combinatorial-optimization

Plugin combinatorial-optimization from marketplace combinatorial-optimization-skills in hajibabaie/combinatorial-optimization-skills. Commands read from the repo's manifest — 1 month ago.

Skills (76)

• algorithm-benchmarking-statistics

  When the user wants to compare optimization algorithms with a sound empirical protocol — instance and seed design, time limits, best/mean/gap reporting, nonparametric hypothesis tests, effect sizes, and the plots that summarize them. Also use when the user mentions "compare algorithms," "statistical

• ant-colony-optimization

  When the user wants to design, implement, or tune ant colony optimization for combinatorial problems, including pheromone model design, visibility heuristics, and choosing among Ant System, Ant Colony System, and MAX-MIN Ant System. Also use when the user mentions "ant colony," "ACO," "pheromone," "

• assignment-problems

  When the user wants to match agents to tasks at minimum cost - linear assignment via the Hungarian algorithm, LP duality, or linear_sum_assignment; generalized assignment (GAP) via MIP, Lagrangian relaxation, and local search; bottleneck (min-max) assignment. Also use when the user mentions "assignm

• benders-decomposition

  When the user wants to solve a structured MILP or two-stage stochastic program by Benders decomposition — splitting it into an integer master and LP subproblems, deriving optimality and feasibility cuts from subproblem duals, and implementing either the classic iterative loop or branch-and-Benders-c

• biased-random-key-genetic-algorithm

  When the user wants to design, implement, or tune a biased random-key genetic algorithm (BRKGA), where chromosomes are random-key vectors in [0,1), evolution uses elite/mutant partitioning with biased uniform crossover, and a decoder is the only problem-specific component. Also use when the user men

• bin-packing

  When the user wants to pack items into the fewest capacitated bins, compare FFD/BFD heuristics against the L1/L2 lower bounds, or build exact compact MIP and arc-flow models, plus variants with variable bin sizes and item conflicts. Also use when the user mentions "bin packing," "first fit decreasin

• branch-and-bound

  When the user wants to implement a custom branch-and-bound algorithm — designing bounding functions, branching rules, node selection (depth-first vs best-first), dominance rules, and incumbent management — or to decide when custom B&B beats a MIP solver. Also use when the user mentions "custom branc

• column-generation

  When the user wants to solve linear or integer programs whose variable set is too large to enumerate, by iterating between a restricted master problem and a reduced-cost pricing problem, up to full branch-and-price. Also use when the user mentions "column generation," "pricing problem," "restricted

• constraint-handling-techniques

  When the user wants to handle constraints inside metaheuristics by choosing among penalty functions (static, dynamic, adaptive), repair operators, feasibility-preserving operators, decoder-based feasibility, stochastic ranking, and Deb's feasibility rules. Also use when the user mentions "constraint

• constraint-programming

  When the user wants to model and solve combinatorial problems with constraint programming, especially OR-Tools CP-SAT: integer, boolean, and interval variables, AllDifferent, NoOverlap, Cumulative, channeling, and search strategies, plus CP-vs-MIP selection guidance. Also use when the user mentions

• crossover-operators

  When the user wants to choose or implement a crossover operator for a genetic or evolutionary algorithm: one-point, two-point, uniform, arithmetic, blend (BLX-alpha), and SBX plus the permutation family OX, PMX, CX, ERX, AEX, and position-based, with preservation properties and operator-encoding fit

• cutting-planes-valid-inequalities

  When the user wants to strengthen a MIP with cutting planes and valid inequalities — deriving cover, clique, MIR, or Gomory cuts, writing separation routines, and adding them as user cuts or lazy constraints via Gurobi callbacks. Also use when the user mentions "valid inequalities," "cutting planes,

• cutting-stock

  When the user wants to solve one-dimensional cutting stock problems — cutting demanded item widths from standard stock rolls at minimum roll usage or trim loss — with pattern-based (Gilmore-Gomory) or compact MIP models, column generation with knapsack pricing, and integer rounding. Also use when th

• dantzig-wolfe-decomposition

  When the user wants to reformulate a structured LP or MIP via Dantzig-Wolfe decomposition — detect block-angular structure, build the master with convexity constraints, price columns from independent subproblems, and relate the DW bound to LP and Lagrangian bounds. Also use when the user mentions "D

