The “Flaming Datum Problem” is a classic anti-submarine warfare problem in which the presence of an enemy submarine is known only when a friendly ship has been attacked. The last known position of the enemy submarine (the datum) is somewhere in the vicinity of the flaming friendly hull. Searchers immediately converge on datum, and the enemy submarine begins evasive activities so that the submarine itself will not become flaming datum.

So in the Flaming Datum Problem, the searcher wants to find the target while the target doesn’t want to be found. Therefore, as noted by Washburn and Hohzaki, the problem is really a two-sided game. For the searcher, the typical parameters are time – lateness of arrival, search rate and available search time. For the evader, the typical parameters are speed, endurance and counter-detection capability. Washburn and Hohzaki included the important consideration that speed and endurance might be related in a decidedly non-linear way. They found analytic bounding solutions rather far apart and despaired of doing any better analytically.

In a related problem, Alan Breitler used simulated annealing to find optimal search patterns. McCue combined these two previous projects and used simulated annealing to find optimal behavior patterns for both the searcher and the evader in the Flaming Datum problem.

In the case considered, the searchers’ lateness is 30 minutes, speed is 35 knots and the nominal search radius is 1.5 nautical miles with on-station time being 180 minutes. The objective function is the probability of finding the target or, for the evader, the complement of this probability – the probability of not being found. Giving the problem some texture, the target has the ability to counter-detect the finder.

Dr. McCue’s presentation consisted of a basic description of simulated annealing and some sample Monte Carlo runs. In the sample simulation, while the searcher tends to approximate the expected logarithmic spiral, the search path looked like it might be a “squiggle studying to be a spiral,” bringing up the possibility of deep inner meaning to paths that seem to continually cross. The various behaviors of the evader exhibit quite a lot of variety for quite a while, but seem to stabilize towards the end of the “annealing” process. The graphical output helpfully shows the means to the solution, not just the outcome. In colloquy, a workshop participant mentioned the value of Jacobson, Johnson, and Henderson’s The Rise and Fall of Simulated Annealing in explaining this subject. It was noted that this simulation’s biggest drawback is that it takes days to run.

Next McCue initiated a round robin contest among participants to determine who could come up with the best search plan and evasion plan. Each contestant entered a search pattern, characterized as a series of way points, and an evasion policy, characterized as random-walk probability distributions for initial speed, new speed upon "timing out" on the initial leg, course change after "timing out," and course and speed upon counter-detection of the searcher. A major constraint upon the evader was a limited energy "battery" with a consumption rate that was a pronounced non-linear increasing function of speed.

After the workshop McCue entered all of the inputs into the simulation. Each run tested one search pattern against a field of 3,000 agents all independently using the same evasion policy, i.e., sampling from the same distributions. Some evaders would be detected by the searcher and some would not, resulting in an N = 3000 empirical estimate of the probability that that search pattern succeed against that policy. There were eleven entrants so 121 runs were required. McCue completed 144 runs because he wanted to test another pair of entries: the machine-derived "Best of Breed" searcher and evader that had emerged from the simulated annealing process.

The winning searcher was the pattern with the highest average probability of finding the other contestants' evaders and the winning evader was the set of distributions with the lowest average probability of getting caught by the other contestants’ searchers.

The winning searcher’s search pattern succeeded a remarkable 82-per cent of the time. The rest of the contestants' search patterns succeeded somewhere between 69-per cent and 73-per cent of the time. The pattern was a modified spiral that cut back across the origin a couple of times, catching evaders who were lazing around at the start point or who had wandered back there.

The best evader was caught only 20-per cent of the time, whereas the next-most successful evader was caught 31-per cent of the time and the rest were strung out all along up the interval, some being caught 90-per cent of the time or more. This evader started out at a moderate 9 knots and had no chance of timing out until the maximum leg duration of 30 minutes, whereupon it would really not timeout at all because it would always execute a 0 degree turn and continue going at 9 knots. If this evader counter-detected the searcher, the evader threw in a little variety, increasing speed to as much as 12 knots and executing either a 126 degree turn or a 144 degree turn, randomly to port or starboard.

McCue tested the best searcher against the best evader. The result was detection 33-per cent of the time: the best evader gave the best searcher much more trouble than did any other evader, and – conversely – the best searcher found the best more than all but one of the other searchers. Interestingly, the "Best of Breed" patterns were mediocre: the machine-derived searcher was the third-worst searcher and the machine-derived evader were in about the middle of the pack.