Emmental Algorithm

Real-world optimization problems are very often limited by multiple constraints. For example, the optimization of a chemical process may exhibit known physical and/or manufacturing constraints. These constraints have a direct impact on the parameter space of the optimization problem by effectively reducing its volume to only the subset of points that fulfill all the constraints (i.e. the feasible regions). Therefore, optimization techniques that lack the ability to incorporate this knowledge may choose parameter points that do not lie in the feasible regions. 

Optimization problems with constraints are ubiquitous in nature, including in relevant applications in pharma, biotech, materials science, chemistry and beyond. For example:

● Mass balance constraints: In many chemical processes, it is required that the compositions of the input constituents add up to a specific total value. In certain cases, when optimizing the composition of A, B and C in a given chemical compound, it is necessary that the mass fractions mi add up to 1: mA+mB+mC=1. 

● Thermodynamic constraints: Certain reactions and phase changes can only happen at particular thermodynamic conditions of pressure and temperature.

● Stoichiometric constraints: All the reactants of a chemical reaction should be present in specific proportions such that they are all consumed. This is particularly important in redox reactions to ensure that the correct reactants are consumed instead of producing undesired corrosion byproducts.

● Conditional constraints: Real-world scenarios such as “if pH < 5, then T ≤ 50°C”.

● Cardinality constraints: In some formulation applications, it may be required to choose a fixed subset of components from a larger pool while optimizing their relative contributions.