{ "cells": [ { "cell_type": "markdown", "id": "0c61266d", "metadata": {}, "source": [ "# Constrained Optimization\n", "\n", "## Overview, Objectives, and Key Terms\n", "\n", "In [Lesson 22](L22_UnconstrainedOptimization.ipynb), the question was simply, \"Where is the objective function best?\" That is already useful, but it is rarely the engineering question. Engineering problems usually sound more like this:\n", "\n", "> Find the best design we are allowed to use.\n", "\n", "A constraint is an engineering promise: do not exceed this dose, do not ask for a negative thickness, do not violate a balance law, do not use more material than the system can hold.\n", "\n", "### Objectives\n", "\n", "By the end of this lesson, you should be able to\n", "\n", "- identify design variables, objective functions, bounds, equality constraints, and inequality constraints,\n", "- translate technical specifications into the constraint convention used by `scipy.optimize.minimize`,\n", "- use `minimize` for small constrained optimization problems written as Python functions,\n", "- recognize when a problem is a linear program and use `scipy.optimize.linprog`,\n", "- check solver output for success, feasibility, active constraints, and units.\n", "\n", "### Key Terms\n", "\n", "- objective function\n", "- design variable\n", "- feasible region\n", "- bound\n", "- equality constraint\n", "- inequality constraint\n", "- active constraint\n", "- linear programming\n", "- `scipy.optimize.minimize`\n", "- `scipy.optimize.linprog`\n" ] }, { "cell_type": "markdown", "id": "3a60125b", "metadata": {}, "source": [ "## Start With the `minimize` Convention\n", "\n", "We will use `minimize` as the default language for constrained optimization. A typical problem is\n", "\n", "$$\n", " \\min_{\\mathbf{x}} f(\\mathbf{x})\n", "$$\n", "\n", "subject to inequality constraints\n", "\n", "$$\n", " g_i(\\mathbf{x}) \\ge 0,\n", "$$\n", "\n", "equality constraints\n", "\n", "$$\n", " h_j(\\mathbf{x}) = 0,\n", "$$\n", "\n", "and bounds\n", "\n", "$$\n", " \\mathbf{x}_{\\min} \\le \\mathbf{x} \\le \\mathbf{x}_{\\max}.\n", "$$\n", "\n", "In `minimize`, an old-style inequality constraint has `type: \"ineq\"`, and the function must return a value that is **nonnegative when the constraint is satisfied**. Equality constraints use `type: \"eq\"`, and the function should return zero when the equality is satisfied.\n", "\n", "That means the first job is translation. If a dose specification says $D(\\mathbf{x}) \\le D_{\\max}$, the `minimize` constraint function can be\n", "\n", "$$\n", " g(\\mathbf{x}) = D_{\\max} - D(\\mathbf{x}).\n", "$$\n", "\n", "Now the satisfied condition is $g(\\mathbf{x}) \\ge 0$.\n" ] }, { "cell_type": "markdown", "id": "19404369", "metadata": {}, "source": [ "## Where `linprog` Deviates\n", "\n", "`linprog` is not wrong; it just speaks a different dialect. It wants the linear-programming form\n", "\n", "$$\n", " \\min_{\\mathbf{x}} \\mathbf{c}^T\\mathbf{x}\n", "$$\n", "\n", "subject to matrix rows\n", "\n", "$$\n", " \\mathbf{A}_{ub}\\mathbf{x} \\le \\mathbf{b}_{ub}, \\qquad\n", " \\mathbf{A}_{eq}\\mathbf{x} = \\mathbf{b}_{eq},\n", "$$\n", "\n", "plus bounds. So a technical requirement like\n", "\n", "$$\n", " \\mu^T\\mathbf{x} \\ge R\n", "$$\n", "\n", "is passed to `linprog` as\n", "\n", "$$\n", " -\\mu^T\\mathbf{x} \\le -R.\n", "$$\n", "\n", "Same engineering statement, different solver convention.\n" ] }, { "cell_type": "markdown", "id": "fb3ff39a", "metadata": {}, "source": [ "## Picking the Right SciPy Tool\n", "\n", "Use `minimize` when the objective or constraints are most naturally written as Python functions. That includes nonlinear functions, tabulated models wrapped in interpolation, simulation-based objective functions, and cases where the feasible region is curved.\n", "\n", "Use `linprog` when the objective and constraint functions are linear functions of $\\mathbf{x}$, then `linprog` and the linear-programming form are probably clearer.\n", "\n", "The solver handles bookkeeping. We still own the variables, objective, and constraints.\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "688997c6", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:23.472713Z", "iopub.status.busy": "2026-07-07T18:13:23.472631Z", "iopub.status.idle": "2026-07-07T18:13:24.213468Z", "shell.execute_reply": "2026-07-07T18:13:24.213017Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import Bounds, linprog, minimize\n", "\n", "COLORS = {\n", " \"ink\": \"#1f2937\",\n", " \"muted\": \"#64748b\",\n", " \"grid\": \"#e5e7eb\",\n", " \"panel\": \"#fafaf7\",\n", " \"purple\": \"#512888\",\n", " \"orange\": \"#D55E00\",\n", " \"blue\": \"#2563eb\",\n", " \"green\": \"#059669\",\n", " \"red\": \"#dc2626\",\n", "}\n", "\n", "plt.rcParams.update({\n", " \"figure.facecolor\": \"white\",\n", " \"figure.figsize\": (8,3),\n", " \"axes.facecolor\": COLORS[\"panel\"],\n", " \"axes.edgecolor\": COLORS[\"muted\"],\n", " \"axes.labelcolor\": COLORS[\"ink\"],\n", " \"axes.titlecolor\": COLORS[\"ink\"],\n", " \"xtick.color\": COLORS[\"ink\"],\n", " \"ytick.color\": COLORS[\"ink\"],\n", " \"grid.color\": COLORS[\"grid\"],\n", " \"font.size\": 11,\n", "})\n", "\n", "\n", "def style_axes(ax):\n", " ax.grid(True, alpha=0.55)\n", " ax.spines[\"top\"].set_visible(False)\n", " ax.spines[\"right\"].set_visible(False)" ] }, { "cell_type": "markdown", "id": "d2bb1c9a", "metadata": {}, "source": [ "## Case Study 1: When Should We Count an Activated Sample?