# Enhanced Multi-Objective Energy Optimization by a Signaling Method

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}) emissions, and the results compared. The metaheuristics implemented are: weighted particle swarm optimization (W-PSO), multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II). The performance of these methods with the use of multi-dimensional signaling is also compared with this technique, which has previously been shown to boost metaheuristics performance for single-objective problems. Hence, multi-dimensional signaling is adapted and implemented here for the proposed multi-objective problem. In addition, parallel computing is used to mitigate the methods’ computational execution time. To validate the proposed techniques, a realistic case study for a chosen area of the northern region of Portugal is considered, namely part of Vila Real distribution grid (233-bus). It is assumed that this grid is managed by an energy aggregator entity, with reasonable amount of electric vehicles (EVs), several distributed generation (DG), customers with demand response (DR) contracts and energy storage systems (ESS). The considered case study characteristics took into account several reported research works with projections for 2020 and 2050. The findings strongly suggest that the signaling method clearly improves the results and the Pareto front region quality.

## 1. Introduction

_{2}) emissions corresponding to about 40% [2] and regulations are currently in place for controlling the level of emissions in this sector [1]. In Portugal the 2000s level of CO

_{2}emissions from electricity generation was 480 kgCO

_{2}/MWh [3]. In 2020 and 2050, it is expected that this level will drop to 190 kg CO

_{2}/MWh and 20 kgCO

_{2}/MWh, respectively [3]. The emissions from power sector decline as more renewable based generation is integrated. This raises an interesting research issue which is discussed in this work: understanding the impact of considering CO

_{2}emissions in the energy management problem up to 2050 within smart grids operation context.

_{2}emissions due to environmental concerns [5,6]. For that reason it is necessary to find an optimal solution that considers two or more objectives. Hence, in most real-world circumstances system operators are faced with a multi-objective problem [7,8,9,10].

_{2}emissions. In [19], the tradeoff between cost and environment emissions is presented using a regular and a binary particle swarm optimization (PSO). The computational intelligence-based scheduling seems promising to reduce cost and emissions, while maximizing the renewable energy sources use. The multi-objective problem is solved using a weighted sum approach with PSO, instead of a multi-objective evolutionary algorithm or multi-objective PSO (MOPSO) [20]. Moreover, the network constraints are not considered in the mentioned approach. In [15], a multi-objective energy management for a micro-grid using both intelligent techniques and linear programming is presented to minimize the operation costs and the environment impacts. However, the work proposes a linear formulation without power flow equations and not considering the possibility of vehicle-to-grid (V2G). A modified PSO methodology is developed in [21,22] to solve the problem of ERM with high penetration of DG and EVs with V2G, with the aim to improve the performance of PSO. However, the reported work considers a single objective function, i.e., the operation cost minimization. In [18], a multi-objective model is presented, introducing the ERM model reliability concern through a multi-objective formulation. Pareto solutions provide multiple alternatives for the energy aggregator, namely by picking the most appropriate solution, taking into account the preference between minimum operation cost and the maximum available reserve. Weighted PSO (W-PSO) is proposed to solve the multi-objective problem, which uses a Pareto set scheme.

_{2}emissions. Three metaheuristics are compared, namely, the W-PSO, MOPSO and non-dominated sorting genetic algorithm II (NSGA-II). Hence, the previous signaling method for PSO used in [23] is adapted and used here to help W-PSO, MOPSO and NSGA-II to escape violations and improve fitness function. That way, this paper reviews the signaling method influence in the multi-objective problem. This validation has not been addressed before in the literature, so it constitutes its major contribution.

_{2}impact and without constraint violations. Furthermore, W-PSO seems to present better results, but requiring more computational times. The robustness test and sensitivity analysis suggest that signaling method is robust and works well under variations of important parameters.