• decoder-based-representations

  When the user wants to design an indirect encoding where a decoder maps a simple genotype (random keys, priority vectors, rule choices) to a feasible solution, including serial/parallel schedule-generation schemes and feasibility-enforcing decoders. Also use when the user mentions "decoder," "random

• differential-evolution

  When the user wants to solve continuous or mixed black-box optimization problems with differential evolution, choose among DE strategies (rand/1/bin, best/1/bin, current-to-best), tune F and CR, or adapt DE to permutation problems through random keys. Also use when the user mentions "differential ev

• diversity-and-population-management

  When the user wants to diagnose or prevent premature convergence in population-based metaheuristics by measuring and managing diversity: entropy and distance-based diversity measures, fitness sharing, crowding, niching, duplicate elimination, restart policies, and adaptive parameter control driven b

• dynamic-programming

  When the user wants to design and implement dynamic programming for combinatorial optimization — state-space design, Bellman recursions, memoization vs tabulation, solution recovery, and labeling algorithms for resource-constrained shortest paths. Also use when the user mentions "dynamic programming

• estimation-of-distribution-algorithms

  When the user wants to design or implement an estimation of distribution algorithm — UMDA, PBIL, compact GA, tree models, BOA, or permutation EDAs with position-frequency, edge-histogram, or Mallows models — building and sampling probabilistic models over good solutions instead of using crossover. A

• evolution-strategies

  When the user wants to design or implement an evolution strategy — (mu+lambda) or (mu,lambda) selection, self-adaptive step sizes, or CMA-ES — for continuous, integer, or mixed-integer search, including tuning another algorithm's parameters. Also use when the user mentions "evolution strategy," "CMA

• facility-location-problem

  When the user wants to choose facility sites and assign customers to them — UFLP, CFLP, p-median, or p-center — with strong MIP formulations, Benders or Lagrangian solution paths, and greedy, interchange, or VNS heuristics. Also use when the user mentions "facility location," "p-median," "p-center,"

• fitness-evaluation-and-caching

  When the user wants to speed up objective evaluation in a metaheuristic or local search — profiling, delta/incremental evaluation, memoization with solution hashing, surrogate, vectorized batch, and parallel evaluation. Also use when the user mentions "fitness evaluation," "delta evaluation," "incre

• fitness-landscape-analysis

  When the user wants to analyze a fitness landscape before or while designing a search algorithm — measuring ruggedness with random-walk autocorrelation and correlation length, fitness-distance correlation, plateaus and neutrality, and sampled local optima networks — and to use those measurements to

• flow-shop-scheduling

  When the user wants to model or solve flow-shop scheduling problems - permutation flow-shop makespan computation, the NEH heuristic, MIP models in gurobipy, and iterated greedy as the state-of-the-art metaheuristic, with a makespan-plus-tardiness multi-objective extension. Also use when the user men

• genetic-algorithms

  When the user wants to design, implement, or tune a genetic algorithm for combinatorial optimization: the canonical GA loop, encoding choice, selection, crossover, mutation, elitism, population sizing, premature convergence, and numpy-vectorized population implementations. Also use when the user men

• git-for-research-code

  When the user wants to version-control optimization research code - small commits per experiment change, tags for paper result snapshots, .gitignore for solver logs, linking result tables to commit hashes, and branch strategy for risky refactors. Also use when the user mentions "git workflow," "vers

• graph-coloring

  When the user wants to assign colors (labels, slots, frequencies) to graph vertices so adjacent vertices differ, minimize the number of colors used, or bound the chromatic number with exact or heuristic methods. Also use when the user mentions "graph coloring," "chromatic number," "DSATUR," "tabucol

• grasp

  When the user wants to implement GRASP — multi-start greedy randomized construction with a restricted candidate list followed by local search — including alpha tuning, reactive GRASP, and path relinking hybrids. Also use when the user mentions "GRASP," "greedy randomized," "restricted candidate list

• guided-local-search

  When the user wants to escape local optima by penalizing solution features and re-optimizing an augmented objective — guided local search (GLS) design, implementation, lambda calibration, penalty decay, and pairing with fast local search. Also use when the user mentions "guided local search," "GLS,"

• gurobi-advanced-features

  When the user wants to use Gurobi beyond plain model building — callbacks for lazy constraints, user cuts, heuristic solution injection, and early termination; IIS computation for diagnosing an infeasible model; the solution pool; the multi-objective API; the matrix API (addMVar/addMConstr); MIP sta

