Improve support for vehicle routing

informarte · May 1, 2021 · 8eee363 · 8eee363
1 parent 899311d
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diff --git a/README.md b/README.md
@@ -8,8 +8,9 @@
 * Yuck's approach to problem solving is based in local search.
 * Yuck implements Boolean, integer, and integer set variables, see [FlatZinc support](#flatzinc-support).
 * Yuck implements many global constraints and their reified counterparts, see [Global constraints](#global-constraints).
+* Yuck comes with support for vehicle routing, see [Extending Yuck for Vehicle Routing](https://github.com/informarte/yuck/releases/download/20210501/Extending_Yuck_for_Vehicle_Routing.pdf).
 * Yuck features a mechanism to turn Boolean MiniZinc expressions (including applications of global constraints) into soft constraints, see [bool2costs](#bool2costs).
-* Yuck supports lexicographic multi-objective optimization, see [goal hierarchies](#goal-hierarchies).
+* Yuck supports lexicographic multi-objective optimization, see [Goal hierarchies](#goal-hierarchies).
 * Yuck is provided under the terms of the [Mozilla Public License 2.0](https://www.mozilla.org/en-US/MPL/2.0).
 * Yuck ranked second among local-search solvers at the [MiniZinc Challenge 2017](http://www.minizinc.org/challenge2017/results2017.html), the [MiniZinc Challenge 2018](http://www.minizinc.org/challenge2018/results2018.html), and the [MiniZinc Challenge 2019](http://www.minizinc.org/challenge2019/results2019.html), and it won a gold medal at the [MiniZinc Challenge 2020](https://www.minizinc.org/challenge2020/results2020.html).
 

diff --git a/resources/mzn/lib/verification/yuck/delivery.mzn b/resources/mzn/lib/verification/yuck/delivery.mzn
@@ -0,0 +1 @@
+../../yuck/delivery.mzn
diff --git a/resources/mzn/lib/verification/yuck/domain.mzn b/resources/mzn/lib/verification/yuck/domain.mzn
@@ -0,0 +1 @@
+../../yuck/domain.mzn
diff --git a/resources/mzn/lib/verification/yuck/fzn_delivery.mzn b/resources/mzn/lib/verification/yuck/fzn_delivery.mzn
@@ -0,0 +1,30 @@
+predicate fzn_delivery(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime)
+=
+    let {
+        set of int: Nodes = index_set(succ),
+        bool: WithServiceTimes = index_set(ServiceTimes) != {},
+        bool: WithTravelTimes = index_set_1of2(TravelTimes) != {}
+    }
+    in forall(i in Nodes diff EndNodes)(
+        let {
+            var int: j = succ[i],
+            var int: st = if WithServiceTimes then ServiceTimes[i] else 0 endif,
+            var int: tt = if WithTravelTimes then TravelTimes[i, j] else 0 endif,
+            var int: t = arrivalTimes[i] + st + tt,
+            var int: u = arrivalTimes[j]
+        }
+        in if WithWaiting then u >= t else u = t endif
+    )
+    /\
+    (if WithTravelTimes
+     then totalTravelTime = sum(i in Nodes diff EndNodes)(TravelTimes[i, succ[i]])
+     else totalTravelTime = 0
+     endif);
diff --git a/resources/mzn/lib/verification/yuck/fzn_delivery_reif.mzn b/resources/mzn/lib/verification/yuck/fzn_delivery_reif.mzn
@@ -0,0 +1,33 @@
+predicate fzn_delivery_reif(
+    set of int: StartNodes,
+    set of int: CityNodes,
+    array[int] of var int: succ,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime,
+    var bool: satisfied)
+=
+    satisfied
+    <->
+    let {
+        set of int: Nodes = index_set(succ),
+        bool: WithServiceTimes = index_set(ServiceTimes) != {},
+        bool: WithTravelTimes = index_set_1of2(TravelTimes) != {}
+    }
+    in forall(i in Nodes diff EndNodes)(
+        let {
+            var int: j = succ[i],
+            var int: st = if WithServiceTimes then ServiceTimes[i] else 0 endif,
+            var int: tt = if WithTravelTimes then TravelTimes[i, j] else 0 endif,
+            var int: t = arrivalTimes[i] + st + tt,
+            var int: u = arrivalTimes[j]
+        }
+        in if WithWaiting then u >= t else u = t endif
+    )
+    /\
+    (if WithTravelTimes
+     then totalTravelTime = sum(i in Nodes diff EndNodes)(TravelTimes[i, succ[i]])
+     else totalTravelTime = 0
+     endif);
diff --git a/resources/mzn/lib/verification/yuck/fzn_domain.mzn b/resources/mzn/lib/verification/yuck/fzn_domain.mzn
@@ -0,0 +1,2 @@
+predicate fzn_domain(array[int] of var int: x, set of int: d) =
+    forall(i in index_set(x))(x[i] in d);
diff --git a/resources/mzn/lib/verification/yuck/giant_tour.mzn b/resources/mzn/lib/verification/yuck/giant_tour.mzn
@@ -0,0 +1 @@
+../../yuck/giant_tour.mzn
diff --git a/resources/mzn/lib/yuck/delivery.mzn b/resources/mzn/lib/yuck/delivery.mzn
@@ -0,0 +1,84 @@
+include "fzn_delivery.mzn";
+include "fzn_delivery_reif.mzn";
+include "giant_tour.mzn";
+
+function bool: delivery_requirements_are_met(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes) :: promise_total
+=
+    let {
+        set of int: Nodes = index_set(succ)
+    }
+    in giant_tour_requirements_are_met(StartNodes, EndNodes, succ)
+    /\ index_set(arrivalTimes) = Nodes
+    /\ (index_set(ServiceTimes) = {} \/ index_set(ServiceTimes) = Nodes)
+    /\ ((index_set_1of2(TravelTimes) = {} /\ index_set_2of2(TravelTimes) = {}) \/
+        (index_set_1of2(TravelTimes) = Nodes /\ index_set_2of2(TravelTimes) = Nodes));
+
+/**
+  Helps with solving single-depot vehicle-routing problems with or without
+  time windows.
