Our Most Versatile Solver for the Full Range of Optimization Problems

The Hexaly Solver handles Large-Scale LP, QP, QCP, SOCP, NLP (smooth nonlinear) and NSP (non-smooth) problems. 

Frontline Systems is pleased to offer the Hexaly Solver Engine, for use inside Microsoft Excel (only).

Hexaly uses a hybrid combination of exact and heuristic search methods, together with advanced constraint propagation and reformulation techniques, to solve a wide range of optimization problems.

Search Methods

Hexaly’s engine integrates multiple search strategies, both exact and heuristic, that can be applied depending on the problem structure and solver needs:

  • Branch-and-Bound – an exact method for exploring the solution space by branching on variables and bounding subproblems.
  • Branch-and-Cut – extends branch-and-bound with cutting planes to tighten bounds and prune infeasible regions.
  • Dual Simplex Method – for solving linear subproblems efficiently within the branch-and-bound framework.
  • Simplex Method – another exact method for linear subproblems.
  • Interior-Point Methods – used for certain linear and nonlinear subproblems.
  • Local Search – iteratively improves a feasible solution by exploring neighborhoods.
  • Variable Neighborhood Search (VNS) – systematically changes the neighborhood structure to escape local optima.
  • Large Neighborhood Search (LNS) – removes and reinserts parts of the solution to find better ones.
  • Direct Search – derivative-free optimization for black-box or non-smooth functions.
  • Surrogate Modeling – builds approximations of complex functions to guide search.

These methods are combined in a hybrid framework so that exact methods provide strong bounds, while heuristics help find high-quality solutions quickly.

Constraint Handling Methods

Hexaly’s constraint handling is both propagation-based and reformulation-based:

  • Propagation Methods – enforce consistency between variables and constraints, pruning infeasible values early.
  • Automatic Dantzig–Wolfe Reformulation – decomposes large problems into subproblems, improving scalability.
  • Column and Row Generation – dynamically adds variables or constraints to improve the formulation.
  • Global Constraint Support – in CPMpy integration, Hexaly can handle global constraints directly.
  • Black-Box Function Handling – allows constraints or objectives defined via external functions, with internal reformulation when possible solver.

How They Work Together

Hexaly’s unified optimization engine runs these methods in coordination:

Exact methods (branch-and-bound, branch-and-cut, simplex, interior-point) provide global optimality and strong bounds.

Heuristic methods (VNS, LNS, local search) deliver fast, high-quality solutions when optimality is hard to prove.

Constraint propagation and reformulation techniques reduce problem size and improve search efficiency.

Hence, Hexaly’s search and constraint methods are a blend of exact MIP/NLP techniques, advanced heuristic search, and intelligent constraint handling, designed to handle combinatorial, nonlinear, and mixed models efficiently.