## 2. Multi-Objective Energy Resource Management

#### 2.1. Mathematical Model

_{2}emissions, as shown in Equation (2):

_{2}emissions:

#### 2.2. Model Constraints

#### 2.3. Uncertainties

## 3. Technical Solutions

#### 3.1. Weighted Particle Swarm Optimization

_{2}(Em), as follows:

pw_{1} | is the weight concerning the maximization of total profit |

pw_{2} | is the weight concerning the minimization of total emissions |

penalties | is the sum of penalties associated with solution’s violations |

s_{1} | is the normalization factor of profit |

s_{2} | is the normalization factor of emissions |

_{1}and pw

_{2}are applied to the profit and the CO

_{2}emissions, respectively. When pw

_{1}tends to 1 (pw

_{2}→ 0), the optimization will give more importance to maximize the profit. In the opposite case, when pw

_{1}tends to 0 (pw

_{2}→ 1), the optimization will give more importance to minimize the total emissions of CO

_{2}. Parameters s

_{1}and s

_{2}are normalization factors that must be adjusted for the optimization problem. The term penalties correspond to the violations detected in the evaluation phase. The penalties configured in W-PSO are the following: 100 for voltage limits violations, 1000 for line limits violations and 1000 for the solutions with insufficient generation. A full AC power flow is used [28] to check the network conditions.

#### 3.2. Multi-Objective Particle Swarm Optimization

_{2}:

#### 3.3. Non-Dominated Sorting Genetic Algorithm II

^{3}) to O(mN

^{2}), introducing elitism and less parameters. The crossover and mutation operators remain as usual implemented in genetic algorithms, but selection operator works differently [40]. Selection is done with help of crowed-comparison operator, based on ranking, and crowding distance. Initially a random parent population is created. The population space is sorted based on the non-domination. Then each solution is assigned a fitness rank based on the non-domination level. The new generation is created using the tournament selection, crossover, and mutation. Elitism is introduced by comparing current population with the previously found best NDS. In the next step, parent and children are merged to form a new set of individuals and next generation is selected among this collection [34]. Like MOPSO, NSGA-II has the ability to find Pareto-optimal solutions in one single run. MOPSO and NSGA-II are selected as references techniques in this paper for multi-objective approaches due to their high relevance in the literature, namely in power systems problems. The fitness function in Equation (7), used in MOPSO is also implemented in NSGA-II.

#### 3.4. Multi-Dimensional Signaling Method

#### 3.4.1 Signaling Matrix Definition

_{z}(S) and sigFun

_{i}(S) changes the matrix S values in each iteration at the evaluation stage if a violation of a given constraint z is found, i.e., g(c

_{z}(x

^{e}))≥0, or if a custom condition i (ϑ

_{i}) is true:

_{i}to the i condition.

#### 3.4.2 Implementation and Knowledge Base

_{2}emissions. This signaling codes are applied by sigFun

_{i}(S). In W-PSO the signaling may switch, in evaluation stage, between rules to improve profit (light grey) or reduce emissions (dark grey) according to the weights of the objective function (see Section 3.1, which refers to W-PSO weights scheme). In MOPSO and NSGA-II, the switching occurs according to a uniform random probability of 50%. Yet, Pr

_{sig}is the global probability of signalling to be later applied in the movement phase, which is 80% in this case. Then an individual probability for each rule can be configured if desired, which influences the final probability of the signalling to really occur. It is important to remark that only 50% of the population individuals are selected to be signalled. The MC

_{(t)}represents the marginal cost of the system in period t.

_{2}emissions are: signal V2G/ESS resources with code 0 and a signaling probability of 50%. This will set the variables to 0 in the following iteration; signal DR use to increase by using code 1 and a signaling probability of 50%; signal suppliers and DG units that generate CO

_{2}emissions with a probability of 50% and with code 0; signal market energy offers with code 0 and a probability of 50%, to avoid more energy demand and consequently more CO

_{2}emissions.

## 4. Case Study

#### 4.1. Scenario Description

_{2}. It is expected that solutions with higher profits are also those with higher CO

_{2}emissions. The 14,000 network consumers are aggregated by bus totaling 162 aggregated bus-loads. In addition, 89 of the 162 aggregated loads offer DR possibility. The DG units are also aggregated by bus and by type as can be seen in Table 2. The external supplier located in the substation represents the energy imported from the main grid and is modeled with a 10 MW contract for 2020 and 15 MW for 2050. The EVs are considered individually, increasing 3.3 times in 2050 when compared with 2020. The maximum energy that VPP can export is depicted in the table as the “market” resource, i.e., a maximum of 4 MW.

_{2}emission rate taken into account the values presented in [3,45]. A considerable reduction of CHP emission rate in the 2050 scenario from 2020 is considered.

