Evolving a Swarm's Conversation Schedule: EVO-SCHIRP

Press Next round with the CHIRP rule selected: the agents pair off, and after five rounds all ten pairs of five agents have met. Now choose Random. Agents call partners who are busy calling someone else (the dashed arrows), and many pairs never meet. Evolved shows what this page’s evolution found after 25 generations. Watch closely: it repeats the same two handshakes every round. The score rewarded that habit, and the next demos show why.

The table below the circle is the schedule in the paper’s “unique encoding.” Read row 1 of the CHIRP schedule: agent 1 writes 4 and agent 4 writes 1, so they shake hands. A star means the agent sits out that round. The paper turns its three goals into three counts: how many different entries the worst column holds (did the worst-off agent meet many partners), how many different entries the worst row holds (did anyone get double-booked), and how many cells point at each other. Add the three to get the score. CHIRP earns 5 + 5 + 10 = 20 with five agents, the highest score possible.

For odd N, CHIRP fills every column with all N − 1 partners plus one idle slot, every row with N distinct entries, and (N − 1)/2 pairs per round, for a score of 2N + N(N − 1)/2. For even N, rounds with even R idle two agents, so the worst row holds N − 1 distinct entries and the cycle has N(N − 1)/2 pairs; with ten agents CHIRP scores 64 of a possible 70, the cost of the full N-round cycle the paper chooses for consistency. The evolved schedule scores 16 with five agents by repeating a perfect matching: the row and pair terms reach their maxima (5 and 10) while the column term collapses to 1.

The pair term counts pairs per round, not distinct pairs, so it rewards repeating one perfect matching N times as much as cycling through N different matchings. Coverage enters only through the worst-column term, which carries weight N against the pair term’s N⌊N/2⌋. A schedule that repeats one matching therefore scores 1 + N + N⌊N/2⌋ (16 with five agents, 61 with ten, 326 with 25), well above anything a random table reaches, while meeting only ⌊N/2⌋ of the N(N − 1)/2 pairs. This page’s evolution reaches that optimum for five agents in 11 of 12 runs (seeds 1 to 6, five and ten layers); the twelfth also repeats its pairs every round and scores 15. Any schedule search that sums these terms needs either a distinct-pair count or a penalty on repeats; the paper’s own suggestion to scale fitness to [0, 1] would not change the ranking.

The same schedule can be written down in two ways. In the left table, two agents who show the same letter in a round talk to each other, like two people holding up matching cards. In the right table, each agent writes the number of the agent it wants to call. With the CHIRP rule and five agents, these tables are the paper’s Figure 2.

Letters carry less information than numbers: a letter only says “find the other person holding this card,” so a one-sided call cannot be written in the paired table at all. That makes paired tables easier for evolution to get right, and the paper found that paired encodings “worked much better than unique encodings.” The catch appears when three agents pick the same letter; this page treats that as no handshake for any of them, because the paper does not say.

The unique encoding is a function from (round, agent) to a partner index; the paired encoding is a partition of each round’s agents by symbol. Converting paired to unique is exact when every symbol is held by at most two agents. Figure 2’s unique panel equals CHIRP’s schedule with round k printed as R = k − 1, and its paired panel induces the same matching in all five rounds, although its letters are assigned by hand (round 1 uses B and C, round 3 uses A and C). The paper converts paired protocols to unique ones before scoring, so the encodings differ in what evolution can express, not in how a finished table is graded.

Press Evolve. Each colored line is one run: the average score of 50 small networks, generation by generation. Gray dots are the best network in each generation, and the dashed line is the CHIRP formula. Evolution climbs quickly from the shaded band of random tables but stays well below CHIRP, the same story the paper tells: the formula still wins when a single swarm talks among itself.

Each network takes the previous round’s row of the table and produces the next row. Evolution copies every network once with small random changes, then holds 49 small contests among parents and copies (four entrants each, the winner survives) and keeps the single best network no matter what. Try 25 agents: a random table already scores near 38, and evolution reaches the 40s, yet CHIRP scores 350 because it fits 12 handshakes into every round.

