# Multiobjective feed formulation for swine - economic and environmental aspects

Florence Garcia-Launay

► To cite this version:

Florence Garcia-Launay. Multiobjective feed formulation for swine - economic and environmental aspects. 34. Annual meeting of CBNA (Colégio Brasileiro de Nutrição Animal), Colégio Brasileiro de Nutrição Animal, Mar 2023, Campinas & Sao Paolo, Brazil. hal-05426236

HAL Id: hal-05426236

https://hal.inrae.fr/hal-05426236v1

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# Multiobjective feed formulation for swine - economic and environmental aspects

Florence Garcia-Launay

PEGASE, INRAE, Institut Agro, 35 590 Saint-Gilles, France

florence.garcia-launay@inrae.fr

<figure><img src="image_4.png" /></figure>

34ª Reunião Anual do CBNA – 2023

A Nutrição e as Demandas do Consumidor: Bem-Estar Animal e Meio Ambiente

AVES . SUÍNOS. BOVINOS

21, 22 e 23
de março
> Swine production systems (SPS) and the environment

<figure><img src="image_5.png" /></figure>

Feed production and manure emissions are major contributors to most environmental impacts
> Life Cycle Assessment framework into 4 steps

Goal and scope
definition

<figure><img src="image_6.png" /></figure>

Product labelling
Eco-design...

<figure><img src="image_7.png" /></figure>

Functionnal unit

<figure><img src="image_8.png" /></figure>

System
boundaries

<figure><img src="image_9.png" /></figure>

Multifunctionality

<figure><img src="image_10.png" /></figure>

Inventory
analysis

<figure><img src="image_11.png" /></figure>

Foreground/
background data

<figure><img src="image_12.png" /></figure>

Surveys,
experiments,
models

<figure><img src="image_13.png" /></figure>

Databases

<figure><img src="image_14.png" /></figure>

Life Cycle Impact
Assessment

<figure><img src="image_15.png" /></figure>

Impact
categories

<figure><img src="image_16.png" /></figure>

Characterization
factors

<figure><img src="image_17.png" /></figure>

Normalization

<figure><img src="image_18.png" /></figure>

Interpretation

<figure><img src="image_19.png" /></figure>

Scenario
analysis

<figure><img src="image_20.png" /></figure>

Contribution
analysis

<figure><img src="image_21.png" /></figure>

Uncertainty
analysis

LCA offers a comprehensive framework to support eco-design
in many areas, including swine production
> Goal and scope in Swine Production Systems (SPS) LCAs

<figure><img src="image_22.png" /></figure>
> Contribution of feed production to most environmental impacts

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

Andretta et al. 2021

<figure><img src="image_25.png" /></figure>

Basset-Mens &
van der Werf, 2005
Dourmad et al. 2014

Decreasing the environmental impacts of pig feeds is potentially an
interesting lever of mitigation
Associating LCA to feed formulation
for swine production systems
should contribute
to mitigate the environmental impacts
of swine production
while addressing the best trade-off with feed cost

<figure><img src="image_26.png" /></figure>
> The story of multiobjective feed formulation

1. First story - Dealing with multiple objectives to overcome potential transfer of impacts

2. Second story - Dealing with multiple objectives to overcome potential transfer of impacts

3. Supporting decision with multiobjective feed formulation

4. Conclusions and implications
> Step 1 : traditional least-cost feed formulation

$$ \begin{cases} \min \mathbf{c}^\mathrm{T}\mathbf{x} \\ \begin{pmatrix} \mathbf{q}_{\mathrm{min}} \\ \mathbf{n}_{\mathrm{min}} \\ 1 \end{pmatrix} \le \begin{pmatrix} \mathbf{Q} \\ \mathbf{N} \\ \mathbf{1}^\mathrm{T} \end{pmatrix} \mathbf{x} \le \begin{pmatrix} \mathbf{q}_{\mathrm{max}} \\ \mathbf{n}_{\mathrm{max}} \\ 1 \end{pmatrix} \\ 0 \le \mathbf{x} \le 1 \end{cases} $$