+
+  Requires the model to be based on the giant-tour representation where,
+  in addition to the city nodes, there is a pair of start and end nodes
+  for each vehicle.
+
+  Constrains the arrival times to consider the given travel times:
+
+    delivery(StartNodes, EndNodes, succ, arrivalTimes, ServiceTimes, TravelTimes, WithWaiting, totalTravelTime)
+
+  is equivalent to
+
+    let {
+        set of int: Nodes = index_set(succ)
+    }
+    in forall(i in Nodes diff EndNodes)(
+        let {
+            var int: j = succ[i],
+            var int: t = arrivalTimes[i] + ServiceTimes[i] + TravelTimes[i, j],
+            var int: u = arrivalTimes[j]
+        }
+        in if WithWaiting then u >= t else u = t endif
+    )
+    /\
+    totalTravelTime = sum(i in Nodes diff EndNodes)(TravelTimes[i, succ[i]]);
+*/
+predicate delivery(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime)
+=
+    assert(
+        delivery_requirements_are_met(StartNodes, EndNodes, succ, arrivalTimes, ServiceTimes, TravelTimes),
+        "delivery requirements not met",
+        fzn_delivery(StartNodes, EndNodes, succ, arrivalTimes, ServiceTimes, TravelTimes, WithWaiting, totalTravelTime));
+
+/**
+  Reified version of delivery
+ */
+predicate delivery_reif(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime,
+    var bool: satisfied)
+=
+    assert(
+        delivery_requirements_are_met(StartNodes, EndNodes, succ, arrivalTimes, ServiceTimes, TravelTimes),
+        "delivery_reif requirements not met",
+        fzn_delivery_reif(
+            StartNodes, EndNodes, succ, arrivalTimes, ServiceTimes, TravelTimes, WithWaiting, totalTravelTime,
+            satisfied));
diff --git a/resources/mzn/lib/yuck/domain.mzn b/resources/mzn/lib/yuck/domain.mzn
@@ -0,0 +1,4 @@
+include "fzn_domain.mzn";
+
+predicate domain(array[int] of var int: x, set of int: d) =
+    fzn_domain(x, d);
diff --git a/resources/mzn/lib/yuck/fzn_circuit.mzn b/resources/mzn/lib/yuck/fzn_circuit.mzn
@@ -3,5 +3,4 @@ include "alldifferent.mzn";
 predicate yuck_circuit(array [int] of var int: succ, int: offset);
 
 predicate fzn_circuit(array [int] of var int: succ) =
-    forall(i in index_set(succ))(succ[i] in index_set(succ) diff {i}) /\
     yuck_circuit(succ, min(index_set(succ)));
diff --git a/resources/mzn/lib/yuck/fzn_delivery.mzn b/resources/mzn/lib/yuck/fzn_delivery.mzn
@@ -0,0 +1,30 @@
+include "yuck.mzn";
+
+predicate yuck_delivery(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    int: offset,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime);
+
+predicate fzn_delivery(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime)
+=
+    let {
+        int: offset = min(index_set(succ))
+    }
+    in yuck_delivery(
+        StartNodes, EndNodes, succ, offset, arrivalTimes, ServiceTimes, TravelTimes, WithWaiting, totalTravelTime)
+        :: defines_vars([arrivalTimes[i] | i in index_set(arrivalTimes) diff StartNodes])
+        :: defines_var(totalTravelTime);
diff --git a/resources/mzn/lib/yuck/fzn_delivery_reif.mzn b/resources/mzn/lib/yuck/fzn_delivery_reif.mzn
@@ -0,0 +1,34 @@
+include "yuck.mzn";
+
+predicate yuck_delivery_reif(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    int: offset,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime,
+    var bool: satisfied);
+
+predicate fzn_delivery_reif(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ,
+    array[int] of var int: arrivalTimes,
