Optimization Pipelines
Verteego supports linear optimization, characterized by:
Objective Function: Linear with respect to the variables, meaning variables are combined linearly without multiplicative interactions between them.
Constraints: All constraints are linear in nature, allowing only constants as coefficients. This excludes any non-linear operations such as variables multiplying themselves within the objective function or constraints.
It is not possible to multiply variables by themselves in the objectives, nor in the constraints. Variables can only be weighted by a constant.
Practical problems
Verteego handles several types of optimization, categorized into three primary groups:
Optimization of a Quantity:
The simplest form of optimization, where the platform determines the optimal values based on a defined objective and constraints. The system retains the same number of elements (cardinality), altering only the values of the quantities being optimized.
Example: Adjusting a pricing grid where the number of prices is predetermined.
Scenario Selection (Filtering):
Verteego selects relevant scenarios from a given set, based on the constraints and optimization goals. The initial system typically has a higher cardinality than the resulting optimized set.
Example: Choosing a product assortment for specific store ranges.
Selection of Scenarios and Optimization of a Quantity:
The most complex category, requiring both the selection of optimal scenarios and the adjustment of quantities within those scenarios. The initial system again starts with a higher cardinality than the resulting optimized set.
Example: Determining which vehicles to purchase from which supplier and in what quantities.
Scope of application of constraints
In Verteego, optimized quantities are identified using unique key combinations. Constraints can be applied in various ways:
On a variable
On a group of variables
Between variables
Between groups of variables
The table below summarizes the possible cases:
Variable
Comparison, Ordered
Comparison
Group
Aggregation+Comparison
Aggregation+Comparison
Constraint implementation
Mathematically, constraints are typically defined as imposing a lower or upper bound, or enforcing equality. They can address different challenges:
Uniqueness: Selecting a single scenario among several possible ones within a group.
n among: A variation of uniqueness, where 'n' scenarios are selected.
Framing: Restricting the value to be optimized within a specific range. Values may be aggregated, such as limiting a sum or an average.
Graduation: Distributing values according to a predefined sequence, useful for setting multiple constraints at different thresholds.
Constraints applicable by use case
Depending on the use case, all the possibilities offered by the Verteego platform do not necessarily make sense:
Optimization
N
N
Y
Y
Selection
Y
N
N
Selection + Optimization
Y
Y
Dynamic constraints
Hard Constraints: In simpler optimization scenarios, it is feasible to predefine hard constraints, such as setting fixed bounds within which variables must operate. This straightforward approach is suitable for cases with predictable and stable parameters.
Generated Constraints: For more complex situations where predefined hard constraints are insufficient or inapplicable, the Verteego platform leverages its advanced capabilities to dynamically generate constraints from datasets. Users can specify which dataset to utilize through the front end, detail how each column should contribute to forming a constraint, and define the type of constraint needed. This flexibility allows for precise tailoring of constraints to fit the unique requirements of each optimization scenario.
System assembly
The Core Structure: The foundational element of Verteego’s AI-driven optimization is the 'system'—a dataset containing all pertinent information and scenarios required to conduct the optimization.
Types of Optimization Systems:
Simple Optimization:
Structure: The system contains a fixed number of lines corresponding to the variables to be optimized. The size and structure of the system remain constant throughout the optimization process.
Content: It includes columns with unique keys for identifying variables and columns loaded with crucial data for optimization, such as costs, volumes, and other physical quantities.
Selection with or Without Optimization:
Exploratory Nature: Initially, this system explores all conceivable scenarios, resulting in a greater number of lines at the start than at the conclusion of the optimization.
Structure Post-Optimization: After the optimization, the system will typically contain fewer rows than it started with, though the columns maintain the same organizational structure as in the simple optimization case.
These systems enable Verteego to efficiently navigate through various optimization landscapes, whether they involve straightforward parameter adjustments or complex scenario selections and modifications.
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