feat: Expand underpopulated optimization categories (social_inspired, probabilistic, constrained)

[Anselmoo]

Summary

Several optimization categories have significantly fewer algorithms compared to well-populated categories like swarm_intelligence (50+ algorithms). This issue tracks potential algorithms to add to balance the library.

Current State

Category	Count	Algorithms
social_inspired	4	TeachingLearningOptimizer, PoliticalOptimizer, SoccerLeagueOptimizer, SocialGroupOptimizer
probabilistic	5	LDAnalysis, ParzenTreeEstimator, BayesianOptimizer, SequentialMonteCarloOptimizer, AdaptiveMetropolisOptimizer
constrained	5	AugmentedLagrangian, SuccessiveLinearProgramming, BarrierMethodOptimizer, PenaltyMethodOptimizer, SequentialQuadraticProgramming

Proposed Additions

Social-Inspired Algorithms

• Election Algorithm (EOA) - Meta-heuristic based on election processes (MDPI 2024)
• Greedy Politics Optimization - Political strategies during state elections
• Social Learning Optimizer (SLO) - Human social learning behaviors
• Anarchic Society Optimization (ASO) - Anarchic social behaviors
• Brain Storm Optimization (BSO) - Human brainstorming process

Probabilistic Algorithms

• Hamiltonian Monte Carlo (HMC) - MCMC using Hamiltonian dynamics
• Slice Sampling - Adaptive MCMC method
• Gibbs Sampling - Component-wise MCMC sampling
• Parallel Tempering - Multiple temperature MCMC chains
• Nested Sampling - Bayesian evidence computation

Constrained Algorithms

• Interior Point Method - Primal-dual interior point optimization
• ADMM - Alternating Direction Method of Multipliers
• Filter Method - Constraint violation filter approach
• Exact Penalty Method - L1 exact penalty approach
• Projection Method - Gradient projection for constraints

References

• Election Algorithm: https://www.mdpi.com/2227-7390/12/10/1513
• Hamiltonian Monte Carlo: Neal, R. M. (2011) "MCMC using Hamiltonian dynamics"
• Interior Point Methods: Nocedal & Wright, "Numerical Optimization"
• ADMM: Boyd et al. (2011) "Distributed Optimization and Statistical Learning"

Acceptance Criteria

• Each new algorithm follows AbstractOptimizer pattern
• Includes proper docstrings with references
• Added to respective __init__.py exports
• Included in test suite
• All tests pass

[boomelio]

can i work on this?

[Anselmoo]

You are welcome 🤗

[Anselmoo]

@boomelio sorry, I accidentally closed it