Satellite scheduling app

src/lava/lib/optimization/apps/scheduler/problems.py

@@ -0,0 +1,329 @@
+# Copyright (C) 2023 Intel Corporation
+# SPDX-License-Identifier: BSD-3-Clause
+# See: https://spdx.org/licenses/
+
+
+from typing import Optional, Union
+import numpy as np
+import networkx as ntx
+
+import matplotlib.pyplot as plt
+from matplotlib.patches import PathPatch
+from matplotlib.path import Path
+
+
+class SchedulingProblem:
+    def __init__(self,
+                 num_agents: int = 3,
+                 num_tasks: int = 3,
+                 sat_cutoff: Union[float, int] = 0.99,
+                 seed: int = 42):
+        """Schedule `num_tasks` tasks among `num_agents` agents such that
+        every agent performs exactly one task and every task gets assigned
+        to exactly one agent.
+
+        Parameters
+        ----------
+        num_agents (int) : number of agents available to perform all tasks.
+        Default is arbitrarily chosen as 3.
+
+        num_tasks (int) : number of tasks to be performed. Default is
+        arbitrarily chosen as 3.
+
+        sat_cutoff (float or int) : If provided as a float, it is interpreted
+        as satisfiability cut-off, which is the ratio between the number
+        of tasks for which an agent gets assigned to the total number of
+        tasks. Needs to be a fraction between 0 and 1 in this case.
+        If provided as an int, this is the target cost for the underlying QUBO
+        solver. Default is 0.99 (i.e., 99% of the total number of tasks get
+        assigned an agent).
+
+        seed (int) : Seed for PRNG used in problem generation.
+        """
+        self._num_agents = num_agents
+        self._agent_ids = range(num_agents)
+        self._agent_attrs = None
+        self._num_tasks = num_tasks
+        self._task_ids = range(num_tasks)
+        self._task_attrs = None
+        self._sat_cutoff = sat_cutoff
+        self.graph = None
+        self.adjacency = None
+        self._random_seed = seed
+
+    @property
+    def num_agents(self):
+        return self._num_agents
+
+    @num_agents.setter
+    def num_agents(self, val: int):
+        self._num_agents = val
+
+    @property
+    def agent_ids(self):
+        return self._agent_ids
+
+    @property
+    def agent_attrs(self):
+        return self._agent_attrs
+
+    @agent_attrs.setter
+    def agent_attrs(self, attr_vec):
+        self._agent_attrs = attr_vec
+
+    @property
+    def num_tasks(self):
+        return self._num_tasks
+
+    @num_tasks.setter
+    def num_tasks(self, val: int):
+        self._num_tasks = val
+
+    @property
+    def task_ids(self):
+        return self._task_ids
+
+    @property
+    def task_attrs(self):
+        return self._task_attrs
+
+    @task_attrs.setter
+    def task_attrs(self, attr_vec):
+        self._task_attrs = attr_vec
+
+    @property
+    def sat_cutoff(self):
+        return self._sat_cutoff
+
+    @sat_cutoff.setter
+    def sat_cutoff(self, val: float):
+        self._sat_cutoff = val
+
+    @property
+    def random_seed(self):
+        return self._random_seed
+
+    @random_seed.setter
+    def random_seed(self, val: int):
+        self._random_seed = val
+
+    def is_node_valid(self, *args):
+        """Checks if a node is valid to be included in the problem graph.
+
+        Over-ridden by derived child classes to suit their purpose. The base
+        class method always returns True, indicating that all nodes are valid
+        in the case of a base Scheduling Problem.
+        """
+        return True
+
+    def is_edge_conflicting(self, node1, node2):
+        nodes = self.graph.nodes
+        is_same_agent = (nodes[node1]["agent_id"] == nodes[node2]["agent_id"])
+        is_same_task = (nodes[node1]["task_id"] == nodes[node2]["task_id"])
+        return True if is_same_agent or is_same_task else False
+
+    def generate(self, seed=None):
+        """ Generate a new scheduler problem. """
+        if self.random_seed:
+            np.random.seed(self.random_seed)
+        if not self.random_seed or seed != self.random_seed:
+            # set seed only if it's different
+            self.random_seed = seed
+            np.random.seed(seed)
+        self.graph = ntx.Graph()
+        self._generate_valid_nodes()
+        self._generate_edges_from_constraints()
+        self._rescale_adjacency()
+
+    def _generate_valid_nodes(self):
+        """Generate nodes and check if they are valid before adding them to
+        the problem graph.