#### 4.2. Results–Scenario Portugal 2020

_{2}emissions, the range varies between 64.11 tCO

_{2}and 67.79 tCO

_{2}(tCO

_{2}is equivalent to 1000 kg CO

_{2}where t stands for tonne) in MOPSO; 63.67 tCO

_{2}and 71.26 tCO

_{2}in W-PSO; and 65.02 tCO

_{2}and 67.46 tCO

_{2}in NSGA-II.

_{2}, but will lead to a lower profit due to the need to remunerate customers against the implementation of these measures.

_{2}emissions was obtained in W-PSO, with 63.67 tCO

_{2}. The highest difference between NDS-R and NDS-L in CO

_{2}emissions was achieved with W-PSO, i.e., 7.59 tCO

_{2}, while the lowest difference was achieved in NSGA-II with 2.44 tCO

_{2}. In MOPSO the difference was 3.68 tCO

_{2}. Regarding profit, the highest difference was reported by W-PSO, with 4209 m.u., while NSGA-II presented the lowest difference of the tested methods, with 2500 m.u. Similarly to the previous scenario, this results indicated that W-PSO method performed better with a higher diversity and better convergence than NSGA-II and MOPSO when signaling method was used. Nevertheless, execution time in W-PSO was much higher than in those methods (65,100 s). However, in parallel mode the execution time was greatly improved (16×) to about 3973 s. In MOPSO this improvement is far less (3×) from 7020 s to 2021 s. In NSGA-II the execution time is 6096 s in single-core, while the parallel mode did not improved the performance.

#### 4.3. Results–Scenario Portugal 2050

_{2}emissions, the range varies between 25.75 tCO

_{2}and 26.76 tCO

_{2}in MOPSO; 25.68 tCO

_{2}and 28.05 tCO

_{2}in W-PSO; and 26.01 tCO

_{2}and 26.62 tCO

_{2}in NSGA-II.

_{2}, but will lead to a lower profit due to the need to remunerate customers that use DR measures [46].

_{2}. The highest difference between NDS-R and NDS-L in CO

_{2}emissions was achieved with W-PSO, i.e., 2.37 tCO

_{2}, while the least difference was achieved in NSGA-II, i.e., 0.61 tCO

_{2}. In MOPSO the difference was 1.01 tCO

_{2}. Regarding profit, the highest difference was reported by W-PSO, with 6985 m.u., while NSGA-II presented the least difference of the tested methods, with 1883 m.u. Similarly to the previous scenario, this results indicated that W-PSO method performed better with a higher diversity and better convergence than NSGA-II and MOPSO when signaling method was used. Nevertheless, execution time in W-PSO was much higher than those methods.

#### 4.4. Robustness Test

#### 4.5. Parameter Sensitivy Analysis

_{2}. A trade-off between the Pareto front quality and the experimented parameters is recommend. Therefore, the recommended settings for W-PSO with signaling, based on this experiment are:

- -
- 10 or less particles (a higher number will exponentiallly increase execution times due to the Pareto front selection procedure);
- -
- Between 500 and 2000 iterations (the execution time increases with a higher number of iterations, but it is more reasonable than increasing the number of particles and also more effective, particularly in parallel mode);
- -
- At least 100 weight sets (more weight sets will mean more NDS but much higher computation times).

## 5. Conclusions

_{2}emissions. The metaheuristics implemented to tackle the ERM large-scale optimization are the weighted particle swarm optimization (W-PSO), multi-objective particle swarm optimization (MOPSO), and NSGA-II. A comparison between these methods was made using the signaling method adapted to the multi-objective problem. To validate the proposal, two realistic scenarios were developed using as basis a real distribution grid from Vila Real in Portugal. Several heterogeneous DERs managed by a VPP were considered in the grid. The considered characteristics of the cases studied took into account several research work and forecasts available in the literature for 2020 and 2050.

_{2}emissions between 2020 and 2050 may drastically reduce if renewable share increases according to available projections. EVs will certainly contribute to increase the average load consumption, despite other loads consumption decrease with energy efficiency improvements. This study also reveals that pursuing CO

_{2}goals reduction within next decades may lose its significance for electricity entities and other similar players. Indeed, the results showed that the profits are substantially affected in exchange for little emission in 2050.

