优化建模
Optimization modeling
Formulate and solve LP/MIP/scheduling problems to a verified optimum.
20 条本项目编写的提案 · 分类 v1.1 · 新增基准运行 0 次。下方验证方式与部分得分规则是设计，不是执行结果。
- 典型应用
- Gurobi · OR-Tools · AMPL · Excel Solver
- 小类 GUI 需求标签
CL· CLI 足够
任务提案 · 20
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R03.07.01.01-T01 Production planning LP
原始指令
Using fixtures/opt/products.csv (per-product profit, machine-hours, and labor) and the resource limits in limits.txt, formulate and solve an LP that maximizes total profit. Write the optimal production quantities and objective to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools · Gurobi
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 2 / 5
建议验证方式
solution.json objective equals the reference optimum within 1e-6 relative; all resource constraints satisfied; reported quantities feasible and matching an optimal vertex. Graded by re-solving and checking objective + feasibility.
建议部分得分
30% feasible plan; 30% constraints satisfied; 40% objective = optimum
R03.07.01.01-T02 Least-cost diet blending LP
原始指令
Given fixtures/opt/ingredients.csv (cost and nutrient content per unit) and nutrient minimums/maximums in diet_reqs.csv, build and solve an LP minimizing cost while meeting every nutrient bound. Output the ingredient amounts and total cost to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools · AMPL
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
Objective within 1e-6 of the reference minimum; all nutrient min/max constraints satisfied; solution re-verified feasible. Graded by re-solve + feasibility check.
建议部分得分
30% feasible blend; 30% all nutrient bounds met; 40% cost = optimum
R03.07.01.01-T03 Transportation problem
原始指令
From fixtures/opt/supply.csv, demand.csv, and cost_matrix.csv, solve the balanced transportation LP minimizing shipping cost. Write the shipment matrix and total cost to solution.json. Handle any supply-demand imbalance with a dummy node if needed.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools · Gurobi
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
Total cost within 1e-6 of the reference optimum; row sums = supply, column sums = demand; shipments nonnegative. Graded by re-solve + balance checks.
建议部分得分
30% feasible shipment plan; 30% supply/demand balance; 40% cost = optimum
R03.07.01.01-T04 Assignment problem
原始指令
Given the worker-task cost matrix in fixtures/opt/assign.csv, solve the assignment problem minimizing total cost (one worker per task, one task per worker). Output the assignment pairs and cost to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 2 / 5
建议验证方式
Objective equals the reference optimum exactly (integral costs); assignment is a perfect matching. Graded by re-solve + matching validity.
建议部分得分
50% valid perfect matching; 50% cost = optimum
R03.07.01.01-T05 0/1 knapsack MIP
原始指令
From fixtures/opt/items.csv (value, weight) and the capacity in knap.txt, solve the 0/1 knapsack as a MIP maximizing value. Write the chosen item set and objective to solution.json; the model must use binary variables.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools · Gurobi
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
Objective equals the reference optimum; total weight <= capacity; selected variables binary; MIP gap 0. Graded by re-solve + feasibility.
建议部分得分
30% feasible selection; 30% within capacity; 40% value = optimum (gap 0)
R03.07.01.01-T06 Cutting-stock minimization
原始指令
Given stock length and the order of pieces (length, quantity) in fixtures/opt/cutting.csv, minimize the number of stock bars used via a MIP (or column generation). Output the chosen cutting patterns, their counts, and the total bars to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- Gurobi · OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
licensed· 授权专业软件- 提案难度
- 3 / 5
建议验证方式
Total bars equals the reference optimum; each pattern fits within stock length; piece demands fully met. Graded by re-solve + pattern/demand validation.
建议部分得分
30% valid patterns; 30% demand met; 40% bar count = optimum
R03.07.01.01-T07 Capacitated facility location
原始指令
Using fixtures/opt/facilities.csv (open cost, capacity), customers.csv (demand), and ship_cost.csv, solve a capacitated facility-location MIP minimizing open + shipping cost. Output which facilities open and the customer assignments to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- Gurobi · AMPL
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
licensed· 授权专业软件- 提案难度
- 4 / 5
建议验证方式
Objective equals the reference optimum (gap 0); capacity not exceeded at any open facility; every customer served; open vars binary. Graded by re-solve + capacity/assignment checks.