• hyper-heuristics

  When the user wants to build a hyper-heuristic — a search method that selects or generates low-level heuristics instead of searching solutions directly — covering selection hyper-heuristics (heuristic selection plus move acceptance), low-level heuristic pool design, learning and reward schemes, and

• instance-generation-and-benchmarks

  When the user wants to assemble instances for optimization experiments by parsing standard benchmarks (TSPLIB, CVRPLIB/Solomon, OR-Library, MIPLIB, QAPLIB, Taillard), writing seeded generators with controlled hardness, reporting instance features, or building train/test splits for tuning. Also use w

• integer-programming-techniques

  When the user wants to diagnose and fix slow MIP solves — branch-and-bound mechanics inside modern solvers, LP relaxation strength, MIP gap interpretation, formulation tightening, symmetry breaking, big-M versus indicator constraints, and presolve effects. Also use when the user mentions "branch and

• iterated-local-search

  When the user wants to design, implement, or tune iterated local search (ILS) — the local-search + perturbation + acceptance loop that is the strongest simple baseline for permutation and routing problems. Also use when the user mentions "iterated local search," "ILS," "perturbation," "kick move," "

• job-shop-scheduling

  When the user wants to model and solve job-shop scheduling problems, sequencing job operations on machines under fixed per-job routes, minimizing makespan or tardiness, via disjunctive MIP, CP-SAT interval models, or critical-path tabu search. Also use when the user mentions "job shop," "disjunctive

• knapsack-problems

  When the user wants to formulate and solve knapsack problems — 0-1, bounded, multiple, multidimensional, or quadratic — using dynamic programming, branch-and-bound, MIP, greedy bounds, or metaheuristics. Also use when the user mentions "knapsack," "0-1 knapsack," "multidimensional knapsack," "subset

• lagrangian-relaxation

  When the user wants to compute strong dual bounds for integer programs by dualizing complicating constraints, optimizing the Lagrangian dual with subgradient methods, and recovering feasible solutions with Lagrangian heuristics. Also use when the user mentions "Lagrangian relaxation," "subgradient,"

• large-neighborhood-search

  When the user wants to implement or tune large neighborhood search (LNS) or adaptive LNS (ALNS), covering destroy/repair operator design, adaptive operator weights, acceptance criteria, and noise, for routing, scheduling, and tightly constrained problems. Also use when the user mentions "large neigh

• linear-programming-fundamentals

  When the user wants to formulate linear programs, solve them with simplex or barrier methods, and interpret the result through duality — shadow prices, reduced costs, sensitivity ranges, degeneracy. Also use when the user mentions "linear programming," "dual values," "shadow price," "sensitivity ana

• linearization-techniques

  When the user wants to turn nonlinear terms — variable products, absolute values, min/max, piecewise-linear functions, logical implications, or fractional objectives — into mixed-integer linear constraints, or needs tight big-M values. Also use when the user mentions "linearize," "big-M," "bilinear,

• local-search-and-neighborhoods

  When the user wants to design or implement neighborhood-based local search - choosing moves (swap, insertion, 2-opt, Or-opt, exchange), writing O(1)/O(n) delta evaluation, first vs best improvement, scan order, and move data structures. Also use when the user mentions "local search," "2-opt," "neigh

• lot-sizing

  When the user wants to model and solve dynamic lot-sizing problems, from uncapacitated single-item lot sizing to multi-item capacitated lot sizing (CLSP) with setup times, covering Wagner-Whitin DP, facility-location reformulation, (l,S) valid inequalities, big-bucket vs small-bucket models, and fix

• matheuristics

  When the user wants to hybridize a MIP solver with heuristic search — fix-and-optimize, relax-and-fix, MIP-based destroy-and-repair (LNS with exact repair), local branching, or solution polishing — including budgeting solver calls inside the loop. Also use when the user mentions "matheuristic," "fix

• matplotlib-optimization-visualization

  When the user wants to turn optimization experiment data into figures: convergence curves with bands over seeds, Gantt charts, route plots, Pareto front plots, and performance profiles, at publication quality with vector output and single-column sizing. Also use when the user mentions "convergence p

• memetic-algorithms

  When the user wants to build or tune a memetic algorithm - a genetic algorithm hybridized with local search - covering Lamarckian vs Baldwinian learning, local-search frequency and depth budgeting, restart management, and population diversity under strong local search. Also use when the user mention