## Nomenclature

## Indices

I | Index of DG units |

t | Index of time periods |

L | Index of loads |

S | Index of external suppliers |

V | Index of EVs |

E | Index of ESSs |

M | Index of energy buyers |

## Sets

${\mathsf{\Omega}}_{DG}^{d}$ | Set of DG units with CO_{2} emissions |

${\mathsf{\Omega}}_{SP}^{e}$ | Set of suppliers with CO_{2} emissions |

## Parameters

N_{DG} | Total number of distributed generators |

N_{L} | Total number of loads |

N_{ST} | Total number of storage units |

N_{S} | Total number of external suppliers |

N_{V} | Total number of EVs |

N_{E} | Total number of ESSs |

N_{M} | Total number of energy buyers |

c_{Discharge}_{(V,t)} | Discharging cost of EV V in period t (m.u.) |

c_{Discharge}_{(E,t)} | Discharging cost of ESS E in period t (m.u.) |

c_{DG}_{(I,t)} | Generation price of DG unit I in period t (m.u.) |

c_{GCP}_{(I,t)} | Generation curtailment power price of DG unit I in period t (m.u.) |

c_{NSD}_{(L,t)} | Non-supplied demand price of load L in period t (m.u.) |

c_{Supplier}_{(S,t)} | Energy price of external supplier S in period t (m.u.) |

c_{LoadDR}_{(L,t)} | Demand response cost of load L in period t (m.u.) |

E_{DG}_{(I,t)} | CO_{2} emissions of DG unit I in period t (kgCO_{2}/MWh) |

E_{SP}_{(SP,t)} | CO_{2} emissions of the external supplier S in period t (kgCO_{2}/MWh) |

MP_{Charge}_{(E,t)} | Price for the charge process of ESS E in period t (m.u./MWh) |

MP_{Charge}_{(V,t)} | Price for the charge process of vehicle V in period t (m.u./MWh) |

MP_{Load}_{(L,t)} | Price of load L in period t (m.u./MWh) |

MP_{Sell}_{(M,t)} | Forecast price of the market M in period t (m.u./MWh) |

## Variables

P_{DG}_{(I,t)} | Active power generation of I unit in period t (MW) |

P_{Supplier}_{(S,t)} | Active power generation of the external supplier S in period t (MW) |

P_{LoadDR}_{(I,t)} | Demand response program active power activated for load L in period t (MW) |

P_{Charge}_{(E,t)} | Power charge of ESS unit E in period t (MW) |

P_{Charge}_{(V,t)} | Power charge of EV V in period t (MW) |

P_{Discharge}_{(E,t)} | Power discharge of ESS unit E in period t (MW) |

P_{Discharge}_{(V,t)} | Power discharge of EV V in period t (MW) |

P_{NSD}_{(L,t)} | Non-supplied demand for load L in period t (MW) |

P_{GCP}_{(I,t)} | Generation curtailment power in DG unit I in period t (MW) |

P_{Load}_{(L,t)} | Active power demand of load L in period t (MW) |

Em | Total emissions CO_{2} (kg) |

In | Total income (m.u.) |

OC | Total operation cost (m.u.) |

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

_{DG(I,t)}, is necessary to schedule the DG units that have dispatchable nature (set ${\mathsf{\Omega}}_{DG}^{d}$). A value of 1 means that the DG unit is operating at period t. The maximum and minimum limits for active (P

_{DGMaxLimit(I,t}

_{)}) (kW) and reactive (Q

_{DGMaxLimit(I,t}

_{)}) power of each DG unit I in each period t can be formulated as in Equations (A1) and (A2):

_{DGForecast(I,t}

_{)}is an input parameter representing the forecast of non dispatchable DG I in period t (kW). Non-dispatchable DG units are represent by the set ${\mathsf{\Omega}}_{DG}^{nd}$:

_{SMaxLimit(I,t}

_{)}(kW) and Q

_{SMaxLimit(I,t}

_{)}(kvar):

_{ESS(E,t}

_{)}for discharging and Y

_{ESS(E,t}

_{)}for charging guarantee this condition for each ESS in each period t:

_{Stored(E,t}

_{)}represents the energy stored in ESS E in period t (kWh). The ∆t parameter converts power to energy, i.e., for t = 1 h, ∆t = 1, t = 30 min, ∆t = 0.5. The parameters η

