Water Wave Optimization
Water wave optimization（WWO）is a heuristic algorithm based on shallow water wave theory. It was proposed by Professor Zheng Yujun in 2015.[1]
Algorithm introduction
Water Wave Optimization (WWO) is a novel meta-heuristic algorithm based on shallow water wave theory. The algorithm compares each solution in the population to a water wave with wavelength λ and wave height h, and efficiently searches in the solution space by simulating the propagation, refraction and breaking motion mechanism of water waves. The algorithm compares the optimization problem to be solved with the shallow water wave model, as shown in Table 1.
Table 1 Correspondence between shallow water wave model and actual problem
The core of the water wave optimization algorithm is to assign each solution a wavelength that is inversely proportional to its fitness, and make each solution propagation (search) range proportional to its wavelength: the closer to the sea level, the better the corresponding solution, the corresponding The higher the water wave, the larger the wave height of the water wave and the smaller the wavelength, as shown in Figure 1 . During each iteration, the propagation operation causes each wave x to move each dimension d within a range proportional to its wavelength λx to create a new wave x', as shown in the following equation.
The function rand is used to generate a random number in the specified range, and L(d) is the length of the solution space in the `d` dimension.
Fig.1 Relationship between fitness, wavelength and wave height of solutions in WWO
WWO also provides two operations, reflection and breaking. When a solution has not been improved after a specified iteration, its energy is exhausted and the wave height will be zero, then the reflection operation is replaced by a random solution between it and the current optimal solution to avoid the algorithm search stalling. . Whenever a new current optimal solution is found, applying the shattering operation splits it into several isolated waves, each wave moving a new distance from the new optimal wave in a random direction, thereby enhancing the local search for. Through the above operations, the WWO algorithm can achieve a good dynamic balance between global search and local search.
Relevant research
Since the WWO algorithm was proposed, it has attracted a lot of attention because of its simple framework, easy implementation, fewer control parameters, and superior performance. The current research is mainly in two aspects: one aspect is to improve the algorithm and population learning mechanism in the algorithm to improve the performance and convergence of the algorithm by changing its own operators [2-5] or combining WWO with other heuristics and meta heuristics [6-11]. Currently, the WWO algorithm and its variants have been applied to many industrial problems [12-23]. Another aspect of research is primarily to adapt WWO to a specific combinatorial optimization problem (COP). A class of COP can be expressed as an integer programming (IP) problem [24-28], and another variant of the algorithm proposes the use of a single wave rather than a wave group [29,30].
Recent progress
Professor Zheng, in 2019, published his paper Water Wave Optimization for Combination Optimization: Design Strategies and Applications [31] in Applied Soft Computing Journal. This paper proposes a systematic approach that consists of a set of basic steps and strategies for adapting water wave optimization (WWO), a simple and generic metaheuristic, to concrete heuristic algorithms for different COPs. Taking advantages of the generic algorithmic framework, designers can only focus on adapting the prorogation operator and the wavelength calculation method according to the combinatorial properties of the given problem, and thus easily derive efficient problem-solving algorithms.