• metaheuristic-design-principles

  When the user wants to choose or design a metaheuristic for a combinatorial problem — picking a representation, designing operators, handling constraints, balancing intensification and diversification, and setting stopping criteria and evaluation budgets. Also use when the user mentions "which metah

• milp-modeling-gurobi

  When the user wants to build, solve, and debug mixed-integer linear programs in Python with Gurobi — creating variables, writing constraint-builder functions, setting objectives and parameters, handling solver status, and extracting solutions safely. Also use when the user mentions "gurobipy," "buil

• multi-objective-optimization

  When the user wants to optimize two or more conflicting objectives and reason about Pareto trade-offs — Pareto dominance and efficient sets, exact front generation with weighted-sum and epsilon-constraint scalarizations in Gurobi, NSGA-II mechanics (fast non-dominated sorting, crowding distance, cro

• mutation-and-perturbation-operators

  When the user wants to design or tune mutation and perturbation operators — bit-flip, creep, Gaussian, polynomial; swap, insertion, inversion, scramble, segment moves for permutations; destroy-style perturbations; and mutation-strength adaptation. Also use when the user mentions "mutation operator,"

• nature-inspired-metaheuristics-overview

  When the user needs a critical, operator-level assessment of metaphor-based metaheuristics — what harmony search, cuckoo search, firefly, grey wolf, whale, or bat algorithms actually compute, and when to just use an established method. Also use when the user mentions "harmony search," "cuckoo search

• network-flow-optimization

  When the user wants to solve flow problems on a network - max-flow/min-cut, min-cost flow, multicommodity flow, or shortest paths via Dijkstra, Bellman-Ford, and label-correcting methods - using networkx, gurobipy, or specialized algorithms, including when total unimodularity makes LP solutions inte

• numpy-vectorization-for-optimization

  When the user wants to remove slow Python loops from metaheuristic or optimization code using NumPy — population-level operations, batch fitness evaluation, distance matrices, broadcasting, argsort/argpartition idioms, default_rng, and memory layout. Also use when the user mentions "vectorize," "num

• open-source-solvers

  When the user wants to solve LPs, MIPs, or CP models without a commercial license — choosing among HiGHS, SCIP, CBC, OR-Tools (CP-SAT and MathOpt), PuLP, Pyomo, and python-mip, comparing licenses, setting realistic performance expectations versus Gurobi, and migrating gurobipy models to an open-sour

• optimization-project-structure

  When the user wants to organize optimization research code into a reproducible project — separating the src package, scripts, configs, and results; JSON/YAML config systems; factory registration of algorithms and problems; seed discipline; atomic result writing; and light testing. Also use when the

• optuna-hyperparameter-tuning

  When the user wants to tune metaheuristic or solver parameters with Optuna, including search-space definition, TPE sampling, pruning weak configurations early, multi-instance objectives (mean/median over an instance set), and held-out validation against overtuning. Also use when the user mentions "O

• pandas-experiment-management

  When the user wants to record, store, and aggregate computational-experiment results for optimization algorithms with pandas - tidy one-row-per-run tables, run metadata (instance, seed, algorithm, parameters, runtime, objective), atomic CSV/parquet writing, aggregation across instances and seeds, an

• parallel-and-hybrid-metaheuristics

  When the user wants to parallelize a metaheuristic or combine several searches — island models with migration, master-slave fitness evaluation, parallel multistart, cooperative search, or algorithm portfolios — with the Python practicalities (multiprocessing, joblib, vectorization-first). Also use w

• parallel-machine-scheduling

  When the user wants to schedule jobs on one machine or on identical, uniform, or unrelated parallel machines: dispatching rules (SPT, WSPT, EDD, Moore-Hodgson), LPT and list scheduling with worst-case bounds, exact MIP models for makespan and due-date objectives, and LNS for large instances. Also us

• particle-swarm-optimization

  When the user wants to design, implement, or tune particle swarm optimization, covering velocity and position updates, inertia weight, constriction, swarm topologies, and discrete adaptations such as random-key and binary PSO. Also use when the user mentions "particle swarm," "PSO," "inertia weight,

• problem-formulation

  When the user wants to translate a word problem or real-world planning situation into a formal optimization model — identifying decision variables, objective function, and constraints, choosing the model type (LP, MIP, CP, or heuristic), estimating model size, and auditing the data before any solver

• quadratic-assignment-problem

  When the user wants to model or solve the quadratic assignment problem — assigning n facilities to n locations to minimize the total flow-times-distance cost — with linearized MIP models or robust tabu search built on O(n) swap delta evaluation. Also use when the user mentions "quadratic assignment,

