Improve annealer performance by about 4-fold.

...as measured on tuning readability:

    Got to 14.74 4x faster.
    Got to 11.97 in 7 vs. 27 minutes (3.8x faster).
    Got to 11.85 in 8 vs. 69 minutes (8.6x faster).

We do this by adding caching of solution costs (hit rate ≈ 90% for the sort of single-coefficient-at-a-time nudging we've often used, 3% for the coeff-swapping approach of the bin-packing problem). We also make sure to report the best-encountered solution rather than merely the one that's current when time runs out.

At the moment, the caching leaks memory since entries never expire, but the leakage is bounded by the max iterations of the annealer and is insignificant in practice. It is an open question why cache hit rate for readability is near zero: comparable single-coeff-nudgers yield a higher rate, and we wouldn't expect such a speedup for a low one. Stochasticity could be a factor.

Also allow the annealer hyperparameters to be modified through constructor params. I haven't yet found any that are both faster and better, but various useful balances are achievable, like [10643.296506954695, 113.30886882813805, 0.023803813406736214, 4.231731642265747], which finds solutions about half as good but finds them 32x faster.

optimizers.js

@@ -1,7 +1,7 @@
 const {readFileSync} = require('fs');
 const {basename, join} = require('path');
 
-const {dirsIn, staticDom} = require('./utils');
+const {dirsIn, setDefault, staticDom} = require('./utils');
 
 
 // This is based on public-domain code from
@@ -21,11 +21,11 @@ const {dirsIn, staticDom} = require('./utils');
  * as the algorithim progresses.
  */
 class Annealer {
-    constructor() {
-        this.INITIAL_TEMPERATURE = 5000;
-        this.COOLING_STEPS = 5000;
-        this.COOLING_FRACTION = 0.95;
-        this.STEPS_PER_TEMP = 1000;
+    constructor(initialTemperature = 5000, coolingSteps = 5000, coolingFraction = .95, stepsPerTemp = 1000) {
+        this.INITIAL_TEMPERATURE = initialTemperature;
+        this.COOLING_STEPS = coolingSteps;
+        this.COOLING_FRACTION = coolingFraction;
+        this.STEPS_PER_TEMP = stepsPerTemp;
         this.BOLTZMANNS = 1.3806485279e-23;
     }
 
@@ -38,21 +38,36 @@ class Annealer {
     anneal() {
         let temperature = this.INITIAL_TEMPERATURE;
         let currentSolution = this.initialSolution();
+        let bestSolution = currentSolution;
         let currentCost = this.solutionCost(currentSolution);
+        let bestCost = currentCost;
         let m = 0;
         let n = 0;
+        let hits = 0, misses = 0;
+        const seenSolutions = new Map();  // solution => cost
         for (let i = 0; i < this.COOLING_STEPS; i++) {
             console.log('Cooling step', i, 'of', this.COOLING_STEPS, '...');
             const startCost = currentCost;
             for (let j = 0; j < this.STEPS_PER_TEMP; j++) {
                 let newSolution = this.randomTransition(currentSolution);
-                let newCost = this.solutionCost(newSolution);
+                if (seenSolutions.has(newSolution.toString())) {
+                    hits += 1;
+                } else {
+                    misses += 1;
+                }
+                let newCost = setDefault(seenSolutions, newSolution.toString(), () => this.solutionCost(newSolution));
 
                 if (newCost < currentCost) {
+                    // Always take improvements.
                     currentCost = newCost;
                     currentSolution = newSolution;
-                    console.log('New best solution is ', newSolution, ' with fitness ', newCost);
+                    if (newCost < bestCost) {
+                        bestCost = newCost;
+                        bestSolution = newSolution;
+                        console.log('New best solution is ', newSolution, ' with cost ', newCost);
+                    }
                 } else {
+                    // Sometimes take non-improvements.
                     const minusDelta = currentCost - newCost;
                     const merit = Math.exp(minusDelta / (this.BOLTZMANNS * temperature));
                     if (merit > Math.random()) {
@@ -68,7 +83,9 @@ class Annealer {
             temperature *= this.COOLING_FRACTION;
         }
         console.log('Iterations:', n, 'using', m, 'jumps.');
-        return currentSolution;
+        console.log('Cache hits', hits, 'misses', misses);
+        console.log('Cache hit rate', hits/(hits + misses));
+        return bestSolution;
     }
 
     /**