建议部分得分
25% feasible assignment; 25% capacity respected; 20% all demand served; 30% cost = optimum
R03.07.01.01-T08 Capacitated vehicle routing
原始指令
From fixtures/opt/cvrp.json (depot, customer demands, vehicle capacity, distance matrix), solve the CVRP minimizing total distance with OR-Tools routing. Output the per-vehicle routes and total distance to solution.json; no route may exceed capacity.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
long· 长流程- 提案难度
- 5 / 5
建议验证方式
Every customer visited exactly once; each route starts/ends at depot and respects capacity; total distance is within 2% of the reference best-known. Graded by route validation + distance recompute.
建议部分得分
30% all customers visited once; 30% capacity respected; 40% distance within 2 percent of reference
R03.07.01.01-T09 Nurse shift scheduling (CP)
原始指令
Using fixtures/opt/nurses.json (staff, shifts, coverage minimums, max consecutive shifts, days off requests), build a CP-SAT model that produces a feasible 2-week roster meeting all hard constraints and maximizing satisfied requests. Output the roster to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
long· 长流程- 提案难度
- 5 / 5
建议验证方式
All hard constraints hold (coverage per shift, max-consecutive, rest rules); the satisfied-request count equals the reference optimum (or within the stated bound). Graded by constraint validation + objective.
建议部分得分
40% feasible roster (hard constraints); 30% coverage minimums; 30% requests = optimum
R03.07.01.01-T10 Job-shop makespan minimization
原始指令
From fixtures/opt/jobshop.json (jobs, ordered operations, machine, duration), build a CP-SAT model minimizing makespan. Output the start time of every operation and the makespan to solution.json; no machine may run two operations at once.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
long· 长流程- 提案难度
- 5 / 5
建议验证方式
Precedence within each job respected; no machine overlap; makespan equals the reference optimum (or proven bound). Graded by schedule validation + makespan.
建议部分得分
30% precedence respected; 30% no machine overlap; 40% makespan = optimum
R03.07.01.01-T11 Set covering
原始指令
Given fixtures/opt/cover.csv (candidate sets and the elements each covers) and per-set costs, solve a set-covering MIP that covers every element at minimum cost. Output the chosen sets and total cost to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools · Gurobi
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
Every element covered by at least one chosen set; objective equals the reference optimum (gap 0). Graded by coverage check + objective.
建议部分得分
50% full coverage; 50% cost = optimum
R03.07.01.01-T12 Multi-commodity flow
原始指令
From fixtures/opt/network.json (nodes, arcs with capacity and cost, commodities with source/sink/demand), solve the min-cost multi-commodity flow. Output per-arc per-commodity flows and total cost to solution.json; respect arc capacities shared across commodities.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- Gurobi · AMPL
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
licensed· 授权专业软件- 提案难度
- 4 / 5
建议验证方式
Flow conservation holds per commodity; shared arc capacities not exceeded; all demands routed; total cost within 1e-6 of the reference optimum. Graded by re-solve + conservation/capacity checks.
建议部分得分
25% conservation; 25% capacities respected; 20% demands met; 30% cost = optimum
R03.07.01.01-T13 Bin packing
原始指令
Given item sizes in fixtures/opt/bins.csv and a fixed bin capacity, solve a bin-packing MIP minimizing the number of bins used. Output the item-to-bin assignment and bin count to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools · Gurobi
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
No bin exceeds capacity; every item assigned once; bin count equals the reference optimum (gap 0). Graded by assignment validation + objective.
建议部分得分
30% valid assignment; 30% capacity respected; 40% bin count = optimum
R03.07.01.01-T14 Exact TSP on a small instance
原始指令
From the symmetric distance matrix in fixtures/opt/tsp.csv (<=15 cities), solve the TSP to proven optimality using a MIP with subtour elimination (lazy constraints) or OR-Tools exact. Output the optimal tour order and length to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- Gurobi · OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
licensed· 授权专业软件- 提案难度
- 4 / 5
建议验证方式
The tour visits every city once and returns to start (no subtours); length equals the reference optimum exactly. Graded by tour validation + length.
建议部分得分
30% valid Hamiltonian tour; 30% no subtours; 40% length = optimum
R03.07.01.01-T15 Mean-variance portfolio optimization
原始指令
Using fixtures/opt/returns.csv (expected returns) and cov.csv (covariance), solve the QP that minimizes portfolio variance for a target expected return of 8% with weights summing to 1 and no shorting. Output the weights and resulting variance to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- Gurobi
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
licensed· 授权专业软件- 提案难度
- 4 / 5
建议验证方式
Weights sum to 1, all nonnegative, expected return >= 8%; variance within 1e-6 of the reference optimum. Graded by re-solve + constraint checks.
