. Moreover, the ALGSA is also tested on neural network optimization to further verify its effectiveness. Finally, the time complexity of the ALGSA is analyzed to clarify its search performance.

An aggregative learning gravitational search algorithm with self-adaptive gravitational constants

A multiyear DG-incorporated framework for expansion planning of distribution networks using binary chaotic shark smell optimization algorithm

We analyse the results of our experimental laboratory approximation of motorway networks with slime mould Physarum polycephalum . Motorway networks of 14 geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK and USA. For each geographical entity, we represented major urban areas by oat flakes and inoculated the slime mould in a capital. After slime mould spanned all urban areas with a network of its protoplasmic tubes, we extracted a generalised Physarum graph from the network and compared the graphs with an abstract motorway graph using most common measures. The measures employed are the number of independent cycles, cohesion, shortest paths lengths, diameter, the Harary index and the Randic index. We obtained a series of intriguing results, and found that the slime mould approximates best of all the motorway graphs of Belgium, Canada and China, and that for all entities studied the best match between Physarum and motorway graphs is detected by the Randic index molecular branching index.

Are motorways rational from slime mould's point of view?

This study introduces a variant of Gravitational Search Algorithm (GSA) for discrete optimization problems, namely, Fast Discrete Gravitational Search Algorithm (FDGSA). The main difference between the proposed FDGSA and the existing Binary Gravitational Search Algorithm (BGSA) is that an agent's position is updated based on its direction and velocity. Both the direction and velocity determine the candidates of integer values for the position update of an agent and then the selection is done randomly. Unimodal test functions, such as De Jong's function, Scwefel's function and Rosenbrock's valley are used to evaluate the performance of the proposed FDGSA. Comparison with BGSA is done to benchmark the proposed FDGSA in terms of speed of convergence and quality of solution. The experimental result shows that the proposed FDGSA converges faster compared to the BGSA.

A Fast Discrete Gravitational Search Algorithm

Electrical discharge machining (EDM) is a nonconventional milling in which holes or shape can be created without any contact between electrode and work piece during the material removal process. Throughout the machining process a series of stochastic sparks are produced when the gap between electrode and work piece is very narrow just about 10 to 50 microns. Controlling this gap in micro dimension not only depends on electrode position but also on work piece surface. So a combination of PID controller and EDM process is used to monitor the gap. In this study an indirect measurement of surface position is carried out by implementing voltage average gap model. And Simulink models have been done to simulate the dynamic behavior of EDM system.

Dynamic Modeling of Electrical Discharge Machining (EDM) System Using Matlab

Malaysian expressways network is designed based on human logic, but does the Malaysian transport system have anything in common with biological transport systems? We employ slime mould Physarum polycephalum in our search for an answer. We represent twenty major urban areas in Malaysia with sources of nutrients and inoculate slime mould in Kuala Lumpur. We wait till the slime mould colonises all urban areas and then analyse the network of slime mould’s protoplasmic tubes and compare it with existing transport network of Malaysia. Experiments with Physarum polycephalum shows that the protoplasmic network is largely a super-graph of most famous planar proximity graphs and include a minimum spanning tree. With regards to man-made transport network, the slime mould approximates almost all major transports routes. Our results do not have any immediate engineering applications but shed light onto ‘living logic’ of transport systems and could contribute to future planning of transport networks. Keywords-biological transport networks; slime mould; unconventional computing

Sophan Wahyudi

Papers

A Fast Discrete Gravitational Search Algorithm

Dynamic Modeling of Electrical Discharge Machining (EDM) System Using Matlab

Slime mould approximates Malaysian expressways: Is there a bio-logic behind the transport network?