• robust-optimization

  When the user wants to optimize under uncertainty with hard feasibility guarantees by building robust counterparts of LPs and MIPs over box, budget (Bertsimas-Sim), or ellipsoidal uncertainty sets and tuning the price of robustness. Also use when the user mentions "robust optimization," "uncertainty

• scatter-search-path-relinking

  When the user wants to implement scatter search (reference set management, diversification generation, subset combination, improvement method) or path relinking as intensification between elite solutions, standalone or inside GRASP. Also use when the user mentions "scatter search," "path relinking,"

• selection-and-replacement-strategies

  When the user wants to choose, implement, or tune parent selection and survivor replacement in evolutionary algorithms — tournament, roulette-wheel, rank, stochastic universal sampling, and Boltzmann selection, plus generational vs steady-state replacement, elitism, and (mu+lambda) vs (mu,lambda) —

• set-covering-packing-partitioning

  When the user wants to model or solve set covering, set packing, or set partitioning problems with exact MIP models, the greedy heuristic and its ln(n) guarantee, LP rounding, or Lagrangian-based heuristics in the Caprara-Fischetti-Toth style. Also use when the user mentions "set covering," "set par

• simulated-annealing

  When the user wants to design, implement, or tune simulated annealing for combinatorial optimization, covering Metropolis acceptance, cooling schedules (geometric, Lundy-Mees, adaptive), initial temperature calibration, reheating, and restarts. Also use when the user mentions "simulated annealing,"

• solution-encodings

  When the user wants to choose or design a solution representation for a metaheuristic — binary, integer, real-valued, permutation, matrix, set-based, or mixed — and judge candidates by locality, redundancy, feasibility coverage, and bias. Also use when the user mentions "solution representation," "e

• solution-validation-testing

  When the user wants to verify optimization code: independent feasibility checkers, objective recomputation separate from the solver, unit tests for constraint builders and operators, known-optimum regression tests, and exact-vs-heuristic cross-validation on small instances. Also use when the user me

• stochastic-optimization

  When the user wants to optimize decisions under uncertainty with two-stage stochastic programming — extensive (deterministic-equivalent) form in Gurobi, scenario generation and reduction, sample average approximation (SAA), and EVPI/VSS analysis. Also use when the user mentions "stochastic programmi

• tabu-search

  When the user wants to design or implement tabu search — tabu lists and tenure, move attributes, aspiration criteria, frequency-based diversification, candidate list strategies, and elite-restart intensification. Also use when the user mentions "tabu search," "tabu list," "tabu tenure," "aspiration

• timetabling-and-rostering

  When the user wants to model and solve educational timetabling (course or exam scheduling) or personnel rostering problems with hard and soft constraints, using MIP, CP-SAT, or heuristic methods. Also use when the user mentions "timetabling," "course scheduling," "nurse rostering," "shift scheduling

• traveling-salesman-problem

  When the user wants to model or solve the traveling salesman problem - exact MIP formulations (MTZ vs DFJ with lazy subtour-elimination cuts), construction heuristics (nearest neighbor, greedy edge, Christofides), 2-opt/3-opt/Or-opt improvement, and Lin-Kernighan-style moves. Also use when the user

• variable-neighborhood-search

  When the user wants to design or implement variable neighborhood search and its family — VND, basic VNS, general VNS, and skewed VNS — choosing and ordering neighborhoods, designing shaking moves, and deciding when systematic neighborhood change beats a single neighborhood. Also use when the user me

• vehicle-platooning-optimization

  When the user wants to coordinate truck platoons — choosing routes with bounded detours, scheduling departures and waiting under time windows, and pairing trucks on shared arcs so followers save air-drag fuel — via an exact MIP or a metaheuristic. Also use when the user mentions "platooning," "truck

• vehicle-routing-problem

  When the user wants to model and solve vehicle routing problems — the capacitated VRP and its main variants (time windows, multi-depot, heterogeneous fleet, pickup-and-delivery) — via two- and three-index MIP formulations, savings and sweep construction, ALNS improvement, and OR-Tools routing. Also

• warm-starts-and-initial-solutions

  When the user wants to construct an initial solution and feed it into a solver — construction heuristics by problem class, MIP starts and variable hints in Gurobi, partial fixing, and seeding metaheuristic populations from exact solution pools. Also use when the user mentions "warm start," "MIP star

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