劣モジュラ最適化の概要と適用事例および実装例

maximize f(S)
subject to S ⊆ V, |S| ≤ k

import numpy as np

def distance(p1, p2):
    # 2つの点の距離を計算する関数
    return np.sqrt((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)

def uncovered_area(sensors, area):
    # エリア内の未監視領域の面積を計算する関数
    total_area = area[0] * area[1]
    covered_area = 0
    for x in range(area[0]):
        for y in range(area[1]):
            covered = False
            for sensor in sensors:
                if distance((x, y), sensor) <= sensor_range: covered = True break if not covered: covered_area += 1 return total_area - covered_area def greedy_sensor_placement(area, sensor_count, sensor_range): sensors = [] for i in range(sensor_count): best_sensor = None best_area = -np.inf for x in range(area[0]): for y in range(area[1]): if (x, y) not in sensors: sensors.append((x, y)) new_area = uncovered_area(sensors, area) if new_area > best_area:
                        best_area = new_area
                        best_sensor = (x, y)
                    sensors.remove((x, y))
        if best_sensor is not None:
            sensors.append(best_sensor)
    return sensors

# パラメータの設定
area_size = (10, 10)  # エリアのサイズ
sensor_count = 3  # センサーの数
sensor_range = 2  # センサーの通信範囲

# 最適なセンサーネットワークの配置を求める
sensors = greedy_sensor_placement(area_size, sensor_count, sensor_range)

# 結果の表示
print("最適なセンサーネットワークの配置:")
for sensor in sensors:
    print(sensor)

import numpy as np

def click_rate(selected_slots):
    # 選択された広告枠のクリック率を計算する関数
    total_clicks = sum(slot["clicks"] for slot in selected_slots)
    total_views = sum(slot["views"] for slot in selected_slots)
    return total_clicks / total_views

def revenue(selected_slots):
    # 選択された広告枠の収益を計算する関数
    total_revenue = sum(slot["revenue"] for slot in selected_slots)
    return total_revenue

def greedy_slot_selection(slots, budget, objective):
    selected_slots = []
    remaining_budget = budget
    while remaining_budget > 0 and slots:
        best_slot = None
        best_value = -np.inf if objective == "click_rate" else 0
        for slot in slots:
            if slot["cost"] <= remaining_budget: selected_slots.append(slot) if objective == "click_rate": new_value = click_rate(selected_slots) else: new_value = revenue(selected_slots) if new_value > best_value:
                    best_value = new_value
                    best_slot = slot
                selected_slots.pop()
        if best_slot is not None:
            selected_slots.append(best_slot)
            remaining_budget -= best_slot["cost"]
            slots.remove(best_slot)
    return selected_slots

# 広告枠のリスト (各広告枠は辞書として表現)
slots = [
    {"id": 1, "cost": 10, "clicks": 100, "views": 1000, "revenue": 50},
    {"id": 2, "cost": 20, "clicks": 120, "views": 1500, "revenue": 60},
    {"id": 3, "cost": 15, "clicks": 80, "views": 800, "revenue": 40},
    {"id": 4, "cost": 12, "clicks": 90, "views": 1200, "revenue": 45},
    {"id": 5, "cost": 18, "clicks": 110, "views": 1000, "revenue": 55},
]

# パラメータの設定
budget = 40  # 広告枠の予算
objective = "click_rate"  # 目的関数の選択 ("click_rate" or "revenue")

# 最適な広告枠の選択を求める
selected_slots = greedy_slot_selection(slots, budget, objective)

# 結果の表示
print("最適な広告枠の選択:")
for slot in selected_slots:
    print(slot["id"])

import numpy as np
from nltk.tokenize import sent_tokenize

def importance_score(sentence):
    # 文の重要度スコアを計算する関数
    # ここでは例として文の単語数を重要度としていますが、実際の問題に応じて適切な重要度スコアを定義してください
    return len(sentence.split())

def summary_selection(document, summary_length):
    sentences = sent_tokenize(document)  # 文章を文に分割する

    # 重要度スコアを計算
    importance_scores = [importance_score(sentence) for sentence in sentences]

    # 重要度スコアに基づいて文をソート
    sorted_sentences = [sentence for _, sentence in sorted(zip(importance_scores, sentences), reverse=True)]

    selected_sentences = []
    remaining_length = summary_length
    for sentence in sorted_sentences:
        if len(sentence.split()) <= remaining_length:
            selected_sentences.append(sentence)
            remaining_length -= len(sentence.split())
        if remaining_length <= 0:
            break

    return selected_sentences

# 入力文書
document = """
自然言語処理（Natural Language Processing, NLP）は、人間が普段使っている自然言語（日本語や英語など）をコンピュータで処理するための技術の総称です。NLPは、機械翻訳や情報検索、文書要約などの応用分野で活用されています。NLPの中でも、要約生成は重要なタスクの一つです。要約生成では、与えられた文章から短い要約を生成するため、代表的な文の選択が重要です。
"""

# 要約の長さ（選択する文の最大単語数）
summary_length = 20

# 代表的な文の選択を行い、要約を生成
selected_sentences = summary_selection(document, summary_length)

# 結果の表示
summary = " ".join(selected_sentences)
print("要約:")
print(summary)

def uncovered_elements(subsets, universe):
    # 未カバーの要素を返す関数
    uncovered = set(universe)
    for subset in subsets:
        uncovered -= set(subset)
    return uncovered

def greedy_set_cover(subsets, universe):
    selected_subsets = []
    remaining_elements = set(universe)
    while remaining_elements:
        best_subset = None
        best_coverage = -1
        for subset in subsets:
            coverage = len(set(subset) & remaining_elements)
            if coverage > best_coverage:
                best_coverage = coverage
                best_subset = subset
        if best_subset is not None:
            selected_subsets.append(best_subset)
            remaining_elements -= set(best_subset)
    return selected_subsets

# カバーセットのリスト
subsets = [
    [1, 2, 3, 4],
    [2, 4, 6],
    [1, 3, 5],
    [4, 5, 6],
    [1, 2, 5, 6]
]

# 全要素の集合（universe）
universe = [1, 2, 3, 4, 5, 6]

# 最小のカバーセットを求める
selected_subsets = greedy_set_cover(subsets, universe)

# 結果の表示
print("最小のカバーセット:")
for subset in selected_subsets:
    print(subset)