\n", "\n", "### Technical Specification\n", "\n", "A sample is removed from an irradiation position at $t=0$. We must choose when to start a fixed-live-time count. The target signal decays moderately slowly. The interfering signal has a short-lived component, which clears quickly, and a smaller long-lived/background component, which does not disappear as fast.\n", "\n", "Waiting can improve the target-to-interference balance at first, but waiting too long throws away the target. The detector also has a practical total-rate limit.\n", "\n", "Let $t$ be the delay, in hours, from sample removal to the start of counting. For this fixed live time, model the expected target and interfering counts as\n", "\n", "$$\n", "S(t) = 95e^{-t/28},\n", "$$\n", "\n", "$$\n", "B(t) = 220e^{-t/7} + 18e^{-t/85}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "id": "86202e96", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.214794Z", "iopub.status.busy": "2026-07-07T18:13:24.214649Z", "iopub.status.idle": "2026-07-07T18:13:24.217613Z", "shell.execute_reply": "2026-07-07T18:13:24.217243Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input block\n", "time bounds : 0 to 72 h\n", "minimum target : 20.0 relative counts\n", "maximum total rate : 85.0 relative count-rate units\n", "initial guess : 18.0 h\n" ] } ], "source": [ "# Input block: signal model and limits for a one-time counting decision.\n", "COUNTING_TIME_BOUNDS = (0.0, 72.0) # h after removal from irradiation position\n", "MIN_TARGET_COUNTS = 20.0 # relative counts\n", "MAX_TOTAL_RATE = 85.0 # relative count-rate units\n", "INITIAL_COUNTING_TIME = 18.0 # h\n", "\n", "\n", "def target_counts(t):\n", " return 95.0*np.exp(-t/28.0)\n", "\n", "\n", "def interfering_counts(t):\n", " return 220.0*np.exp(-t/7.0) + 18.0*np.exp(-t/85.0)\n", "\n", "\n", "def total_rate(t):\n", " return target_counts(t) + interfering_counts(t)\n", "\n", "\n", "def figure_of_merit(t):\n", " return target_counts(t) / np.sqrt(total_rate(t) + 1.0)\n", "\n", "\n", "print(\"Input block\")\n", "print(f\"time bounds : {COUNTING_TIME_BOUNDS[0]:.0f} to {COUNTING_TIME_BOUNDS[1]:.0f} h\")\n", "print(f\"minimum target : {MIN_TARGET_COUNTS:.1f} relative counts\")\n", "print(f\"maximum total rate : {MAX_TOTAL_RATE:.1f} relative count-rate units\")\n", "print(f\"initial guess : {INITIAL_COUNTING_TIME:.1f} h\")" ] }, { "cell_type": "markdown", "id": "75172e81", "metadata": {}, "source": [ "The plot below shows the tradeoff. The target fraction improves as the short-lived interference decays, but the target signal is also fading. These ratios help us see the physics; the optimization objective below uses a counting-statistics figure of merit." ] }, { "cell_type": "code", "execution_count": 3, "id": "68310ca5", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.218460Z", "iopub.status.busy": "2026-07-07T18:13:24.218366Z", "iopub.status.idle": "2026-07-07T18:13:24.385305Z", "shell.execute_reply": "2026-07-07T18:13:24.384777Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_plt = np.linspace(COUNTING_TIME_BOUNDS[0], COUNTING_TIME_BOUNDS[1], 400)\n", "c_target = target_counts(t_plt)\n", "c_interfering = interfering_counts(t_plt)\n", "c_total = total_rate(t_plt)\n", "\n", "fig, ax = plt.subplots(figsize=(8, 3), constrained_layout=True)\n", "ax.plot(t_plt, c_target/c_total, label=\"$S/(S+B)$\", ls=\"-\", color=COLORS[\"purple\"])\n", "ax.plot(t_plt, c_interfering/c_total, label=\"$B/(S+B)$\", ls=\"-.\", color=COLORS[\"orange\"])\n", "ax.plot(t_plt, c_target/c_interfering, label=\"$S/B$\", ls=\":\", color=COLORS[\"blue\"])\n", "ax.set_xlabel(\"time after irradiation [h]\")\n", "ax.set_ylabel(\"dimensionless signal measure\")\n", "ax.set_title(\"signal tradeoff before choosing an objective\")\n", "ax.legend(fontsize=8, loc=\"center right\")\n", "style_axes(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "135f4d6b", "metadata": {}, "source": [ "For this example, choose $0 \\le t \\le 72$ hr to maximize\n", "\n", "$$\n", "\\operatorname{FOM}(t) =\n", "\\frac{S(t)}{\\sqrt{S(t) + B(t) + 1}},\n", "$$\n", "\n", "where $S(t)$ is the target signal and $B(t)$ is the interfering signal. The denominator is a simple Poisson-style uncertainty proxy for the total count, with a small regularizing term.\n", "\n", "The constraints are:\n", "\n", "- target signal $S(t) \\ge 20$ relative counts,\n", "- total rate proxy $S(t) + B(t) \\le 85$ relative count-rate units.