BreathWideSearch&de​apthWideSearch Algorithm

sphere function is implemented

The Breath-Wide Search (BWS) and Depth-Wide Search (DWS) are optimization algorithms inspired by different exploration strategies for solving complex problems. Both of these methods are variations of search-based optimization techniques, and they differ in how they explore the search space.Breath-Wide Search (BWS)

• Concept: The Breath-Wide Search algorithm mimics a strategy of broad exploration of the search space in a shallow manner. It systematically explores a wide area, usually at a constant depth level before diving deeper into more specific areas. The focus is on covering as much of the search space as possible in the early stages.
• Application: BWS is effective when the problem space is very large, and the goal is to avoid premature convergence to local optima. The wide search helps ensure that no promising region is overlooked in the beginning stages of optimization.
• Mechanism:
• Start at a central or initial point.
• Explore surrounding regions, generating a variety of solutions.
• Gradually expand the exploration as more information is gathered, but focus on spreading out rather than going deep into specific regions initially.

Depth-Wide Search (DWS)

• Concept: The Depth-Wide Search algorithm takes a more focused approach compared to BWS by prioritizing exploration along a particular direction or path before branching out to other regions. It explores the space in greater depth before considering other alternatives.
• Application: DWS works well in scenarios where there is a need to exploit a promising region more thoroughly before jumping to other parts of the search space.
• Mechanism:
• Start by exploring a particular region or direction intensively.
• Once a deep understanding of that region is gained, the algorithm moves on to the next possible promising regions.
• The exploration follows a "depth-first" pattern but will switch between areas if significant improvements are found.

Differences:

• BWS explores broadly at a shallow level, aiming to map out the entire search space before diving deep.
• DWS focuses on exploring a smaller part of the space in depth, ensuring that local optima or deep solutions are fully explored before branching out.

Hybridization

In practice, these algorithms can be combined into a hybrid strategy, where a breadth-first search is used initially to explore the space broadly, followed by a depth-first search to explore promising areas deeply. This can balance exploration and exploitation, improving the efficiency and effectiveness of the optimization process.

Would you like to know more about the implementation of either algorithm?