+    array[int] of int: ServiceTimes,
+    array[int, int] of int: TravelTimes,
+    bool: WithWaiting,
+    var int: totalTravelTime,
+    var bool: satisfied)
+=
+    let {
+        int: offset = min(index_set(succ))
+    }
+    in yuck_delivery_reif(
+        StartNodes, EndNodes, succ, offset, arrivalTimes, ServiceTimes, TravelTimes, WithWaiting, totalTravelTime,
+        satisfied)
+        :: defines_vars([arrivalTimes[i] | i in index_set(arrivalTimes) diff StartNodes])
+        :: defines_var(totalTravelTime)
+        :: defines_var(satisfied);
diff --git a/resources/mzn/lib/yuck/fzn_domain.mzn b/resources/mzn/lib/yuck/fzn_domain.mzn
@@ -0,0 +1,4 @@
+predicate yuck_int_domain(array[int] of var int: x, set of int: d);
+
+predicate fzn_domain(array[int] of var int: x, set of int: d) =
+    yuck_int_domain(x, d);
diff --git a/resources/mzn/lib/yuck/giant_tour.mzn b/resources/mzn/lib/yuck/giant_tour.mzn
@@ -0,0 +1,35 @@
+include "circuit.mzn";
+include "domain.mzn";
+
+function bool: giant_tour_requirements_are_met(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ) :: promise_total
+=
+    let {
+        set of int: Nodes = index_set(succ)
+    }
+    in StartNodes != {}
+    /\ card(StartNodes) = card(EndNodes)
+    /\ max(StartNodes) < min(EndNodes)
+    /\ StartNodes subset Nodes
+    /\ EndNodes subset Nodes
+    /\ dom_array(succ) subset Nodes;
+
+% Hamiltonian circuit where start nodes succeed end nodes
+predicate giant_tour(
+    set of int: StartNodes,
+    set of int: EndNodes,
+    array[int] of var int: succ)
+=
+    let {
+        set of int: Nodes = index_set(succ),
+        int: K = card(StartNodes)
+    }
+    in assert(
+        giant_tour_requirements_are_met(StartNodes, EndNodes, succ),
+        "giant tour requirements not met",
+        circuit(succ)
+        /\ forall(i in 1..(K - 1))(succ[min(EndNodes) + i - 1] = min(StartNodes) + i)
+        /\ succ[max(EndNodes)] = min(StartNodes)
+        /\ domain([succ[i] | i in Nodes diff EndNodes], Nodes diff StartNodes));
diff --git a/resources/mzn/tests/front-end-tests/A-n37-k5.dzn b/resources/mzn/tests/front-end-tests/A-n37-k5.dzn
@@ -0,0 +1,47 @@
+% CVRP instance A-n37-k5 by Augerat et al.
+
+N = 36;
+MinK = 5;
+Capacity = 100;
+
+TravelTimes = array2d(0..N, 0..N, [|
+   0,  21,  58,  17,  33,  49,  70,  21,  55,  55,  48,  70,  36,  34,  42,   3,  12,  37,  53,  60,  56,   6,  26,  44,  47,  42,  35,  62,  34,  29,  29,  37,  30,  46,  14,  47,  17 |
+  21,   0,  37,  19,  45,  41,  54,  30,  47,  42,  29,  56,  16,  26,  22,  23,  17,  18,  67,  39,  37,  16,  22,  27,  35,  47,  51,  52,  52,  50,  43,  56,  49,  45,  34,  59,  38 |
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+  17,  19,  53,   0,  51,  58,  73,  37,  37,  39,  48,  54,  33,  43,  31,  17,  25,  26,  48,  52,  45,  19,  36,  31,  31,  29,  33,  45,  36,  40,  25,  40,  35,  59,  22,  40,  26 |
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+  36,  16,  22,  33,  55,  37,  41,  41,  50,  42,  16,  52,   0,  26,  16,  38,  30,  15,  81,  26,  27,  31,  27,  23,  37,  59,  66,  54,  67,  65,  57,  71,  65,  47,  49,  73,  53 |
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+  53,  67,  99,  48,  78, 102, 120,  71,  58,  68,  96,  83,  81,  87,  76,  50,  65,  72,   0,  97,  87,  59,  79,  73,  63,  27,  19,  65,  25,  42,  24,  23,  30,  98,  40,   8,  40 |