\n", "\n", "Because the objective and constraints are Python functions of time, this is a `minimize` problem." ] }, { "cell_type": "code", "execution_count": 4, "id": "7a5cb302", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.386478Z", "iopub.status.busy": "2026-07-07T18:13:24.386368Z", "iopub.status.idle": "2026-07-07T18:13:24.388780Z", "shell.execute_reply": "2026-07-07T18:13:24.388335Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model check\n", "t= 0 h: target= 95.00, total=333.00, FOM= 5.20\n", "t= 12 h: target= 61.89, total=117.14, FOM= 5.69\n", "t= 24 h: target= 40.32, total= 61.02, FOM= 5.12\n", "t= 48 h: target= 17.11, total= 27.57, FOM= 3.20\n" ] } ], "source": [ "# Model check block.\n", "t_sample = np.array([0.0, 12.0, 24.0, 48.0], dtype=float)\n", "target = target_counts(t_sample)\n", "interference = interfering_counts(t_sample)\n", "total = total_rate(t_sample)\n", "fom = figure_of_merit(t_sample)\n", "\n", "print(\"Model check\")\n", "for t, s, b, tot, f in zip(t_sample, target, interference, total, fom):\n", " print(f\"t={t:4.0f} h: target={s:6.2f}, total={tot:6.2f}, FOM={f:5.2f}\")" ] }, { "cell_type": "markdown", "id": "d062027b", "metadata": {}, "source": [ "### Translation to `minimize`\n", "\n", "`minimize` passes the decision variables as a vector. Here $x=[t]$, so the explicit inequality constraints are\n", "\n", "$$\n", "g_1(x) = S(x_0) - S_{\\min} \\ge 0,\n", "$$\n", "\n", "$$\n", "g_2(x) = R_{\\max} - [S(x_0)+B(x_0)] \\ge 0.\n", "$$\n", "\n", "The time limits $0 \\le x_0 \\le 72$ are passed separately as bounds. The objective is also translated because `minimize` minimizes:\n", "\n", "$$\n", "f(x) = -\\operatorname{FOM}(x_0).\n", "$$" ] }, { "cell_type": "code", "execution_count": 5, "id": "ce25b3a6", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.389779Z", "iopub.status.busy": "2026-07-07T18:13:24.389688Z", "iopub.status.idle": "2026-07-07T18:13:24.392527Z", "shell.execute_reply": "2026-07-07T18:13:24.392106Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Constraint translation at initial guess\n", "objective(x0) = -5.5050\n", "target-count margin g1(x0) = 29.9499\n", "rate-limit margin g2(x0) = 3.6716\n" ] } ], "source": [ "def counting_objective(x):\n", " return -float(figure_of_merit(x[0]))\n", "\n", "def enough_target_counts(x):\n", " # Technical spec: target_counts(t) >= MIN_TARGET_COUNTS\n", " # minimize ineq form: target_counts(t) - MIN_TARGET_COUNTS >= 0\n", " return float(target_counts(x[0]) - MIN_TARGET_COUNTS)\n", "\n", "\n", "def not_too_much_total_rate(x):\n", " # Technical spec: total_rate(t) <= MAX_TOTAL_RATE\n", " # minimize ineq form: MAX_TOTAL_RATE - total_rate(t) >= 0\n", " return float(MAX_TOTAL_RATE - total_rate(x[0]))\n", "\n", "\n", "counting_constraints = [\n", " {\"type\": \"ineq\", \"fun\": enough_target_counts},\n", " {\"type\": \"ineq\", \"fun\": not_too_much_total_rate},\n", "]\n", "counting_bounds = Bounds([COUNTING_TIME_BOUNDS[0]], [COUNTING_TIME_BOUNDS[1]])\n", "\n", "print(\"Constraint translation at initial guess\")\n", "x0_counting = np.array([INITIAL_COUNTING_TIME])\n", "print(f\"objective(x0) = {counting_objective(x0_counting): .4f}\")\n", "print(f\"target-count margin g1(x0) = {enough_target_counts(x0_counting): .4f}\")\n", "print(f\"rate-limit margin g2(x0) = {not_too_much_total_rate(x0_counting): .4f}\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "84bceaec", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.393395Z", "iopub.status.busy": "2026-07-07T18:13:24.393307Z", "iopub.status.idle": "2026-07-07T18:13:24.397015Z", "shell.execute_reply": "2026-07-07T18:13:24.396656Z" } }, "outputs": [], "source": [ "# Solve block.\n", "counting_solution = minimize(\n", " counting_objective,\n", " x0=np.array([INITIAL_COUNTING_TIME]),\n", " bounds=counting_bounds,\n", " constraints=counting_constraints,\n", " method=\"SLSQP\",\n", ")\n", "\n", "t_star = counting_solution.x[0]" ] }, { "cell_type": "code", "execution_count": 7, "id": "2fc606c2", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.397879Z", "iopub.status.busy": "2026-07-07T18:13:24.397795Z", "iopub.status.idle": "2026-07-07T18:13:24.400617Z", "shell.execute_reply": "2026-07-07T18:13:24.400221Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output block\n", "success: True\n", "message: Optimization terminated successfully\n", "t* = 17.189 h\n", "minimized objective -FOM = -5.544\n", "figure of merit = 5.544\n", "target counts = 51.42\n", "total rate proxy = 85.00\n", "target-count g1 : margin= 3.14e+01, active=False\n", "rate-limit g2 : margin=-2.84e-12, active=True\n", "lower time bound : margin= 1.72e+01, active=False\n", "upper time bound : margin= 5.48e+01, active=False\n" ] } ], "source": [ "# Output/check block.