---
type: claim
domain: mechanisms
description: "Greedy optimization finds nearby peaks but misses distant higher ones -- the mathematical basis for why incremental improvement fails in complex landscapes"
confidence: proven
source: "Stuart Kauffman (NK landscapes, 1993), Herbert Simon (satisficing, 1956), Sewall Wright (fitness landscapes, 1932)"
created: 2026-04-21
secondary_domains: [grand-strategy, ai-alignment]
related_claims:
  - "simulated-annealing-maps-the-physics-of-cooling-onto-optimization-by-starting-with-high-randomness-and-gradually-reducing-it"
  - "punctuated-equilibrium-emerges-from-darwinian-microevolution-without-additional-principles-because-extremal-dynamics-on-coupled-fitness-landscapes-self-organize-to-criticality"
  - "comfortable-stagnation-is-a-self-terminating-attractor-basin-because-the-stability-it-optimizes-for-degrades-capacity-to-respond-to-external-shocks"
---

# Hill climbing gets trapped at local maxima because it can only accept improvements and has no way to see beyond the nearest peak

Hill climbing is any optimization process that evaluates its current state, considers nearby alternatives, and moves to whichever is better. It is the default behavior of markets, evolution, institutional reform, and individual careers. The trap is mathematical, not behavioral: in any landscape with multiple peaks (a "rugged" fitness landscape), an agent that only accepts improvements will climb the nearest peak and stop -- even if a vastly higher peak exists elsewhere. It cannot reach the higher peak because every path there passes through a valley of worse states.

This matters because most real optimization landscapes are rugged. Kauffman's NK model showed that as the number of interacting components (K) increases, the landscape becomes exponentially more rugged -- more local optima, each further from the global optimum. Stuart Kauffman demonstrated that biological evolution itself gets trapped this way: organisms optimize locally but cannot "see" configurations that would require temporarily becoming less fit.

The implications cascade across domains. Markets hill-climb toward local profit maxima, producing efficient firms that collectively create fragile systems. Institutions reform incrementally, each step locally improving performance while drifting further from globally optimal designs. AI training via gradient descent is literally hill climbing -- neural networks converge to local minima of the loss function, and techniques like learning rate scheduling, random restarts, and ensemble methods exist precisely because the landscape is rugged.

The escape mechanisms are few and costly: random perturbation (simulated annealing), wholesale replacement (punctuated equilibrium), or external forcing (regulation, catastrophe). Each requires tolerating temporary degradation in service of long-term improvement -- which is precisely what greedy optimizers cannot do.

## Evidence
- Kauffman NK model (1993) -- as K increases, number of local optima grows exponentially, average fitness of optima decreases
- Wright fitness landscapes (1932) -- original formalization showing evolution explores a surface with peaks and valleys
- Simon satisficing (1956) -- organisms don't optimize, they accept "good enough" precisely because optimization is computationally intractable
- Gradient descent in deep learning -- techniques like SGD with momentum, Adam, learning rate warmup all exist to escape local minima

## Challenges
- Some landscapes are nearly convex (few local optima), making hill climbing sufficient -- but these are the exception in complex systems, not the rule
- Evolutionary algorithms show that recombination (crossover) can escape local optima without explicit cooling schedules
