Multi-objective optimization, also known as multi-criteria optimization, is the process of simultaneously optimizing two or more conflicting objectives subject to certain constraints.
Multi-objective optimization problems can be found wherever optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
In many issues of balancing diet according to nutritional models, objectives under consideration conflict with each other, and optimizing a particular solution with respect to a single objective can result in fewer results with respect to the other objectives. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution.
Maximizing IOFC while maximizing milk efficiency or minimizing ration cost while maximizing productive nitrogen are examples of multi-objective optimization problems in the field of formulation of ruminant diets.
If a multi-objective problem is well-formed, there should not be a single solution that simultaneously minimizes/maximizes each objective to its fullest. In each case, we are looking for a solution for which each objective has been optimized to the extent that if we try to optimize it any further, then the other objective will suffer as a result. Finding such a solution, and quantifying how much better this solution is compared to other such solutions (there will generally be many) is the goal when setting up and solving a multi-objective optimization problem.
In this context, it is also possible to optimize the microbial yield. Checking the dedicated checkbox even with a secondary objective selected, the optimizer finds solutions oriented to maximize microbial efficiency and supply of MP from this source. This is not a function to maximizing microbial yield per se, but it works within and together with primary and/or secondary objectives selected.
The consideration of economic aspects as the only decision criterion could be a rigid and, sometimes, unrealistic assumption when a ruminant diet is tackled, especially at the farm level. In this context, we are not necessarily interested, for example, in the least cost ration but in a real optimum ration which achieves an equilibrium or trade-off amongst several objectives, most of them potentially in conflict.
These considerations move the formulation problem from the traditional single-objective framework to a multi-criteria decision-making approach.
In animal nutrition, in contrast to the high number of techniques available for single-objective optimization, relatively few techniques have been developed for multi-objective optimization.
The multi-objective optimization is a new feature, implemented for NDS Optimizer, provided for solving complicated problems about ration formulation with the CNCPS model. It allows the user of the platform to optimize the recipes for two objectives simultaneously.
Generally speaking, are contemplated in the following two groups of objectives:
− primary objectives - are considered economical objectives and allow you to optimize the recipes for the reduction of feeding costs or the increase of profitability;
− secondary objectives - are objectives related to efficiency and productivity predicted from the recipes formulated.
Selecting only a primary objective, the recipe will be optimized non-linearly considering only that goal, while also selecting a secondary objective, the optimizer will seek solutions considering both objectives.
The optimizer, considering all the analytical and model constraints set, selects solutions that will tend to have the highest possible level for the secondary objective, in the context of those that minimize/maximize the primary objective, whether they are optimum or sub-optimal solutions.
In other words, by selecting a secondary objective, very often, though not always, this will reach higher levels than those achievable by setting only the primary objective, which may even, but not always, get worse slightly.
We should not expect “revolutionary” formulations because the search of solutions, is always subdued to the constraints set, but we have at our disposal a tool able to offer a wider range of solutions, working with objectives that are difficult to simultaneously optimize in other ways.