_{c(E}

_{)}and η

_{d(E}

_{)}corresponds to charging and discharging efficiency of ESS E (%), respectively:

_{DischargeLimit(E,t}

_{)}is an input regarding the maximum discharge rate of ESS E in period t (kW). Similarly, Equation (A9) represents the maximum charge limit for each ESS E in each period t, where P

_{ChargeLimit(E,t}

_{)}is an input parameter (kW):

_{Stored(E,t}

_{)}, and E

_{BatCap(E}

_{)}is an input parameter representing the maximum battery capacity of ESS E (kWh):

_{MinCharge(E,t}

_{)}is the minimum energy stored required in ESS E in period t (kWh):

_{EV(V,t}

_{)}for discharging and Y

_{EV(V,t}

_{)}for charging guarantee this condition for each EV in each period t:

_{Stored(V,t}

_{)}), Equation (A13), and the energy consumption for period t travel (E

_{Trip(V,t}

_{)}) has to be considered jointly with the energy remaining from the previous period (t − 1) and the charge/discharge occurred in period t. Parameters η

_{c}

_{(E)}and η

_{d}

_{(E)}corresponds to charging and discharging efficiency of EV V (%), respectively:

_{DischargeLimit(V,t}

_{)}) (kW). The discharge limit for each EV considering battery discharge rate can be formulated as in Equation (A14):

_{DischargeLimit(V,t}

_{)}is the maximum active discharge rate of EV V in period t (kW).

_{ChargeLimit(V,t}

_{)}) (kW). The charge limit for each EV considering battery charge rate can be formulated as in Equation (A15):

_{MinCharge(V,t}

_{)}, fixed by the EVs’ users or estimated by the operator) that can be used for a regular travel or an unexpected travel in each period t:

_{LoadDR(L,t}

_{,)}, load reduced for load L in period t can be formulated as in Equation (A17). The maximum load reduce is limited by P

_{LoadDRMaxLimit(L,t}

_{)}(kW) parameter:

_{Market(M,t}

_{)}is a binary variable that represents the choice of market M in period t:

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**Figure 2.**Pareto front for weighted particle swarm optimization (W-PSO), multi-objective particle swarm optimization (MOPSO), and NSGA-II: scenario 2020.

**Figure 8.**Variability of the Pareto front obtained in W-PSO method for the 2020 scenario (100 trials). (

**a**) 3D perspective (all runs); and (

**b**) Pareto front 2D perspective.

**Figure 9.**Sensitivity analysis: (

**a**) number of particles; (

**b**) number of iterations; and (

**c**) number of weight sets.

**Table 1.**Signaling codes to improve fitness. EVs: electric vehicles; ESS: energy storage system; DR: demand response; and DG: distributed generation.

Variables | Rule/Condition | Signal Code | Probability of Signal | Benefit |
---|---|---|---|---|

EVs | MC_{(t)} ≥ C_{Discharge}_{(V,t)} | −1 | Pr_{sig} | Profit improve |

MC_{(t)} ≤ MP_{Charge}_{(V,t)} | 1 | |||

(Random) | 2 | Pr_{sig}/2 | ||

ESS | MC_{(t)} ≥ C_{Discharge}_{(E,t)} | −1 | Pr_{sig}/2 | |

MC_{(t)} ≤ MP_{Charge}_{(E,t)} | 1 | |||

(Random) | 2 | Pr_{sig}/2 | ||

DR | MC_{(t)} ≥ (C_{LoadDR}_{(L,t)} + MP_{LoadDR}_{(L,t)}) | 1 | Pr_{sig} | |

MC_{(t)} ≤ (C_{LoadDR}_{(L,t)} + MP_{LoadDR}_{(L,t)}) | 2 | Pr_{sig} | ||

Market sell | MC_{(t)} ≥ MP_{Sell}_{(M,t)} | 2 | Pr_{sig} | |

MC_{(t)} ≤ MP_{Sell}_{(M,t)} | 1 | Pr_{sig} | ||

EVs | - | 2 | Pr_{sig} | CO_{2} reduction |

ESS | - | 2 | Pr_{sig} | |

DR | - | 1 | Pr_{sig} | |

DG * | - | 2 | Pr_{sig} | |

Market sell | - | 2 | Pr_{sig} |

Energy Resources | Availability (MW) | Prices (m.u./kWh) | Numbers of Units | ||||
---|---|---|---|---|---|---|---|