\n", "constraint_tol = 1e-8\n", "target_margin = enough_target_counts([t_star])\n", "rate_margin = not_too_much_total_rate([t_star])\n", "lower_bound_margin = t_star - COUNTING_TIME_BOUNDS[0]\n", "upper_bound_margin = COUNTING_TIME_BOUNDS[1] - t_star\n", "\n", "print(\"Output block\")\n", "print(f\"success: {counting_solution.success}\")\n", "print(f\"message: {counting_solution.message}\")\n", "print(f\"t* = {t_star:.3f} h\")\n", "print(f\"minimized objective -FOM = {counting_solution.fun:.3f}\")\n", "print(f\"figure of merit = {-counting_solution.fun:.3f}\")\n", "print(f\"target counts = {target_counts(t_star):.2f}\")\n", "print(f\"total rate proxy = {total_rate(t_star):.2f}\")\n", "\n", "for name, margin in [\n", " (\"target-count g1\", target_margin),\n", " (\"rate-limit g2\", rate_margin),\n", " (\"lower time bound\", lower_bound_margin),\n", " (\"upper time bound\", upper_bound_margin),\n", "]:\n", " active = np.isclose(margin, 0.0, atol=constraint_tol)\n", " print(f\"{name:18s}: margin={margin: .2e}, active={active}\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "bda3641f", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.401583Z", "iopub.status.busy": "2026-07-07T18:13:24.401493Z", "iopub.status.idle": "2026-07-07T18:13:24.529222Z", "shell.execute_reply": "2026-07-07T18:13:24.528649Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(COUNTING_TIME_BOUNDS[0], COUNTING_TIME_BOUNDS[1], 500)\n", "feasible = (\n", " (target_counts(t) >= MIN_TARGET_COUNTS)\n", " & (total_rate(t) <= MAX_TOTAL_RATE)\n", ")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 3.8), constrained_layout=True)\n", "ax = axes[0]\n", "ax.plot(t, target_counts(t), color=COLORS[\"blue\"], lw=2.5, label=\"target signal\")\n", "ax.plot(t, interfering_counts(t), color=COLORS[\"orange\"], lw=2.5, label=\"interference/background\")\n", "ax.plot(t, total_rate(t), color=COLORS[\"muted\"], lw=2, ls=\"--\", label=\"total rate proxy\")\n", "ax.axhline(MAX_TOTAL_RATE, color=COLORS[\"red\"], ls=\":\", lw=2, label=\"rate limit\")\n", "ax.axhline(MIN_TARGET_COUNTS, color=COLORS[\"green\"], ls=\":\", lw=2, label=\"minimum target\")\n", "ax.axvline(t_star, color=COLORS[\"purple\"], lw=2)\n", "ax.set_xlabel(\"time after irradiation [h]\")\n", "ax.set_ylabel(\"relative counts\")\n", "ax.set_title(\"signals and constraints\")\n", "ax.legend(fontsize=8, loc=\"upper right\")\n", "style_axes(ax)\n", "\n", "ax = axes[1]\n", "ax.fill_between(t, 0, figure_of_merit(t), where=feasible, color=COLORS[\"green\"], alpha=0.18, label=\"feasible window\")\n", "ax.fill_between(t, 0, figure_of_merit(t), where=~feasible, color=COLORS[\"red\"], alpha=0.10, label=\"infeasible\")\n", "ax.plot(t, figure_of_merit(t), color=COLORS[\"purple\"], lw=2.5, label=\"objective to maximize\")\n", "ax.plot(t_star, figure_of_merit(t_star), marker=\"*\", ms=16, color=COLORS[\"green\"], mec=COLORS[\"ink\"], label=\"chosen time\")\n", "ax.set_xlabel(\"time after irradiation [h]\")\n", "ax.set_ylabel(\"signal separation proxy\")\n", "ax.set_title(\"best feasible counting time\")\n", "ax.legend(fontsize=8, loc=\"upper right\")\n", "style_axes(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "61773c42", "metadata": {}, "source": [ "The rate-limit constraint is active: its margin is zero within numerical tolerance. The target-count constraint still has about 31 relative counts of slack, and neither time bound is active.\n", "\n", "Physically, the detector-rate limit forces us to wait until the short-lived interference has dropped far enough. After that point, waiting longer mostly throws away target signal, so the figure of merit is already decreasing." ] }, { "cell_type": "markdown", "id": "1ab16094", "metadata": {}, "source": [ "## Boundaries, Active Constraints, and a Tiny Bit of Theory\n", "\n", "For unconstrained optimization, we looked for places where the derivative or gradient vanished. With constraints, the optimum can sit on a boundary. In that case, the best feasible move may be no move at all, even if the unconstrained gradient is not zero.\n", "\n", "That idea is the beginning of the Karush-Kuhn-Tucker conditions, usually abbreviated KKT. For this course, the important picture is enough:\n", "\n", "- an interior optimum behaves like the unconstrained case,\n", "- a boundary optimum is held in place by one or more active constraints,\n", "- for convex problems, a local optimum has much stronger global meaning,\n", "- for nonconvex problems, the initial guess and sanity checks matter more.\n", "\n", "We do not need to turn KKT into another hand-calculation method. We need enough of it to read solver answers intelligently.\n" ] }, { "cell_type": "markdown", "id": "80120dd7", "metadata": {}, "source": [ "## Example 2: Minimum-Cost Shielding With a Nonlinear Dose Response\n", "\n", "### Technical Specification\n", "\n", "Now let $\\mathbf{x} = [x_w, x_s]^T$, where $x_w$ is water thickness and $x_s$ is steel thickness. The design goal is to minimize an installed cost index while keeping a dose-rate proxy below a design constraint.\n", "\n", "The dose model is inspired by point-kernel shielding calculations:\n", "\n", "$$\n", "D(\\mathbf{x}) = D_0 B(\\tau)e^{-\\tau},\n", "$$\n", "\n", "where $\\tau = \\mu_w x_w + \\mu_s x_s$ is the optical thickness and $B(\\tau)$ is a simple buildup factor. Real shielding work uses energy-dependent attenuation coefficients and buildup-factor data; here we keep a one-energy teaching surrogate so the optimization structure is visible.\n", "\n", "The technical constraints are:\n", "\n", "- shielded dose $\\le D_{\\max}$,\n", "- total added thickness $\\le 35$ cm,\n", "- $0 \\le x_w \\le 30$ cm,\n", "- $0 \\le x_s \\le 8$ cm.\n", "\n", "This is a `minimize` problem because the dose response includes thickness-dependent buildup.