The Zombie Optimization Problem

The Zombie Optimization Problem

To understand the Zombie Optimization Problem (ZOP), it’s important first to understand the Traveling Salesman Problem (TSP).

For those unfamiliar with the TSP, the problem asks: given a set of cities and the distances between them, how can you determine the shortest route that visits each city exactly once and returns to the starting point?

This problem is already complex in itself, but what if we added a twist where the environment changes dynamically as the scenario progresses?

That’s where the ZOP comes in.

This scenario takes place on a 10×10 grid, featuring a single zombie and a given number of humans. The goal is for the zombie to infect all the humans in the most efficient manner possible. However, unlike the TSP, once a human is infected, they also turn into a zombie, increasing the number of traveling agents.

Potential Solutions to the Zombie Optimization Problem

Traditional methods, like a greedy approach (which makes the best move at each step without considering the bigger picture) and genetic algorithms (which try different combinations and improve them over time, similar to natural evolution), are commonly used in optimization problems. However, the evolving nature of ZOP requires different strategies.

Swarm intelligence can offer a more advanced approach.

Inspired by social insects like bees and ants, swarm intelligence uses decentralized agents (zombies) that communicate indirectly through the environment (the grid) to achieve a collective goal (infecting humans in the fewest steps possible).

In the ZOP, each zombie operates autonomously, adjusting its behavior based on the actions of other nearby zombies. This ensures that no two zombies target the same human, and a zombie will abandon its target if another zombie gets closer. Such a self-organizing system excels in dynamic environments.

The most advanced solution is reinforcement learning (RL), where the zombies (agents) learn optimal infection paths through trial and error. Over time, the zombies improve their strategy based on the evolving environment. A reward system can prioritize maximizing new infections while also minimizing overlap or wasted effort, making RL well-suited for the dynamic nature of the ZOP.

Why the Zombie Optimization Problem Matters: Real-World Applications

What makes the ZOP special is that it's a problem centered around adaptability.

There is no one-size-fits-all solution for dynamic optimization. Every scenario is case-dependent: a strategy that works in one case might fail in another. It all depends on factors like the layout of humans and the starting position of the first zombie.

Consider how vehicles maneuver in large cities. As traffic bottlenecks, intelligent systems can account for road conditions, current traffic, and vehicle behavior, adjusting in real-time and altering signal timings dynamically to reduce congestion.

Additionally, the ZOP can be applied to wildfire management. By using intelligent systems that track moving variables such as landscape, wind patterns, and nearby flammable materials, firefighters can better determine where to set firebreaks and containment lines, stopping the fire quicker and with fewer resources.