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+  42,  47,  75,  29,  74,  87, 100,  63,  31,  41,  75,  56,  59,  72,  51,  40,  53,  48,  27,  71,  61,  46,  65,  47,  36,   0,  26,  39,  34,  48,  20,  35,  37,  87,  36,  19,  38 |
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+  34,  52,  88,  36,  53,  81, 103,  49,  63,  69,  81,  85,  67,  67,  67,  31,  45,  63,  25,  88,  81,  40,  59,  67,  62,  34,   9,  71,   0,  17,  15,   4,   5,  75,  19,  24,  17 |
+  29,  50,  87,  40,  38,  71,  97,  37,  73,  77,  76,  93,  65,  59,  70,  27,  38,  64,  42,  89,  84,  35,  50,  71,  70,  48,  25,  81,  17,   0,  28,  19,  12,  62,  18,  41,  14 |
+  29,  43,  77,  25,  57,  78,  96,  49,  47,  54,  72,  70,  57,  63,  55,  26,  41,  50,  24,  76,  68,  35,  55,  53,  48,  20,   9,  55,  15,  28,   0,  17,  17,  74,  18,  18,  19 |
+  37,  56,  92,  40,  56,  85, 107,  52,  65,  72,  84,  88,  71,  71,  71,  34,  49,  66,  23,  92,  84,  44,  62,  70,  65,  35,   9,  73,   4,  19,  17,   0,   8,  78,  23,  23,  21 |
+  30,  49,  86,  35,  48,  77, 100,  44,  64,  70,  77,  86,  65,  63,  66,  27,  41,  61,  30,  87,  80,  36,  55,  66,  63,  37,  13,  72,   5,  12,  17,   8,   0,  70,  16,  29,  13 |
+  46,  45,  61,  59,  27,  16,  46,  26,  92,  87,  41,  98,  47,  21,  63,  48,  34,  60,  98,  69,  73,  41,  23,  69,  80,  87,  79,  97,  75,  62,  74,  78,  70,   0,  57,  93,  58 |
+  14,  34,  71,  22,  39,  62,  84,  31,  57,  60,  62,  76,  49,  48,  52,  12,  26,  47,  40,  72,  66,  21,  40,  53,  52,  36,  21,  65,  19,  18,  18,  23,  16,  57,   0,  36,   4 |
+  47,  59,  91,  40,  74,  96, 113,  67,  50,  60,  88,  75,  73,  81,  68,  45,  59,  64,   8,  89,  79,  53,  73,  65,  55,  19,  16,  57,  24,  41,  18,  23,  29,  93,  36,   0,  36 |
+  17,  38,  75,  26,  38,  64,  87,  32,  60,  64,  65,  80,  53,  50,  56,  15,  29,  51,  40,  76,  71,  24,  42,  57,  56,  38,  21,  68,  17,  14,  19,  21,  13,  58,   4,  36,   0 |
+|]);
+
+Demands = array1d(1..N, [16, 18, 1, 13, 8, 23, 7, 27, 1, 3, 6, 24, 19, 2, 5, 16, 7, 4, 22, 7, 23, 16, 2, 2, 9, 2, 12, 1, 9, 23, 6, 19, 7, 7, 20, 20]);
diff --git a/resources/mzn/tests/front-end-tests/cvrp.mzn b/resources/mzn/tests/front-end-tests/cvrp.mzn
@@ -0,0 +1,22 @@
+% Capacitated VRP
+
+include "vrp.mzn";
+
+% maximum number of vehicles/ tours
+float: MaxKToMinKRatio;
+MaxK = min(N, floor(MinK * MaxKToMinKRatio));
+
+% arrival times
+constraint forall(i in StartNodes)(arrivalTimes[i] = 0);
+
+% demands
+array [CityNodes] of int: Demands;
+array[Nodes] of int: GiantTourDemands = [if i in CityNodes then Demands[i] else 0 endif | i in Nodes];
+
+% vehicle capacities and loads
+int: Capacity;
+set of int: Load = 0..Capacity;
+array[Nodes] of var Load: loads;
+constraint forall(i in StartNodes)(loads[i] = 0);
+predicate track_loads();
+constraint track_loads();
diff --git a/resources/mzn/tests/front-end-tests/delivery_reif_test.mzn b/resources/mzn/tests/front-end-tests/delivery_reif_test.mzn
@@ -0,0 +1,17 @@
+include "delivery.mzn";
+include "yuck.mzn";
+
+include "tsptw.mzn";
+include "n20w20.001.dzn";
+
+predicate track_times() =
+    bool2costs(
+        delivery(StartNodes, EndNodes, succ, arrivalTimes, [], GiantTourTravelTimes, true, totalTravelTime),
+        0);
+
+solve satisfy;
+
+output [
+    "totalTravelTime = ", show(totalTravelTime), ",\n",
+    "arrivalTimes = ", show(arrivalTimes), ",\n",
+    "succ = ", show(succ)];