\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "198c992d", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.530236Z", "iopub.status.busy": "2026-07-07T18:13:24.530135Z", "iopub.status.idle": "2026-07-07T18:13:24.532949Z", "shell.execute_reply": "2026-07-07T18:13:24.532506Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input block\n", "dose limit : 2.00 mrem/h\n", "mu values : water=0.086 cm^-1, steel=0.580 cm^-1\n", "cost coefficients : water=1.0, steel=8.0\n", "thickness limits : total <= 35.0 cm, steel <= 8.0 cm\n" ] } ], "source": [ "# Input block: technical specification for a simplified gamma-shielding problem.\n", "# Variables are x = [water thickness, steel thickness], both in cm.\n", "D0 = 100.0 # mrem/h, unshielded dose-rate proxy\n", "D_LIMIT = 2.0 # mrem/h, design dose-rate constraint\n", "MU = np.array([0.086, 0.58]) # cm^-1, rounded one-energy teaching values\n", "BETA_BUILDUP = 0.25 # simple buildup-factor coefficient\n", "MATERIAL_COST = np.array([1.0, 8.0]) # relative cost per cm for water and steel\n", "BULK_PENALTY = 0.005 # installed bulk/space penalty\n", "MAX_TOTAL_THICKNESS = 35.0 # cm\n", "MAX_WATER_THICKNESS = 30.0 # cm\n", "MAX_STEEL_THICKNESS = 8.0 # cm\n", "INITIAL_SHIELD = np.array([20.0, 5.0])\n", "\n", "print(\"Input block\")\n", "print(f\"dose limit : {D_LIMIT:.2f} mrem/h\")\n", "print(f\"mu values : water={MU[0]:.3f} cm^-1, steel={MU[1]:.3f} cm^-1\")\n", "print(f\"cost coefficients : water={MATERIAL_COST[0]:.1f}, steel={MATERIAL_COST[1]:.1f}\")\n", "print(f\"thickness limits : total <= {MAX_TOTAL_THICKNESS:.1f} cm, steel <= {MAX_STEEL_THICKNESS:.1f} cm\")\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "40f1cb03", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.533812Z", "iopub.status.busy": "2026-07-07T18:13:24.533727Z", "iopub.status.idle": "2026-07-07T18:13:24.537346Z", "shell.execute_reply": "2026-07-07T18:13:24.537001Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x=[0. 0.]: dose=100.0000 mrem/h, cost= 0.00, tau= 0.00\n", "x=[20. 5.]: dose= 2.1233 mrem/h, cost= 63.12, tau= 4.62\n", "x=[30. 3.5]: dose= 2.1421 mrem/h, cost= 63.61, tau= 4.61\n" ] } ], "source": [ "# Response model block: point-kernel-inspired attenuation with a simple buildup factor.\n", "# This is a screening-level teaching model, not a shielding design standard.\n", "def optical_thickness(x):\n", " x = np.asarray(x, dtype=float)\n", " return float(MU @ x)\n", "\n", "\n", "def buildup_factor(x):\n", " tau = optical_thickness(x)\n", " return 1.0 + BETA_BUILDUP*tau\n", "\n", "\n", "def shielded_dose(x):\n", " tau = optical_thickness(x)\n", " return D0*buildup_factor(x)*np.exp(-tau)\n", "\n", "\n", "def shield_cost(x):\n", " x = np.asarray(x, dtype=float)\n", " return float(MATERIAL_COST @ x + BULK_PENALTY*np.sum(x)**2)\n", "\n", "\n", "for x in [np.array([0.0, 0.0]), INITIAL_SHIELD, np.array([30.0, 3.5])]:\n", " print(f\"x={x}: dose={shielded_dose(x):7.4f} mrem/h, cost={shield_cost(x):7.2f}, tau={optical_thickness(x):5.2f}\")\n" ] }, { "cell_type": "markdown", "id": "37cb7fe9", "metadata": {}, "source": [ "### Translation to `minimize`\n", "\n", "The dose constraint is nonlinear, so it stays as a Python function:\n", "\n", "$$\n", " g_1(\\mathbf{x}) = D_{\\max} - D(\\mathbf{x}) \\ge 0.\n", "$$\n", "\n", "The thickness constraint becomes\n", "\n", "$$\n", " g_2(\\mathbf{x}) = 45 - x_c - x_l \\ge 0.\n", "$$\n", "\n", "The nonnegative thicknesses and material upper limits are cleaner as bounds.\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "68be1b41", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.538231Z", "iopub.status.busy": "2026-07-07T18:13:24.538150Z", "iopub.status.idle": "2026-07-07T18:13:24.540651Z", "shell.execute_reply": "2026-07-07T18:13:24.540265Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Constraint translation at initial guess\n", "objective(x0) = 63.1250\n", "dose margin g1(x0) = -0.1233\n", "thickness g2(x0) = 10.0000\n" ] } ], "source": [ "# Translation block: turn design limits into minimize constraints.\n", "def dose_margin(x):\n", " # Technical spec: shielded_dose(x) <= D_LIMIT\n", " # minimize ineq form: D_LIMIT - shielded_dose(x) >= 0\n", " return float(D_LIMIT - shielded_dose(x))\n", "\n", "\n", "def total_thickness_margin(x):\n", " # Technical spec: x_water + x_steel <= MAX_TOTAL_THICKNESS\n", " return float(MAX_TOTAL_THICKNESS - np.sum(x))\n", "\n", "\n", "shield_bounds = Bounds([0.0, 0.0], [MAX_WATER_THICKNESS, MAX_STEEL_THICKNESS])\n", "shield_constraints = [\n", " {\"type\": \"ineq\", \"fun\": dose_margin},\n", " {\"type\": \"ineq\", \"fun\": total_thickness_margin},\n", "]\n", "\n", "print(\"Constraint translation at initial guess\")\n", "print(f\"objective(x0) = {shield_cost(INITIAL_SHIELD): .4f}\")\n", "print(f\"dose margin g1(x0) = {dose_margin(INITIAL_SHIELD): .4f}\")\n", "print(f\"thickness g2(x0) = {total_thickness_margin(INITIAL_SHIELD): .4f}\")\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "452b9ba4", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.541516Z", "iopub.status.busy": "2026-07-07T18:13:24.541435Z", "iopub.status.idle": "2026-07-07T18:13:24.545585Z", "shell.execute_reply": "2026-07-07T18:13:24.545141Z" } }, "outputs": [], "source": [ "# Solve block.