In this first step, we produce a
reference least-cost feed

I := set of feed ingredients

J := set of nutrients

$\mathbf{x} = (\mathbf{x}_i)_{i \in I}$

Ingredient incorporation rate decision vector

$\mathbf{c} = (\mathbf{c}_i)_{i \in I}$

Ingredient cost vector

$\mathbf{Q} = \mathrm{Id} * 1000$

$\mathbf{q}_{\mathrm{min}} = (q_{\mathrm{min}_i})_{i \in I}, \mathbf{q}_{\mathrm{max}} = (q_{\mathrm{max}_i})_{i \in I}$

vectors of ingredient incorporation constraints

$\mathbf{N} = (\mathbf{n}_{ij})_{i \in I, j \in J}$ matrix of nutritional values

$\mathbf{n}_{\mathrm{min}} = (\mathbf{n}_{\mathrm{min}_j})_{j \in J}, \mathbf{n}_{\mathrm{max}} = (\mathbf{n}_{\mathrm{max}_j})_{j \in J}$

Vectors of nutritional constraints
Step 2 : multiobjective feed formulation

$$
\begin{array}{l}
\min (1 - \alpha) \frac{\mathbf{c}^\mathrm{t}\mathbf{x}}{\mathrm{Cost}_{\mathrm{ref}}} + \alpha \times \sum_{i \in I} \mathrm{coef}_i \frac{\mathrm{impact}_i^\mathrm{t}\mathbf{x}}{\mathrm{impact}_{\mathrm{ref}_i}} \\
\\
\left( \begin{array}{c} \mathbf{q}_{\mathrm{min}} \\ \mathbf{n}_{\mathrm{min}} \\ 1 \end{array} \right) \le \left( \begin{array}{c} \mathbf{Q} \\ \mathbf{N} \\ \mathbf{1}^\mathrm{t} \end{array} \right) \mathbf{x} \le \left( \begin{array}{c} \mathbf{q}_{\mathrm{max}} \\ \mathbf{n}_{\mathrm{max}} \\ 1 \end{array} \right) \\
\\
0 \le \mathbf{x} \le 1 \\
\\
\left( \begin{array}{c} \mathrm{impact}_1^\mathrm{t} \\ \mathrm{impact}_2^\mathrm{t} \\ \vdots \\ \mathrm{impact}_m^\mathrm{t} \end{array} \right) \mathbf{x} \le \left( \begin{array}{c} 1,05 * \mathrm{impact}_1^\mathrm{t}_{\mathrm{ref}} \\ 1,05 * \mathrm{impact}_2^\mathrm{t}_{\mathrm{ref}} \\ \vdots \\ 1,05 * \mathrm{impact}_m^\mathrm{t}_{\mathrm{ref}} \end{array} \right)
\end{array}
$$

Impacts: **climate change**, **non-renewable energy demand**, **land occupation**, **phosphorus demand**

**impact**<sub>*i*</sub> → vector of **impact** values *i* for feed ingredients

Variables with subscript "ref" →
values obtained for the reference feed from
least cost feed formulation

$\alpha$ is the weighting factor between cost index and environment index
> Trade-off economy | environment

Environmental index

<figure><img src="image_27.png" /></figure>

Price index

Feed formulas and mitigation of impacts calculated at αlim

<figure><img src="image_28.png" /></figure>
> Mitigation of environmental impacts

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

Current limited availability of feed ingredients (LIM)

Increased potential availability of some feed ingredients such as protein seeds and co-products (NLIM)

PD: phosphorus demand

NRE: non-renewable energy demand

CC: climate change

LO: land occupation

AC: acidification

EU: eutrophication

No transfer of impacts
> However ! Remaining problems...