+        """
+        node_id = 0
+        if self.agent_attrs is None:
+            self.agent_attrs = np.reshape(self.agent_ids,
+                                          (len(self.agent_ids), 1))
+        agent_id_attr_map = dict(zip(self.agent_ids, self.agent_attrs))
+        if self.task_attrs is None:
+            self.task_attrs = (
+                np.tile(np.reshape(self.task_ids,
+                                   (len(self.task_ids), 1)), (1, 2)))
+        task_id_attr_map = dict(zip(self.task_ids, self.task_attrs))
+        for aid, a_attr in agent_id_attr_map.items():  # for all agents
+            for tid, t_attr in task_id_attr_map.items():  # for all tasks
+                # Check if (agent, task) is a valid node
+                if self.is_node_valid(aid, tid):
+                    # If it is, add it to the problem graph
+                    self.graph.add_node(node_id,
+                                        agent_id=aid,
+                                        task_id=tid,
+                                        agent_attr=a_attr,
+                                        task_attr=t_attr)
+                    node_id += 1
+
+    def _generate_edges_from_constraints(self):
+        num_nodes = len(self.graph.nodes)
+        self.adjacency = (
+            np.zeros((num_nodes, num_nodes), dtype=int))
+        for n1 in self.graph.nodes:
+            for n2 in self.graph.nodes:
+                not_same = n1 != n2
+                is_conflict = self.is_edge_conflicting(n1, n2)
+                if not_same and is_conflict:
+                    self.graph.add_edge(n1, n2)
+                    self.adjacency[n1, n2] = 1
+
+    def _rescale_adjacency(self):
+        """ Scale the adjacency matrix weights for QUBO solver. """
+        self.adjacency = np.triu(self.adjacency)
+        self.adjacency += self.adjacency.T - 2 * np.diag(
+            self.adjacency.diagonal())
+
+
+class SatelliteScheduleProblem(SchedulingProblem):
+    """
+    SatelliteScheduleProblem is a synthetic scheduling problem in which a
+    number of vehicles must be assigned to view as many requests in a
+    2-dimensional plane as possible. Each vehicle moves horizontally across
+    the plane, has minimum and maximum view angle, and has a maximum rotation
+    rate (i.e. the rate at which the vehicle can reorient vertically from one
+    target to the next).
+
+    The problem is represented as an infeasibility graph and can be solved by
+    finding the Maximum Independent Set.
+
+    Parameters
+    ----------
+    num_satellites : int, default = 6
+        The number of satellites to generate schedules for.
+    view_height : float, default = 0.25
+        The range from minimum to maximum viewable angle for each satellite.
+    view_coords : Optional[np.ndarray], default = None
+        The view coordinates (i.e. minimum viewable angle) for each
+        satellite in a numpy array. If None, view coordinates will be
+        evenly distributed across the viewable range.
+    num_requests : int, default = 48
+        The number of requests to generate.
+    turn_rate : float, default = 2
+        How quickly each satellite may reorient its view angle.
+    solution_criteria : float, default = 0.99
+        The target for a successful solution. The solver will stop
+        looking for a better schedule if the specified fraction of
+        requests is satisfied.
+    """
+
+    def __init__(
+            self,
+            num_satellites: int = 6,
+            view_height: float = 0.25,
+            view_coords: Optional[np.ndarray] = None,
+            num_requests: int = 48,
+            requests: Optional[np.ndarray] = None,
+            turn_rate: float = 2,
+            solution_criteria: float = 0.99,
+            seed: int = 42,
+    ):
+        """ Create a SatelliteScheduleProblem.