\n", "shield_solution = minimize(\n", " shield_cost,\n", " x0=INITIAL_SHIELD,\n", " bounds=shield_bounds,\n", " constraints=shield_constraints,\n", " method=\"SLSQP\",\n", ")\n", "\n", "x_shield = shield_solution.x\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "c6faa4e3", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.546528Z", "iopub.status.busy": "2026-07-07T18:13:24.546442Z", "iopub.status.idle": "2026-07-07T18:13:24.548823Z", "shell.execute_reply": "2026-07-07T18:13:24.548363Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output block\n", "success: True\n", "message: Optimization terminated successfully\n", "water thickness = 16.179 cm\n", "steel thickness = 5.683 cm\n", "cost index = 64.034\n", "dose proxy = 2.000000 mrem/h\n", "dose margin = 4.41e-12\n", "thickness margin= 1.31e+01\n", "optical thickness tau = 4.688\n" ] } ], "source": [ "# Output/check block.\n", "print(\"Output block\")\n", "print(f\"success: {shield_solution.success}\")\n", "print(f\"message: {shield_solution.message}\")\n", "print(f\"water thickness = {x_shield[0]:.3f} cm\")\n", "print(f\"steel thickness = {x_shield[1]:.3f} cm\")\n", "print(f\"cost index = {shield_solution.fun:.3f}\")\n", "print(f\"dose proxy = {shielded_dose(x_shield):.6f} mrem/h\")\n", "print(f\"dose margin = {dose_margin(x_shield):.2e}\")\n", "print(f\"thickness margin= {total_thickness_margin(x_shield):.2e}\")\n", "print(f\"optical thickness tau = {optical_thickness(x_shield):.3f}\")\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "fee64607", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.549674Z", "iopub.status.busy": "2026-07-07T18:13:24.549590Z", "iopub.status.idle": "2026-07-07T18:13:24.805781Z", "shell.execute_reply": "2026-07-07T18:13:24.805352Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "water = np.linspace(0.0, MAX_WATER_THICKNESS, 240)\n", "steel = np.linspace(0.0, MAX_STEEL_THICKNESS, 200)\n", "W, S = np.meshgrid(water, steel)\n", "D = np.vectorize(lambda w, s: shielded_dose([w, s]))(W, S)\n", "K = np.vectorize(lambda w, s: shield_cost([w, s]))(W, S)\n", "feasible = (D <= D_LIMIT) & (W + S <= MAX_TOTAL_THICKNESS)\n", "\n", "fig, ax = plt.subplots(figsize=(7.2, 4.8), constrained_layout=True)\n", "ax.contourf(W, S, feasible, levels=[-0.5, 0.5, 1.5], colors=[\"white\", COLORS[\"green\"]], alpha=0.18)\n", "cost_contours = ax.contour(W, S, K, levels=10, colors=COLORS[\"purple\"], linewidths=1.0, alpha=0.75)\n", "ax.clabel(cost_contours, fmt=\"%.0f\", fontsize=8)\n", "dose_contour = ax.contour(W, S, D, levels=[D_LIMIT], colors=COLORS[\"orange\"], linewidths=3)\n", "ax.clabel(dose_contour, fmt={D_LIMIT: \"dose limit\"}, fontsize=9)\n", "ax.plot(x_shield[0], x_shield[1], marker=\"*\", ms=18, color=COLORS[\"green\"], mec=COLORS[\"ink\"], label=\"constrained optimum\")\n", "ax.set_xlim(0, MAX_WATER_THICKNESS)\n", "ax.set_ylim(0, MAX_STEEL_THICKNESS)\n", "ax.set_xlabel(\"water thickness [cm]\")\n", "ax.set_ylabel(\"steel thickness [cm]\")\n", "ax.set_title(\"nonlinear dose response with buildup\")\n", "ax.legend(fontsize=8, loc=\"upper right\")\n", "style_axes(ax)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "5fbbbf3c", "metadata": {}, "source": [ "The orange curve is the dose limit. The feasible region is on the safe side of that curve. The purple curves are cost contours, and the optimizer is trying to find the lowest cost contour that still touches the feasible region.\n", "\n", "The numerical coefficients are illustrative. The modeling lesson is real: dose constraints often come from attenuation and buildup calculations, and those constraints are usually easier to express first as physical requirements and then translate into solver form.\n" ] }, { "cell_type": "markdown", "id": "16797316", "metadata": {}, "source": [ "## Example 3: A Linear Attenuation-Budget Model for `linprog`\n", "\n", "### Technical Specification\n", "\n", "Now use a lower-fidelity shielding model. If we ignore thickness-dependent buildup, or reserve for it with a fixed conservative factor, the exponential attenuation model can be converted to a linear optical-thickness requirement:\n", "\n", "$$\n", " \\mu_w x_w + \\mu_s x_s \\ge \\log\\left(\\frac{F D_0}{D_{\\max}}\\right),\n", "$$\n", "\n", "where $F$ is a fixed reserve factor. This is the same idea behind HVL/TVL budgeting: attenuation requirements are linear in shield thickness once we work in log transmission.\n", "\n", "Water is cheap but bulky. Steel is compact but expensive. The design constraints are:\n", "\n", "- optical thickness supplied $\\ge \\log(2D_0/D_{\\max})$ using a fixed reserve factor of 2,\n", "- total thickness $\\le 35$ cm,\n", "- water thickness $\\le 30$ cm,\n", "- steel thickness $\\le 8$ cm,\n", "- nonnegative thicknesses.\n", "\n", "Because the objective and all constraints are linear rows, this is a `linprog` problem. If the buildup factor varies with thickness, we are back in `minimize` territory.