Environmental index

<figure><img src="image_31.png" /></figure>

Normalised impacts

$$ \frac{\text{impact}_i^t \times \text{x}}{\text{impact}_{i\text{ref}}} $$

<figure><img src="image_32.png" /></figure>
> The story of multiobjective feed formulation

1. First story - Dealing with multiple objectives to overcome potential transfer of impacts

2. Second story - Dealing with multiple objectives to overcome potential transfer of impacts

3. Supporting decision with multiobjective feed formulation

4. Conclusions and implications
## Resolving the remaining problems

$$ 
\left\{
\begin{array}{l}
\min \sum_{i \in I} \coefficient_i \frac{\textbf{impact}_i^t \mathbf{x} - \textbf{Min}_i}{\text{impact}_{\text{ref}_i} - \text{Min}_i} \\
\\
\mathbf{c}^t \mathbf{x} \le \epsilon \\
\\
\left( \begin{smallmatrix} \mathbf{q}_{\text{min}} \\ \mathbf{n}_{\text{min}} \\ 1 \end{smallmatrix} \right) \le \left( \begin{smallmatrix} \mathbf{Q} \\ \mathbf{N} \\ \mathbf{1}^t \end{smallmatrix} \right) \mathbf{x} \le \left( \begin{smallmatrix} \mathbf{q}_{\text{max}} \\ \mathbf{n}_{\text{max}} \\ 1 \end{smallmatrix} \right) \\
\\
0 \le \mathbf{x} \le 1 \\
\\
\left( \begin{smallmatrix} \textbf{impact}_1^t \\ \textbf{impact}_2^t \\ \vdots \\ \textbf{impact}_m^t \end{smallmatrix} \right) \mathbf{x} \le \left( \begin{smallmatrix} 1,05 * \textbf{impact}_1^t_{\text{ref}} \\ 1,05 * \textbf{impact}_2^t_{\text{ref}} \\ \vdots \\ 1,05 * \textbf{impact}_m^t_{\text{ref}} \end{smallmatrix} \right)
\end{array}
\right.
$$

### $\epsilon$ - constraint method

$$ \epsilon = \{\text{Cost}_{\text{ref}}, \dots, \text{Cost}_{\text{max}}\} $$

$\textbf{impact}_i \rightarrow$ vector of impact values i for feed ingredients

$\text{Cost}_{\text{max}}$: price of feed when formulating without $\epsilon$-constraint

$\text{Min}_i$: level of impact i when formulating at lowest impact i

De Quelen et al. 2021 -

https://doi.org/10.3389/fvets.2021.689012

Wilfart et al. 2022 -

https://doi.org/10.1016/j.aquaculture.2022.738826
> Resolving the remaining problems !

Environmental index

<figure><img src="image_33.png" /></figure>

Price index

Normalised impacts

$$ \frac{\text{impact}_i^t \times \text{x}}{\text{impact}_{i\text{ref}}} $$

<figure><img src="image_34.png" /></figure>

Feed cost (€/tonne)
> Application to swine production

❖ Formulation considers animal requirements, feed cost and different environmental impacts by Life Cycle Assessment (LCA) approach

❖ 3 different formulation approaches :

> **Control diet** = least-cost formulation in accordance with practices in commercial farms

> **Ecodiet** = multiobjective formulation considering feed cost and environmental impacts calculated by Life Cycle Assessment (LCA) (Ecoalim)

> **Local diet** = multiobjective formulation using feed ingredients locally produced by farmers to reduce the impact of feed transport

<figure><img src="image_35.png" /></figure>
> Environmental impacts of diets calculated through LCA (per kg average feed)

<table><thead><tr><th></th><th>Control diet</th><th>Ecodiet</th><th>Local diet</th><th>Control diet to Ecodiet</th><th>Control diet to Local diet</th><th>Ecodiet to Local diet</th></tr></thead><tbody><tr><td>CC (kg CO<sub>2</sub> eq)</td><td>485</td><td>342</td><td>376</td><td>↓ 29.5%</td><td>↓ 22.5%</td><td>↑ 9.9%</td></tr><tr><td>CED (MJ)</td><td>4073</td><td>3486</td><td>3286</td><td>↓ 14.4%</td><td>↓ 19.3%</td><td>↓ 5.7%</td></tr><tr><td>Acidification (molc H<sup>+</sup> eq)</td><td>9.39</td><td>7.65</td><td>7.76</td><td>↓ 18.5%</td><td>↓ 17.3%</td><td>↑ 1.4%</td></tr><tr><td>Eutrophication (kg PO<sub>4</sub><sup>3-</sup> eq)</td><td>3.68</td><td>3.22</td><td>3.79</td><td>↓ 12.5%</td><td>↑ 3%</td><td>↑ 17.7%</td></tr><tr><td>Land occupation (m<sup>2</sup>.y)</td><td>1412</td><td>1374</td><td>1674</td><td>↓ 2.7%</td><td>↑ 18.5%</td><td>↑ 21.8%</td></tr></tbody></table>

CC (climate change (kg CO₂ eq)) = global warming potential; CED = non-renewable and fossil energy demand (MJ); AC = acidification (molc H⁺ eq); EU = eutrophication (kg PO₄³⁻ eq); LO (land occupation (m²/y)) = area of the land required to produce one kg of feed.

<figure><img src="image_36.png" /></figure>
> Environmental impacts at farm gate (per kg of live pig)

❖ Animals : 96 Pietrain x (Large White x Landrace) pigs

❖ Daily individual recording of animal performance from 40 to 115kg: live weight, feed consumption, water consumption

❖ Slaughterage at 115kg : carcass weight, lean meat percentage

<table><thead><tr><th></th><th>Control diet</th><th>Ecodiet</th><th>Local diet</th><th>RSD</th><th>Statistics</th></tr></thead><tbody><tr><td>CC (kg CO<sub>2</sub> eq)</td><td>2.50<sup>a</sup></td><td>2.06<sup>b</sup></td><td>2.20<sup>c</sup></td><td>0.13</td><td>G**, S***, A***</td></tr><tr><td>CED (MJ)</td><td>14.58<sup>a</sup></td><td>12.47<sup>b</sup></td><td>12.43<sup>b</sup></td><td>0.12</td><td>G**, S***, A***</td></tr><tr><td>AC (molc H<sup>+</sup>eq)</td><td>0.155<sup>a</sup></td><td>0.144<sup>b</sup></td><td>0.154<sup>a</sup></td><td>0.108</td><td>G**, S***, A**</td></tr><tr><td>EU (kg PO<sub>4</sub><sup>3-</sup>eq)</td><td>0.295<sup>a</sup></td><td>0.273<sup>b</sup></td><td>0.308<sup>a</sup></td><td>0.113</td><td>G**, S***, A***</td></tr><tr><td>LO (m<sup>2</sup>.y)</td><td>4.63<sup>a</sup></td><td>4.45<sup>a</sup></td><td>5.69<sup>b</sup></td><td>0.15</td><td>G**, S***, A***</td></tr></tbody></table>

CC (climate change (kg CO₂ eq)) = global warming potential; CED = non-renewable and fossil energy demand (MJ); AC = acidification (molc H⁺ eq); EU = eutrophication (kg PO₄³⁻ eq); LO (land occupation (m²/y)) = area of the land required to produce one kg of feed.

<figure><img src="image_37.png" /></figure>
> The story of multiobjective feed formulation

1. Dealing with multiple objectives to overcome potential transfer of impacts

2. Performing multiobjective formulation without degrading on-farm impacts

3. Supporting decision with multiobjective feed formulation

4. Conclusions and implications
> Performing multiobjective feed formulation based on Net Energy vs. Metabolizable Energy

<figure><img src="image_38.png" /></figure>

NE provides the true energetic value of feed ingredients, which is the energy really available for maintenance, growth...
> Performing multiobjective feed formulation based on Net Energy vs. Metabolizable Energy

Noblet 2015 - https://hal.inrae.fr/hal-02742572

<figure><img src="image_39.png" /></figure>

ME (relatively to basis 100 for wheat)

In practice, the efficiency NE/ME varies between the different feed ingredients, because this efficiency depends on the origin of ME (fat, starch, protein, fibres)
→ the energy value of protein-rich or fibrous feeds is overestimated when expressed on a ME basis.