+        """
+        super(SatelliteScheduleProblem,
+              self).__init__(num_agents=num_satellites,
+                             num_tasks=num_requests,
+                             sat_cutoff=solution_criteria,
+                             seed=seed)
+        self.num_satellites = self.num_agents
+        self.num_requests = self.num_tasks
+
+        self.view_height = view_height * (1 / (num_satellites - 1))
+        if view_coords is None:
+            self.view_coords = np.linspace(0,
+                                           1,
+                                           num_satellites)
+        else:
+            self.view_coords = view_coords
+        self.agent_attrs = list(zip([self.view_height] * num_satellites,
+                                    self.view_coords))
+        self.satellites = self.agent_ids
+        self.turn_rate = turn_rate
+        self.requests = None
+        self.qubo_problem = None
+        self.generate_requests(requests)
+        self.request_density = self.requests.shape[0] / (1 + self.view_height)
+
+    def generate_requests(self, requests=None) -> None:
+        """ Generate a random set of requests in the 2D plane. """
+        if requests is not None:
+            self.requests = requests
+        else:
+            np.random.seed(self.random_seed)
+            self.requests = np.random.random((self.num_requests, 2))
+            self.requests[:, 1] = (1 + self.view_height) * (
+                self.requests[:, 1]) - (self.view_height / 2)
+            order = np.argsort(self.requests[:, 0])
+            self.requests = self.requests[order, :]
+        self.task_attrs = self.requests.tolist()
+
+    def is_node_valid(self, sat_id, req_id):
+        """ Return whether the request is visible to the satellite. """
+        view_height = self.agent_attrs[sat_id][0]
+        satellite_y_coord = self.agent_attrs[sat_id][1]
+        request_y_coord = self.task_attrs[req_id][1]
+        lower_bound = satellite_y_coord - view_height / 2
+        upper_bound = satellite_y_coord + view_height / 2
+        return lower_bound <= request_y_coord <= upper_bound
+
+    def is_req_reachable(self, n1, n2):
+        nodes = self.graph.nodes
+        n1_req_coords = nodes[n1]["task_attr"]
+        n2_req_coords = nodes[n2]["task_attr"]
+        delta_x = abs(n1_req_coords[0] - n2_req_coords[0])
+        delta_y = abs(n1_req_coords[1] - n2_req_coords[1])
+        return self.turn_rate * delta_x >= delta_y
+
+    def is_edge_conflicting(self, node1, node2):
+        nodes = self.graph.nodes
+        is_same_satellite = (nodes[node1]["agent_id"] == nodes[node2][
+            "agent_id"])
+        is_same_request = (nodes[node1]["task_id"] == nodes[node2]["task_id"])
+        return is_same_request or (is_same_satellite and not
+                                   self.is_req_reachable(node1, node2))
+
+    def plot_problem(self):
+        """ Plot the problem state using pyplot. """
+        plt.figure(figsize=(12, 4), dpi=120)
+        plt.subplot(131)
+        plt.scatter(self.requests[:, 0],
+                    self.requests[:, 1],
+                    s=2)
+        for y in self.view_coords:
+            codes = [Path.MOVETO, Path.LINETO, Path.LINETO, Path.CLOSEPOLY]
+            verts = [[-0.05, y],
+                     [0.05, y + self.view_height / 2],
+                     [0.05, y - self.view_height / 2],
+                     [-0.05, y]]
+            plt.gca().add_patch(
+                PathPatch(Path(verts, codes), ec='none', alpha=0.3,
+                          fc='lightblue'))
+            plt.scatter([-0.05], [y],  # + self.view_height / 2
+                        s=10, marker='s', c='gray')
+            plt.plot([0, 1],
+                     [y,  # + self.view_height / 2
+                      y],  # + self.view_height / 2],
+                     'C1--', lw=0.75)
+        plt.xticks([])
+        plt.yticks([])
+        plt.title(
+            f'Schedule {self.num_satellites} satellites to observe '
+            f'{self.num_requests} targets.')
+        plt.subplot(132)
+        ntx.draw_networkx(self.graph, with_labels=False,
+                          node_size=2, width=0.5)
+        plt.title(
+            f'Infeasibility graph with {self.graph.number_of_nodes()} nodes.')
+        plt.subplot(133)
+        plt.imshow(self.adjacency, aspect='auto')
+        plt.title(
+            f'Adjacency matrix has {self.adjacency.mean():.2%} '
+            f'connectivity.')
+        plt.yticks([])
+        plt.tight_layout()
+        plt.show()