\n" ] }, { "cell_type": "code", "execution_count": 15, "id": "708fc853", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.806823Z", "iopub.status.busy": "2026-07-07T18:13:24.806712Z", "iopub.status.idle": "2026-07-07T18:13:24.809070Z", "shell.execute_reply": "2026-07-07T18:13:24.808697Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input block\n", "fixed buildup reserve : 2.0\n", "required tau : 4.605\n", "total thickness : <= 35.0 cm\n", "water/steel limits : water <= 30.0 cm, steel <= 8.0 cm\n" ] } ], "source": [ "# Input block: linearized attenuation budget for the same shielding materials.\n", "BUILDUP_RESERVE = 2.0\n", "REQUIRED_TAU = np.log(BUILDUP_RESERVE*D0/D_LIMIT)\n", "LP_TOTAL_THICKNESS = 35.0\n", "LP_MAX_WATER = 30.0\n", "LP_MAX_STEEL = 8.0\n", "LP_COST = MATERIAL_COST\n", "\n", "print(\"Input block\")\n", "print(f\"fixed buildup reserve : {BUILDUP_RESERVE:.1f}\")\n", "print(f\"required tau : {REQUIRED_TAU:.3f}\")\n", "print(f\"total thickness : <= {LP_TOTAL_THICKNESS:.1f} cm\")\n", "print(f\"water/steel limits : water <= {LP_MAX_WATER:.1f} cm, steel <= {LP_MAX_STEEL:.1f} cm\")\n" ] }, { "cell_type": "markdown", "id": "fe18aaab", "metadata": {}, "source": [ "### Translation to `linprog`\n", "\n", "The attenuation row is a $\\ge$ constraint in the technical specification, but `linprog` wants $\\mathbf{A}_{ub}\\mathbf{x} \\le \\mathbf{b}_{ub}$. Multiply that row by $-1$.\n", "\n", "The other engineering limits are already $\\le$ rows.\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "9115f201", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.809870Z", "iopub.status.busy": "2026-07-07T18:13:24.809782Z", "iopub.status.idle": "2026-07-07T18:13:24.812746Z", "shell.execute_reply": "2026-07-07T18:13:24.812199Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "linprog rows\n", "attenuation : [-0.086 -0.58 ] <= -4.605\n", "total thickness : [1. 1.] <= 35.000\n", "water bound : [1. 0.] <= 30.000\n", "steel bound : [0. 1.] <= 8.000\n" ] } ], "source": [ "# Translation block: linprog uses A_ub @ x <= b_ub, so >= rows must be multiplied by -1.\n", "# Technical spec: MU[0]*water + MU[1]*steel >= REQUIRED_TAU\n", "# linprog row: -MU[0]*water - MU[1]*steel <= -REQUIRED_TAU\n", "c_lp = LP_COST\n", "A_ub_lp = np.array([\n", " [-MU[0], -MU[1]], # attenuation budget >= REQUIRED_TAU\n", " [1.0, 1.0], # total thickness <= LP_TOTAL_THICKNESS\n", " [1.0, 0.0], # water thickness <= LP_MAX_WATER\n", " [0.0, 1.0], # steel thickness <= LP_MAX_STEEL\n", "])\n", "b_ub_lp = np.array([\n", " -REQUIRED_TAU,\n", " LP_TOTAL_THICKNESS,\n", " LP_MAX_WATER,\n", " LP_MAX_STEEL,\n", "])\n", "\n", "row_names = [\"attenuation\", \"total thickness\", \"water bound\", \"steel bound\"]\n", "print(\"linprog rows\")\n", "for name, row, rhs in zip(row_names, A_ub_lp, b_ub_lp):\n", " print(f\"{name:16s}: {row} <= {rhs:.3f}\")\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "3ef58e9a", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.813588Z", "iopub.status.busy": "2026-07-07T18:13:24.813507Z", "iopub.status.idle": "2026-07-07T18:13:24.831250Z", "shell.execute_reply": "2026-07-07T18:13:24.830786Z" } }, "outputs": [], "source": [ "# Solve block.\n", "lp_solution = linprog(\n", " c_lp,\n", " A_ub=A_ub_lp,\n", " b_ub=b_ub_lp,\n", " bounds=[(0.0, None), (0.0, None)],\n", " method=\"highs\",\n", ")\n", "\n", "x_lp = lp_solution.x\n", "active_lp = np.isclose(lp_solution.slack, 0.0, atol=1e-8)\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "8b415830", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.832316Z", "iopub.status.busy": "2026-07-07T18:13:24.832220Z", "iopub.status.idle": "2026-07-07T18:13:24.834604Z", "shell.execute_reply": "2026-07-07T18:13:24.834263Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output block\n", "success: True\n", "message: Optimization terminated successfully. (HiGHS Status 7: Optimal)\n", "water thickness = 30.000 cm\n", "steel thickness = 3.492 cm\n", "cost index = 57.933\n", "slacks\n", " attenuation : slack= 0.000, active=True\n", " total thickness : slack= 1.508, active=False\n", " water bound : slack= 0.000, active=True\n", " steel bound : slack= 4.508, active=False\n", "tau supplied = 4.605\n" ] } ], "source": [ "# Output/check block.\n", "print(\"Output block\")\n", "print(f\"success: {lp_solution.success}\")\n", "print(f\"message: {lp_solution.message}\")\n", "print(f\"water thickness = {x_lp[0]:.3f} cm\")\n", "print(f\"steel thickness = {x_lp[1]:.3f} cm\")\n", "print(f\"cost index = {lp_solution.fun:.3f}\")\n", "print(\"slacks\")\n", "for name, slack, active in zip(row_names, lp_solution.slack, active_lp):\n", " print(f\" {name:16s}: slack={slack:8.3f}, active={active}\")\n", "print(f\"tau supplied = {MU @ x_lp:.3f}\")\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "be3417c5", "metadata": { "execution": { "iopub.execute_input": "2026-07-07T18:13:24.835433Z", "iopub.status.busy": "2026-07-07T18:13:24.835349Z", "iopub.status.idle": "2026-07-07T18:13:24.926990Z", "shell.execute_reply": "2026-07-07T18:13:24.926500Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "water = np.linspace(0.0, 35.0, 360)\n", "steel = np.linspace(0.0, 8.5, 260)\n", "W, S = np.meshgrid(water, steel)\n", "feasible_lp = (\n", " (MU[0]*W + MU[1]*S >= REQUIRED_TAU)\n", " & (W + S <= LP_TOTAL_THICKNESS)\n", " & (W <= LP_MAX_WATER)\n", " & (S <= LP_MAX_STEEL)\n", ")\n", "\n", "fig, ax = plt.subplots(figsize=(7.2, 4.8), constrained_layout=True)\n", "ax.contourf(W, S, feasible_lp, levels=[-0.5, 0.5, 1.5], colors=[\"white\", COLORS[\"green\"]], alpha=0.22)\n", "ax.plot(water, (REQUIRED_TAU - MU[0]*water)/MU[1], color=COLORS[\"orange\"], lw=2.6, label=\"attenuation requirement\")\n", "ax.plot(water, LP_TOTAL_THICKNESS - water, color=COLORS[\"muted\"], lw=2.0, ls=\"--\", label=\"total thickness\")\n", "ax.axvline(LP_MAX_WATER, color=COLORS[\"muted\"], lw=2.0, ls=\":\", label=\"water limit\")\n", "ax.axhline(LP_MAX_STEEL, color=COLORS[\"muted\"], lw=2.0, ls=\"-.\", label=\"steel limit\")\n", "for level, alpha in [(45.0, 0.35), (lp_solution.fun, 0.9), (70.0, 0.35)]:\n", " ax.plot(water, (level - LP_COST[0]*water)/LP_COST[1], color=COLORS[\"purple\"], lw=1.8, alpha=alpha)\n", "ax.annotate(\"lower cost\", xy=(28, 1.5), xytext=(21, 5.9),\n", " arrowprops={\"arrowstyle\": \"->\", \"color\": COLORS[\"purple\"], \"lw\": 1.8},\n", " color=COLORS[\"purple\"])\n", "ax.plot(x_lp[0], x_lp[1], marker=\"*\", ms=18, color=COLORS[\"green\"], mec=COLORS[\"ink\"], label=\"LP optimum\")\n", "ax.set_xlim(0, 35)\n", "ax.set_ylim(0, 8.5)\n", "ax.set_xlabel(\"water thickness [cm]\")\n", "ax.set_ylabel(\"steel thickness [cm]\")\n", "ax.set_title(\"linear log-attenuation model: cheap/bulky vs compact/expensive\")\n", "ax.legend(fontsize=8, loc=\"upper right\")\n", "style_axes(ax)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "e276be0d", "metadata": {}, "source": [ "For a two-variable linear program, the picture is the lesson: the constraints carve out a polygon, and the objective line slides until it hits the last feasible corner. In higher dimensions the picture is harder to draw, but the bookkeeping idea is the same.\n", "\n", "Here the LP approximation uses as much cheap water as allowed, then adds enough compact steel to meet the log-attenuation requirement. That is the competition the simplified model is resolving.\n" ] }, { "cell_type": "markdown", "id": "b5a394bc", "metadata": {}, "source": [ "## A Practical Decision Rule\n", "\n", "If you can write the problem as rows of a matrix, use the row-based tool.\n", "\n", "- `minimize`: nonlinear objective, nonlinear constraints, simulation or model functions, curved feasible regions.\n", "- `linprog`: linear objective, linear equality/inequality rows, bounds.\n", "\n", "If you are unsure, start by writing down the variables and units. Then write the objective in one line. Then write each constraint as a sentence before translating it into code. A surprising number of optimization mistakes are translation mistakes, not algorithm mistakes.\n" ] }, { "cell_type": "markdown", "id": "11dd20a7", "metadata": {}, "source": [ "## Reading Solver Output\n", "\n", "A useful solver result is not just the vector `x`. At minimum, inspect:\n", "\n", "- `success` and `message`,\n", "- the objective value at the proposed optimum,\n", "- the constraint values at the proposed optimum,\n", "- active constraints, usually visible through near-zero slack,\n", "- whether the result changes when you try a reasonable different initial guess for nonlinear problems.\n", "\n", "Do not report an optimization answer without a feasibility check. The number is not the answer until it has survived the check.\n" ] }, { "cell_type": "markdown", "id": "d4a425cd", "metadata": {}, "source": [ "## Further Reading\n", "\n", "- SciPy documentation for [`scipy.optimize.minimize`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html)\n", "- SciPy documentation for [`scipy.optimize.linprog`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html)\n", "- Shultis and Faw, [*Radiation Shielding*](https://books.google.com/books/about/Radiation_Shielding.html?id=HiN3QgAACAAJ), American Nuclear Society, for point-kernel shielding, attenuation, and buildup-factor context\n", "- Health Physics Society, [*Shielding of Gamma Radiation*](https://hps.org/wp-content/uploads/2024/12/shielding_of_gamma_radiation.pdf), for a compact discussion of buildup factors and shield-thickness calculations\n", "- NIST XCOM, [X-Ray Mass Attenuation Coefficients](https://www.nist.gov/pml/x-ray-mass-attenuation-coefficients), for attenuation data context\n", "- ANSI/ANS-6.4.3 material attenuation and buildup-factor data, and [later revision work](https://impact.ornl.gov/en/publications/revision-of-ansians-643/), for where engineering buildup-factor data come from\n", "- NRC, [Regulatory Analysis Guidelines](https://www.nrc.gov/about-nrc/regulatory/rulemaking/regulatory-analysis), and DOE, [ALARA cost-benefit guide](https://www.energy.gov/sites/prod/files/2014/04/f14/alara-v1.pdf), for cost-dose trade-study context\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.13" }, "ne415_schedule": { "lesson": "L23", "notes": "Optimization with constraints", "worksheet": "W23" } }, "nbformat": 4, "nbformat_minor": 5 }