建议部分得分
30% feasible weights; 30% return target met; 40% variance = optimum
R03.07.01.01-T16 Blending LP with dual/sensitivity report
原始指令
Solve the blending LP in fixtures/opt/blend.mod (AMPL/Pyomo) and, in addition to the optimal cost, report the shadow price of each binding constraint and the objective-coefficient ranging for two named variables. Write values to sensitivity.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- AMPL · Gurobi
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
Optimal cost matches reference; reported shadow prices and coefficient ranges match the reference duals/ranges within 1e-4. Graded by re-solve + dual comparison.
建议部分得分
40% optimum; 35% shadow prices; 25% coefficient ranges
R03.07.01.01-T17 Workforce LP in Excel Solver (control pair of T01)
原始指令
Control pair of T01: in Excel, open fixtures/opt/workforce.xlsx and use the Solver add-in (GUI) to set up and solve the staffing LP (decision cells, objective cell, constraint ranges) that minimizes weekly labor cost meeting daily coverage. Save with the solved values and the Solver model stored.
- 平台
win· Windowsmac· macOS- 应用
- Excel Solver
- 交互表面
desk· 桌面 GUI- GUI 需求 · 任务设定
G2· GUI 必要- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
click· 指向与点击type· 文字与表单nav· 平移 / 缩放 / 滚动- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 2 / 5
建议验证方式
The solved decision cells meet all coverage constraints and the objective cell equals the reference optimum within tolerance; the saved workbook contains the Solver model definition (set via the GUI, not a pasted answer). Graded on cell values + stored model. Agent VM has no terminal or Python and Excel macros/VBA are disabled by Trust Center policy, so the Solver model can only be built in the Solver dialog.
建议部分得分
30% model set up in Solver; 30% constraints met; 40% objective = optimum
R03.07.01.01-T18 Capacitated lot-sizing
原始指令
From fixtures/opt/lotsize.json (per-period demand, setup cost, holding cost, production capacity), solve the single-item capacitated lot-sizing MIP minimizing setup + holding cost. Output the production and inventory per period and total cost to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- Gurobi · OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
Inventory balance holds each period, demand met, capacity respected, setup binaries consistent with production; total cost equals the reference optimum (gap 0). Graded by re-solve + balance checks.
建议部分得分
25% inventory balance; 25% demand met; 20% capacity+setup logic; 30% cost = optimum
R03.07.01.01-T19 Constraint feasibility (Sudoku/CP)
原始指令
Given the partially filled grid in fixtures/opt/sudoku.txt, model it as a CP satisfaction problem in OR-Tools CP-SAT and output the unique completed grid to solution.txt. The model must encode row/column/box all-different constraints.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- OR-Tools
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
- 未声明
- 提案难度
- 3 / 5
建议验证方式
solution.txt is a valid completion satisfying all all-different constraints and matching the puzzle's unique solution. Graded by constraint validation against the given clues.
建议部分得分
40% model constraints correct; 60% valid unique completion
R03.07.01.01-T20 Bi-objective goal programming
原始指令
For the planning model in fixtures/opt/biobj.json with objectives (minimize cost, minimize emissions), compute 5 Pareto-efficient points via the epsilon-constraint method and output the trade-off frontier (cost, emissions) plus the chosen weighted-goal solution to solution.json.
- 平台
lin· Linuxmac· macOSwin· Windows- 应用
- Gurobi · AMPL
- 交互表面
term· 终端- GUI 需求 · 任务设定
CL· CLI 足够- GUI 需求 · 普通权限
CL· CLI 足够- 交互原语
code· 代码与命令type· 文字与表单- 工作产物
WP07· 仿真结果- 条件
licensed· 授权专业软件long· 长流程- 提案难度
- 5 / 5
建议验证方式
The 5 reported points are each feasible and non-dominated, matching the reference frontier within 1%; the goal-programming solution meets the stated target deviations. Graded by re-solve at each epsilon + dominance check.
建议部分得分
30% feasible points; 30% non-dominated frontier; 20% matches reference; 20% goal solution correct
已有研究映射
以下沿用研究目录中的基准与小类映射，不是逐题标注、执行记录或产品背书。