JBoss.orgCommunity Documentation

Chapter 12. Exhaustive search

12.1. Overview
12.2. Brute Force
12.2.1. Algorithm description
12.2.2. Configuration
12.3. Branch And Bound
12.3.1. Algorithm description
12.3.2. Configuration
12.4. Scalability of Exhaustive Search

Exact methods will always find the global optimum and recognize it too. That being said, they don't scale (not even beyond toy data sets) and are therefore mostly useless.

To configure Branch And Bound:



For the pruning to work with the default ScoreBounder, the InitializingScoreTrend should be set. Especially an InitializingScoreTrend of ONLY_DOWN (or at least has ONLY_DOWN in the leading score levels) prunes a lot.

Optionally, specify the nodeExplorationType:

  • DEPTH_FIRST (default): Explore deeper nodes first (and secondarily by a better optimistic bound or score first). Deeper nodes (especially leaf nodes) often improve the pessimistic bound. A better pessimistic bound allows pruning more nodes to reduce the search space.

  • BREADTH_FIRST (not recommended): Explore nodes layer by layer (and secondarily by a better optimistic bound or score first). Scales terribly in memory (and usually in performance too).

  • OPTIMISTIC_BOUND_FIRST: Explore nodes with a better optimistic bound or score first (and secondarily deeper nodes first).


Exhaustive Search variants suffer from 2 big scalability issues:

As shown in these time spent graphs from the Benchmarker, Brute Force and Branch And Bound both hit a performance scalability wall. For example, on N queens it hits wall at a few dozen queens:

In most use cases, such as Cloud Balancing, the wall appears out of thin air:

Exhaustive Search hits this wall on small datasets already, so in production these optimizations algorithms are mostly useless. Use Construction Heuristics with Local Search instead: those can handle thousands of queens/computers easily.


Throwing hardware at these scalability issues has no noticeable impact. Newer and more hardware are just a drop in the ocean. Moore's law cannot win against the onslaught of a few more planning entities in the dataset.