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A solver for the generalized assignment problem.
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This problem is interesting because many different optimization methods can and have been applied to solve it (Branch-and-cut, Branch-and-price, Branch-and-relax, Local search, Constraint programming, Column generation heuristics...). Thus, the main goal of this repository is for me to have reference implementations for classical algorithms and optimization solvers.
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The variant handled here is the variant:
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* with a minimization objective (items have costs)
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* where all items have to be assigned
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## Implemented algorithms
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### Lower bounds
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- Linear relaxation
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- solved with CLP `-a linrelax-clp`
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- solved with Gurobi `-a "milp-gurobi --only-linear-relaxation"`
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- solved with Cplex `-a "milp-cplex --only-linear-relaxation"`
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- Lagrangian relaxation of knapsack constraints. The value of this relaxation is the same as the value of the linear relaxation. However, it might be cheaper to compute, especially on large instances.
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- solved with volume method `-a lagrelax-knapsack-volume`
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- solved with L-BFGS method `-a lagrelax-knapsack-lbfgs`
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- Lagrangian relaxation of assignment constraints
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- solved with volume method `-a lagrelax-assignment-volume`
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- solved with L-BFGS method `-a lagrelax-assignment-lbfgs`
- MTHG, greedy with regret measure (+ n shifts) `--algorithm "mthg-regret --desirability wij"`
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- Local search algorithm implemented with [fontanf/localsearchsolver](https://github.com/fontanf/localsearchsolver)`-a "local-search --threads 3"`
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- Mixed-Integer Linear Program
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- MILP `--algorithm milp --solver highs`
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- Linear relaxation `--algorithm linear-relaxation --solver highs`
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- Tree search algorithms based on the Dantzig-Wolfe reformulation branching scheme (i.e. column generation heuristics) implemented with [fontanf/columngenerationsolver](https://github.com/fontanf/columngenerationsolver):
<!-- - with Gecode `--algorithm constraint-programming-gecode`-->
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- Others heuristics:
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- Random feasible solution found with a Local search `-a random`
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- Local search with LocalSolver `-a localsolver`
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<!--- Lagrangian relaxation-->
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<!-- - of knapsack constraints. The value of this relaxation is the same as the value of the linear relaxation. However, it might be cheaper to compute, especially on large instances.-->
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<!-- - solved with volume method `--algorithm lagrangian-relaxation-knapsack-volume`-->
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<!-- - solved with L-BFGS method `--algorithm lagrangian-relaxation-knapsack-lbfgs`-->
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<!-- - of assignment constraints-->
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<!-- - solved with volume method `--algorithm lagrangian-relaxation-assignment-volume`-->
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<!-- - solved with L-BFGS method `--algorithm lagrangian-relaxation-assignment-lbfgs`-->
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### Exact algorithms
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- Local search algorithm implemented with [fontanf/localsearchsolver](https://github.com/fontanf/localsearchsolver)`--algorithm "local-search --threads 3"`
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- Mixed-Integer Linear Programs
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- with CBC `-a milp-cbc`
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- with CPLEX `-a milp-cplex`
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- with Gurobi `-a milp-gurobi`
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- with Knitro `-a milp-knitro`
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- Constraint programming
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- with Gecode `-a constraint-programming-gecode`
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- with CPLEX `-a constraint-programming-cplex`
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- Tree search algorithms based on the Dantzig-Wolfe reformulation branching scheme (i.e. column generation heuristics) implemented with [fontanf/columngenerationsolver](https://github.com/fontanf/columngenerationsolver):
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