The Physics-Based Metaheuristic Algorithms are inspired by the life of physics generated by simulating physical phenomena occurring. These algorithms are efficient and robust in solving high-dimensional and difficult problems.
The most commonly used algorithm is Simulated Annealing (SA), which uses thermodynamic heating phenomena to simulate the changing cooling process of an object. The Archimedes Optimization Algorithm (AOA) mimics the Archimedes principle in physics. It introduces a formula for submerging objects into the iterative update algorithm.
The best-known physics-based algorithm is the Gravity Search Algorithm (GSA), which is based on Newtons laws of motion and individual gravitational control and has the fundamental laws of physics methodology.
The algorithms based on physical phenomena have several optimization methods, such as:
Simulated Annealing (SA): SA is an optimization algorithm inspired by the annealing process in metallurgy. In SA, candidate solutions are treated as particles in a thermal system, and the optimization process is guided by a temperature parameter that controls the acceptance of worse solutions. The algorithm starts with a high temperature, allowing the search process to escape local optima, and gradually decreases the temperature, leading to the convergence of the algorithm to a global optimum.
Electromagnetic Metaheuristic: The electromagnetic metaheuristic is an optimization algorithm that simulates the behavior of charged particles in an electromagnetic field. The candidate solutions are represented as charged particles, and the optimization problem is modeled as an electromagnetic field. The algorithm applies Coulombs and Lorentzs laws to simulate the interaction between particles and electromagnetic fields. The particles move toward the electromagnetic force, and the algorithm converges to the optimal solution when the charges settle into a stable equilibrium.
Gravitational Search Algorithm (GSA): GSA is an optimization algorithm inspired by celestial bodies behavior in a gravitational field. In GSA, candidate solutions are treated as masses, and the gravitational force between the masses guides the optimization process. The algorithm starts with a random distribution of masses and gradually moves them toward the global optimum by calculating the gravitational force between them.
The working function of physics-based metaheuristic approaches can be described as follows:
Objective function: The algorithm starts by defining an objective function, which measures the quality of candidate solutions in terms of the optimization criteria. The objective function can be any function that maps a candidate solution to a real number, such as a cost function or a fitness function.
Initialization: The algorithm randomly initializes a set of candidate solutions or uses some heuristics. The candidate solutions are represented using a suitable representation, such as binary strings, real-valued vectors, or quantum bits.
Evaluation: Each candidate solution is evaluated using the objective function, which measures the quality of the solution in terms of the problem optimization criteria.
Perturbation:The candidate solutions are perturbed using some perturbation operator, which introduces randomness or perturbation in the search process. The perturbation operator can be deterministic or stochastic, depending on the algorithm.
Selection: A subset of the candidate solutions is selected based on some selection criteria, such as fitness, probability, or rank. The selection criteria can be based on the quality of the solutions or some probabilistic measure.
Optimization: The algorithm simulates a physical process to optimize the selected candidate solutions. Depending on the algorithm, the physical process can be based on principles from thermodynamics, electromagnetism, or quantum mechanics. The algorithm uses physical analogies to develop efficient optimization algorithms that can explore the search space and converge to the optimal solution.
Replacement: The best candidate solutions are selected from the new and existing populations to form the next generation of candidate solutions. This step ensures that the overall quality of the population improves over time.
Termination: The algorithm stops when some termination criterion is met, such as reaching a predefined number of iterations, reaching a satisfactory solution, or exceeding a computational budget.
Physics-based metaheuristic algorithms have a wide range of applications in various fields, including:
Engineering Design: These algorithms are employed for engineering design optimization problems, such as optimizing the design of mechanical systems, electrical systems, and structures.
Financial Optimization: used for financial optimization problems, such as portfolio optimization and risk management.
Computational Biology: Physics-based metaheuristics in computational biology to solve problems such as protein folding, drug design, and gene sequencing.
Image Processing: used in image processing applications, such as image segmentation and pattern recognition.
Machine Learning: used for training machine learning algorithms, such as neural networks, support vector machines, and decision trees.
Supply Chain Optimization: utilized for supply chain optimization problems, such as transportation and distribution planning, inventory management, and facility location.
Optimization of Complex Systems: employed for optimizing complex systems, such as energy systems, transportation systems, and communication networks.
Environmental Science: applied for environmental science applications, such as pollution control, waste management, and sustainable energy systems.
Computational complexity: Physics-based metaheuristic approaches often involve complex calculations and simulations, requiring significant computational resources. It limits the size and complexity of the problems that can be solved and increases the optimization time and cost.
Model selection and calibration:Require the selection and calibration of appropriate models to represent the optimization problem accurately. This can be a challenging task, as different models may have different trade-offs in terms of accuracy and computational cost.
Limited interpretability: The solutions generated by physics-based metaheuristic approaches may be difficult to interpret or explain, particularly if the optimization involves complex physical models. It limits its usefulness in some applications, such as decision-making and policy analysis.
Algorithm design: Designing efficient and effective physics-based metaheuristic algorithms requires a deep understanding of the underlying physics principles and the optimization problem. This cannot be easy, as it often requires a multidisciplinary approach and collaboration between experts in different domains.
Sensitivity to input parameters: Involves many input parameters, such as model coefficients and simulation settings. These parameters can significantly impact the quality of the optimization results, making it challenging to find optimal values for all parameters.
Lack of generalization: Physics-based metaheuristic approaches are often designed to address specific optimization or class problems. It limits the ability to generalize to new problems or different problem domains.
Some of the latest research topics in the field of physics-based metaheuristic approaches are: