MAL-Seeker (Antares Ver 3.1.1)

Up until now, I have tackled various nonlinear equations using the "SPICE-oriented analysis method" as my weapon. However, in large-scale all-solution searches where hundreds or thousands of solutions exist, I inevitably began to feel the limitations of using a simulator (in terms of execution speed, memory management, etc.).

"Then why not build an all-solution search program from scratch myself?"

Having made up my mind, I started building my own global solver in C, but I struggled with what kind of algorithm to use. That's when I remembered a casual remark made by a professor at a networking event during an academic conference in my student days.

This quote gave me a hint. Before writing rigid mathematical logic, why not incorporate an intuitive algorithm inspired by the "5 senses" of living creatures?

If we base it on a living creature, who should be the model?
Normally, one would choose "human 5 senses," but I decided to model it after my family's pet Pomeranian, "Maru".

Why? Simply because Maru is the most reliable and put-together member of our family (laughs). Human senses can be surprisingly sloppy, after all.

Here is the division of roles.
First, as a human (the developer), I look over the entire vast forest (search space) of the nonlinear equation from above using a "Scouter." Then, I leave the actual task of descending into the forest to hunt for the solutions (valley bottoms) to the brilliant Maru. Moreover, because Maru is so exceptional, he uses a "Clone Technique" to split into 100,000 Marus, diving all at once into various parts of the forest.

The greatest strength of this solver, "MAL-Seeker (Current codename: Antares Ver 3.1.1)", lies in the fact that it leaves the performance of the powerful drill (Newton's method) untouched, while pushing the "pre-processing by Maru's 5 senses" prior to drilling to the absolute limit.

The 100,000 Marus (initial seeds) released into the forest fully utilize the following 5 senses to completely eliminate wasteful computations:

• 👃 Sense of Smell (Deflation Processing)
  Maru is a genius at marking. Around an already discovered solution $x^*$, a "strong stench penalty (e.g., adding a mathematical pole like $1/\|x - x^*\|$)" is mathematically placed so that other Marus won't approach. This perfectly prevents the waste of finding the same solution over and over again.
• 👅 Sense of Taste (Jacobian/Gradient Test)
  Before spinning the drill, Maru licks the ground at his feet to check the slope (gradient or Jacobian determinant). If there is no taste at all (a too-flat singular point) or if it's too spicy (a steep cliff with a risk of overflow), he judges it dangerous to dig there and cancels the search.
• 👁️ Sense of Sight (Guidance by Steepest Descent)
  Maru surveys his surroundings. If he visually confirms he is on a valley slope, instead of firing up the drill immediately, he confidently trots down a few steps toward the inside of the bowl following the gradient vector. These few steps of fine-tuning dramatically stabilize the subsequent calculations.
• 👂 Sense of Hearing (Clustering by Inter-Seed Distance)
  Maru also listens for the footsteps of his peers. By measuring the Euclidean distance $\|x_A - x_B\|$ with other Marus who dropped down at the same time, if he thinks, "Ah, we're too close," he yields the path to avoid digging the same hole (seed culling via clustering).
• ✋ Sense of Touch (The Core Newton's Method)
  Only the elite Marus who pass the strict "5 Senses Examination" up to this point are allowed to press the switch of the drill (Newton's method) with their front paws, warping straight down to the rock bottom of the valley.

To test "MAL-Seeker" equipped with this Maru's 5-sense algorithm, we made it solve notorious benchmark equations known for high dimensionality and multiple solutions.

This algorithm started from an admittedly unrefined and playful metaphor of "Maru's 5 senses and the Clone Technique." However, unpacking the completed internals academically reveals a surprising fact.

Maru's "Sense of Smell" is exactly the Deflation Method, and the "Sight and Hearing" approaches perfectly merge with state-of-the-art mathematical optimization techniques like the Clustering Multi-Start Method and Trust-Region Method.

Instead of building from a rigid theoretical top-down approach, the on-the-ground mindset cultivated in firmware development—"eliminate waste entirely and optimize computational resources"—ultimately arrived at a highly advanced academic optimal solution. MAL-Seeker is truly a monumental engine that embodies the philosophy of our Laboratory.