The paper evolves fully connected CPPNs whose neurons use mixed activation functions, with N inputs and N outputs and five or ten hidden layers, for 25 generations; each parent produces one child, and tournament selection with elitism keeps 50 survivors. This page uses the same structure with six activation functions (sine, hyperbolic tangent, Gaussian, sigmoid, absolute value, and identity), Gaussian weight steps of 0.5, tournaments of four judged on the Pareto front of the three counts, and outputs binned into N partner indices. The shaded band shows the middle 90% of 2,000 uniformly random tables under the same fitness.

The paper’s Figure 3 shows population averages that wander without trend (“a random walk”) and top performers scattered across generations. Its unique-encoding averages sit near 5 to 15, 7 to 23, and 24 to 45 for 5, 10, and 25 agents, which matches what this page computes for uniformly random tables (averages 7.4, 14.8, and 38.0). This page’s runs instead climb: from 6.4 to 15.6 with five agents (seed 1), 11.9 to 19.7 with ten, and 23.4 to 42.7 with 25, because its elitist Pareto tournament keeps improvements. The two behaviors bracket the paper’s conclusion: with or without selection pressure, CPPN-generated schedules remain far from CHIRP once N exceeds a handful of agents. The paired panels of Figure 3 (averages near 28, 72, and 310) do not reproduce under this page’s conversion rule (random-table averages of 8.4, 23.7, and 126.4), so their scale depends on details of the paired conversion that the paper does not give.

Now several swarms share the airwaves, and agent 3 of one swarm answers to the same number as agent 3 of every other swarm. Each square is one agent in the chosen round, and the legend under the squares names what happened to its call: valid (only its own partner answers), collision (its partner and a stranger both answer), invalid (only strangers answer), or inactive (nobody answers). When every swarm uses the same secret order, every conversation collides. The paper found that its evolved schedules and S-CHIRP both scored about half of the best possible score in this crowded setting.

The crowded score has two halves. One half asks how well each swarm schedules itself (the score from the first demo, divided by the best possible). The other half asks how different the swarms’ tables are: if every swarm writes the same number in the same cell, outsiders hear exactly what insiders hear. S-CHIRP with one shared order earns full marks on the first half and zero on the second, so its score lands at one half. Evolved swarms do the opposite: their tables differ, but each swarm schedules itself poorly.

Multi-clique fitness combines the average single-clique score with the number of distinct elements in corresponding cells across the cliques’ matrices, “scaled against the maximum possible fitness.” This page scales each half to [0, 1] and averages them, which gives S-CHIRP with one shared order exactly 0.500 for 2 × 5 and 10 × 25 agents and 0.457 for 4 × 10 (CHIRP’s 64 of 70 for even N). One evolutionary run per scenario (seed 1, five layers) scores 0.850, 0.521, and 0.360. The channel picture applies Figure 1’s definitions: a call is valid when only the caller’s own partner answers, invalid when only agents from other cliques answer, a collision when both do, and inactive when nobody answers.

The paper calls S-CHIRP’s score unsurprising “since it guarantees overlapping between cliques,” which holds when every clique shares one round order. Giving each clique its own secret order, the defining feature of S-CHIRP in the ICCE paper, is an analysis beyond this paper: it keeps every clique’s schedule perfect and raises the distinct-cells half, so S-CHIRP then scores 0.700, 0.807, and 0.920 on the three scenarios with the orders this page draws, and valid calls rise from none to 32%, 51%, and 70% of agent-rounds. The scaled values depend on this page’s equal weighting; the paper reports neither weights nor per-scenario numbers.

• A simple formula (CHIRP) still schedules a single swarm better than anything evolution found.
• Writing a schedule as matching letters made evolution’s job easier than writing partner numbers.
• With several swarms on one channel, evolved schedules and S-CHIRP both reached about half of the best possible score.
• Better scores will need better ways to measure security, such as counting crossed lines and wrong numbers directly.

• Evolution never beat the CHIRP formula with 5, 10, or 25 agents, and running longer did not help.
• Paired (letter) encodings scored better than unique (number) encodings.
• Both EVO-SCHIRP and S-CHIRP scored about 0.5 on the scaled multi-swarm fitness.
• The authors plan lower mutation rates, fitness that rewards correct pairs more, and swarm sizes drawn from normal and gamma distributions.