Multiobjective optimization may produce ecofeeds with different NE/ME ratios than leas-cost formulated feeds → necessary to formulate on NE basis
> It is necessary to build the Pareto front!

<figure><img src="image_40.png" /><figcaption>Cost index – $\alpha$ = 0.3</figcaption></figure>

Fixed weighting factors

<figure><img src="image_41.png" /><figcaption>Cost index – weight $\alpha$</figcaption></figure>

Weighted sum

<figure><img src="image_42.png" /><figcaption>Feed cost – $\varepsilon$-constraint</figcaption></figure>

$\varepsilon$-constraint

Necessary to get all the Pareto front before choosing a trade-off
> Multiobjective feed formulation with average values for environmental impacts of feed ingredients?

Feed formulation using average values
of feedstuffs impacts in France

<figure><img src="image_43.png" /></figure>

**Ecofeeds**

Multiobjective
formulation

<figure><img src="image_44.png" /></figure>

**Standard feeds**

Least-cost
formulation

<figure><img src="image_45.png" /></figure>

Profile of the feeds in terms of feedstuffs
incorporations

Variability of the feedstuffs impacts in France

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>
> Multiobjective feed formulation with average values for environmental impacts of feed ingredients?

Ecofeed

Sandard feed

Density

Non renewable energy consumption

<figure><img src="image_49.png" /></figure>

Overlap probability = 0

Land occupation

<figure><img src="image_50.png" /></figure>

Overlap probability = 13%

Acidification

<figure><img src="image_51.png" /></figure>

Overlap probability = 99%

<figure><img src="image_52.png" /></figure>
> Multiobjective feed formulation with average values for environmental impacts of feed ingredients?

Espagnol et al. LCA Foods 2018

16 situations

2 feeds of the fattening
period (growing and
finishing)

4 contrasted economic
contexts (2011, 2012,
2013 and 2014)

2 levels of feedstuff
availability

<figure><img src="image_53.png" /></figure>

LCA data on available feedstuffs should be as precise as much as possible
Robustness to variability for climate change and non renewable energy demand
> Eco-design in pig production supported by multiobjective feed formulation and LCA

Feed
factory
gate

❖ Various studies – models proposed – minimizing a single impact (Nguyen et al. 2011 in broilers)

❖ Methodology accounting for 4 global environmental impacts and feed cost (Garcia-Launay et al. 2018) – updated (de Quelen et al. 2021)

Pig farm
gate

❖ Diet formulation tool that seeks for the feed formula and the levels of net energy, CP and AA that minimize a composite function including environmental impacts (McKenzie et al. 2016)

One should be careful when applying multiobjective optimization
that the excretion of nutrients, in particular N & P, is not increased

<figure><img src="image_54.png" /></figure>
> The story of multiobjective feed formulation

1. Dealing with multiple objectives to overcome potential transfer of impacts

2. Performing multiobjective formulation without degrading on-farm impacts

3. Supporting decision with multiobjective feed formulation

4. Conclusions and implications
> Multiobjective optimization to support eco-design in pig production

* Multiobjective optimization of pig feeds is efficient for reducing environmental impacts which are included in the objective-function

* Caution should be taken when applying feed formulation :

* Formulating on a Net Energy basis

* Making sure excretion of N & P are not increased

* Looking at the whole Pareto front

* Checking for effects of uncertainty in the impacts of feed ingredients

<figure><img src="image_55.png" /></figure>
> Perspectives

❖ Optimizing of both feed formulas and feeding program

❖ Multiobjective optimization based on the environmental impacts of pig at farm gate.

❖ Decision support tools to make it easily available for feed producers, and for teaching purpose

<figure><img src="image_56.png" /></figure>
<figure><img src="image_57.png" /></figure>

Thank you for your attention

florence.garcia-launay@inrae.fr

Many thanks to my colleagues Lucile Montagne
(INRAE) and Sandrine Espagnol (Ifip)