An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation (1405.5066v1)

Abstract: The ability of an Evolutionary Algorithm (EA) to find a global optimal solution depends on its capacity to find a good rate between exploitation of found so far elements and exploration of the search space. Inspired by natural phenomena, researchers have developed many successful evolutionary algorithms which, at original versions, define operators that mimic the way nature solves complex problems, with no actual consideration of the exploration/exploitation balance. In this paper, a novel nature-inspired algorithm called the States of Matter Search (SMS) is introduced. The SMS algorithm is based on the simulation of the states of matter phenomenon. In SMS, individuals emulate molecules which interact to each other by using evolutionary operations which are based on the physical principles of the thermal-energy motion mechanism. The algorithm is devised by considering each state of matter at one different exploration/exploitation ratio. The evolutionary process is divided into three phases which emulate the three states of matter: gas, liquid and solid. In each state, molecules (individuals) exhibit different movement capacities. Beginning from the gas state (pure exploration), the algorithm modifies the intensities of exploration and exploitation until the solid state (pure exploitation) is reached. As a result, the approach can substantially improve the balance between exploration/exploitation, yet preserving the good search capabilities of an evolutionary approach.

• The paper introduces the States of Matter Search (SMS) algorithm, a novel nature-inspired optimization method based on the dynamic properties of gas, liquid, and solid states to improve the balance between exploration and exploitation in evolutionary search.
• The SMS algorithm operates through three distinct phases representing states of matter: a Gas state for broad exploration, a Liquid state for balanced exploration/exploitation, and a Solid state for focused exploitation, each phase guided by unique evolutionary operators.
• Comparative analysis against established algorithms like PSO and DE on benchmark functions shows that SMS consistently yields superior results in terms of accuracy and efficiency, indicating its potential for solving complex global optimization problems in various scientific and engineering fields.

States of Matter Search (SMS) Algorithm: A Nature-Inspired Approach for Global Optimization

The paper introduces a novel optimization algorithm called the States of Matter Search (SMS), designed to enhance the balance between exploration and exploitation in evolutionary algorithms (EAs). The SMS algorithm draws inspiration from the dynamic properties of the states of matter—gas, liquid, and solid—to simulate a more balanced search process. This strategy aims to overcome the limitations of existing algorithms concerning premature convergence and lack of diversity in exploration.

Core Concept and Methodology

At the heart of SMS is the representation of individuals as molecules within a multi-dimensional search space. These molecules interact following evolutionary operations inspired by the principles of thermal-energy motion. The algorithm operates in three distinct phases, corresponding to the states of matter:

1. Gas State (Pure Exploration): This initial phase emphasizes exploration by allowing molecules to move and collide freely, incorporating randomness to cover a large search area. The parameters are configured to enable significant displacement, fostering a broad search for local minima.
2. Liquid State (Transition Phase): As the process shifts from exploration to exploitation, the movements of molecules become more restricted, resembling the behavior of molecules in a liquid. This phase balances both exploration and exploitation by adjusting the parameters for a moderated search, ensuring that the search does not prematurely converge on local optima.
3. Solid State (Pure Exploitation): In the final phase, molecules are almost static, mimicking the solid state where exploitation is maximized. This phase focuses on refining solutions, driving towards a global optimum by minimizing movement to precision tune the discoveries made in previous stages.

Algorithm Implementation and Operators

SMS utilizes several evolutionary operation-based operators, which are critical to its functioning:

• Direction Vector Operator: Leads molecular movement considering past directions and attraction towards the best-found solution.
• Collision Operator: Controls the diversity of the search process by exchanging direction vectors between colliding molecules, thus preserving search diversity.
• Random Position Operator: Introduces probabilistic random position generation to simulate randomness inherent to gas molecules, aiding in maintaining diversity and avoiding local optima.

Comparative Performance Analysis

The performance of the SMS algorithm has been critically tested against numerous benchmark functions and compared with well-established evolutionary algorithms including Particle Swarm Optimization (PSO), Differential Evolution (DE), Gravitational Search Algorithm (GSA), and an advanced PSO variant with a diversity-preserving scheme. The experimental results, supported by a suite of tests, indicate that SMS consistently yields superior results in terms of accuracy and efficiency. Notably, SMS achieved statistically significant improvement in several test scenarios, highlighting its robust exploration-exploitation balance.

Implications and Future Directions

The findings have both theoretical and practical ramifications. Theoretically, SMS provides a framework to better understand multi-phase evolution strategies, emphasizing how adaptability across different phases of search can mitigate existing limitations in EAs. Practically, the SMS algorithm is promising for complex optimization tasks prevalent in engineering, economics, and other scientific fields where global optima are sought but computational resources are constrained.

Future research could explore the integration of SMS with other adaptive strategies or its application in dynamic environments where the search landscape evolves over time. Moreover, extending this approach to incorporate additional states of matter or blend with other natural phenomena could offer further insight into the versatility and applicability of nature-inspired computational algorithms in solving complex global optimization problems.