• Single clique (phase 1). CHIRP outperforms every evolved protocol; population fitness behaves like a random walk over 25 generations, and high-fitness individuals appear at random (Fig. 3).
• Encodings. Paired encodings “worked much better” than unique encodings, and future work will use them.
• Multiple cliques (phase 2). EVO-SCHIRP and S-CHIRP both reach approximately 0.5 scaled fitness across the 2 × 5, 4 × 10, and 10 × 25 scenarios.
• Next steps. A security metric built from collisions and invalid communications, normal and gamma distributions of clique size, multi-hop protocols, and malicious agents.

Swarms of small devices will keep sharing crowded airwaves, from delivery drones to bridge-inspection robots to sensors worn on the body. A schedule that lets each swarm talk efficiently while keeping outsiders out has to work on the cheapest chips, with no server to coordinate it. This paper tested whether evolution could design such a schedule and learned that the hand-built formula remains the one to beat. Ultimately, the experiment shows how much the scoring rules shape what a search finds, a lesson that applies far beyond swarms.

Secure-by-design scheduling avoids encryption on devices that cannot afford it. EVO-SCHIRP frames that design as an optimization problem, which opens the door to protocols tuned for overlapping cliques, uneven clique sizes, and adversaries, cases where a closed-form rule such as CHIRP offers no guidance. The paper’s negative result for single cliques sets the baseline that any learned protocol must clear.

The work connects neuroevolution with protocol design at a point where analytic constructions exist for the base case (round-robin 1-factorizations of the complete graph) and do not exist for the security objective across collocated cliques. Its main lesson for follow-on work is about the objective: a fitness built from worst-case column and row diversity plus a per-round pair count admits degenerate optima, and a security term built from cell-wise diversity does not measure what an eavesdropping or colliding clique experiences. The paper names that gap and proposes collision- and invalid-communication counts as the next metric.

Notes from building this page

• No code. The CPPN library, activation set, population size, tournament size, weight-mutation step, output binning, and input scaling are not in the paper. The page’s choices are listed in the evolution demo and marked “PAGE CHOICE” in evo-engine.js.
• Figure 2. Both panels reproduce: the unique panel equals CHIRP for N = 5 with rounds numbered from 1, and the paired panel induces the same matchings with hand-assigned letters.
• Pair term. The fitness counts bidirectional pairs per round, so a schedule that repeats one perfect matching scores 1 + N + N⌊N/2⌋ while covering only ⌊N/2⌋ pairs. This page’s evolution reaches that optimum for five agents (score 16). Figure 3’s top unique scores (up to 18 with five agents) fit the same pattern, which may explain why some top performers appear suddenly.
• “Worse than CHIRP.” The conclusion says the authors “were unable to evolve a communication pattern which performed worse than CHIRP in a single clique environment”; the results section says CHIRP outperforms EVO-SCHIRP, so the sentence presumably means “better than.”
• Paired scale. Figure 3’s paired panels (averages near 28, 72, and 310) exceed CHIRP’s unique-encoding scores for ten agents (64), so the paired conversion must count matches differently from the unique one (for example, every pair of agents sharing a symbol). This page’s rule (a symbol held by exactly two agents forms a pair) gives random-table averages of 8.4, 23.7, and 126.4.
• Multi-clique scaling. The paper says only that fitness was “scaled against the maximum possible.” This page averages two halves scaled to [0, 1], which yields S-CHIRP’s 0.5 exactly for odd clique sizes; other weightings move S-CHIRP away from 0.5. The paper adds that the distinct-cells count registers a collision once and an invalid exchange twice; cell-wise diversity does not identify either event in general, so the page’s channel picture computes Figure 1’s events directly and reports them beside the score.
• Shared versus own orders. Phase 2 treats S-CHIRP as guaranteeing overlap. With independent secret orders per clique (an analysis beyond the paper, shown at graduate and researcher levels), S-CHIRP keeps perfect clique fitness and scores 0.70 to 0.92.

Try this in class

1. Seat five classmates in a circle, numbered 0 to 4. Use the rule partner = (round − own number) mod 5 for rounds 0 to 4, record the pairs in a five-by-five table, and score it with the paper’s three counts.
2. Have each student roll a five-sided die (or draw a number card) to choose a partner each round, record the new table, and score it the same way. Compare the two scores and the number of pairs that met.
3. Find a table that scores at least 16 but lets only two pairs meet, then rewrite the scoring rule so that table scores lower than CHIRP. Explain in one sentence what your new rule rewards.