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

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 explorationexploitation 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. To illustrate the proficiency and robustness of the proposed algorithm, it is compared to other well-known evolutionary methods including novel variants that incorporate diversity preservation schemes. The comparison examines several standard benchmark functions which are commonly considered within the EA field. Experimental results show that the proposed method achieves a good performance in comparison to its counterparts as a consequence of its better exploration-exploitation balance.

Multiobjective Automatic Parameter Calibration of a Hydrological Model

“…The success of the metaheuristic optimization algorithm depends on the balance between the algorithm's exploration (diversification) and exploitation (intensification) capability [44,[60][61][62][63]. This study proposes variable changing methods for the CDI and MDI of SBX and PM, respectively.…”

“…However, some studies reported that the balance should be variable to guarantee the best performance [41][42][43] because the effectiveness of wide search and fine-tuning depends on the optimization phase. Cuevas et al [44] stated that a common strategy for balancing exploration and exploitation is to start with exploration and then gradually increase exploitation as good fitness points are identified. It would be a better strategy in the automatic calibration of a hydrological model to focus on searching various parameter sets broadly in the early optimization phase and to give more weight to fine-tuning the solutions found in the latter phase.…”

Automatic differentiation based for particle swarm optimization Steepest descent direction

“…The steepest descent direction is used to change the direction of modification. The equation is defined as in (5).…”

“…That is, direction for the best estimator that a particle has ever reached, direction for the best one that all particle have ever found and momentum are successfully combined to determine the next iteration. Unfortunately, PSO show some weakness in term of balance between exploitation and exploration during the search [5]. For example in multi-objective problems, the search is not concentrated on the visited areas effectively, and often it shows a premature convergence and lack of diversification during moving from position to another.…”

BAS: Beetle Antennae Search Algorithm for Optimization Problems

“…Two essential common characteristics of these different meta-heuristics are exploration and exploitation. Besides, there are also other heuristic algorithms [6][7][8][9] to solve the optimization problem. Further more, this paper design a new meta-heuristic algorithm, which is named as beetle antennae search (BAS) algorithm to solve the optimization problems, taking inspiration from detecting and searching behavior of long-horn beetles.…”