Minimum–Maximum | Minimum–Maximum | ||||||

2020 | 2050 | 2020 | 2050 | 2020 | 2050 | ||

Biomass | 0–0.20 | 0–0.50 | 0.15 | 0.15 | 1 | 1 | |

CHP | 0–1.80 | 0–4.00 | 0.10 | 0.10 | 3 | 3 | |

Small hydro | 0–1.83 | 0–2.52 | 0.13 | 0.13 | 1 | 1 | |

PV | 0–1.04 | 0–3.75 | 0.20 | 0.20 | 81 | 81 | |

Wind | 0.20–1.15 | 0.38–2.22 | 0.12 | 0.12 | 48 | 48 | |

External supplier | 0–10.00 | 0–15.00 | 0.11 | 0.11 | 1 | 1 | |

Storage | Charge | 0–0.25 | 0–2.00 | 0.12 | 0.12 | 4 | 8 |

Discharge | 0–0.25 | 0–2.00 | 0.18 | 0.18 | |||

EV | Charge | 0–8.33 | 0–31.29 | 0.14 | 0.14 | 1540 | 5080 |

Discharge | 0–7.31 | 0–29.21 | 0.19 | 0.19 | |||

DR | Red | 0–1.06 | 0–1.31 | 0.07 | 0.07 | 89 | 89 |

Load | 6.59–14.76 | 8.20–18.34 | 0.09–0.15 | 0.09–0.15 | 162 | 162 | |

Market | 0–4.00 | 0–4.00 | 0.08–0.10 | 0.08–0.10 | 1 | 1 |

Scenario | Supplier CO_{2} Emissions (kgCO_{2}/MWh) | CHP CO_{2} Emissions (kgCO_{2}/MWh) |
---|---|---|

2020 | 190 | 444–963 |

2050 | 20 | 230 |

**Table 4.**Metaheuristics-based approaches parameters. W-PSO: weighted particle swarm optimization; MOPSO: multi-objective particle swarm optimization; and NSGA-II: non-dominated sorting genetic algorithm II.

Parameters | W-PSO | MOPSO | NSGA-II | |
---|---|---|---|---|

#Individuals | 10 | 50 | 50 | |

Initial solution | Random between variable bounds | |||

Repository size | - | 100 | - | |

Number of divisions | - | 30 | - | |

Inertia weight | Gaussian mutation weights between 0 and 1 | 0.73 | - | |

Acceleration coefficient | 1.50 | - | ||

Cooperation coefficient | 1.50 | - | ||

Perturbation coefficient | 0.97 | - | ||

Mutation learning parameter | 0.20 | - | ||

Mutation rate | - | 0.50 | 0.10 | |

Crossover rate | - | - | 0.70 | |

Crossover range | - | - | 0.30 | |

Maximum velocities | Velocity clamping factor equation | - | ||

Minimum velocities | - | |||

Velocity clamping factor | 1 | 1 | - | |

Stopping criteria | Minimum iterations | 500 | - | - |

Maximum iterations | 2000 | |||

Maximum positions | Equal to the upper bounds of the variables | |||

Minimum positions | Equal to the lower bounds of the variables |

Method | W-PSO | MOPSO | NSGA-II | |
---|---|---|---|---|

Indicator | NDS | |||

Profit (m.u.) | R | 10,563.49 | 10,057.91 | 10,005.88 |

L | 6354.92 | 6770.93 | 7506.04 | |

Emissions (tCO_{2}) | R | 71.26 | 67.79 | 67.46 |

L | 63.67 | 64.11 | 65.02 | |

Execution time single core (s) | 65,100 | 7020 | 6096 | |

Execution time (s) | 3973 | 2021 | - |

Method | W-PSO | MOPSO | NSGA-II | |
---|---|---|---|---|

Indicator | NDS | |||

Profit (m.u.) | R | 15,319.73 | 13,235.01 | 13,029.95 |

L | 8334.39 | 8868.35 | 11,147.06 | |

Emissions (tCO_{2}) | R | 28.05 | 26.76 | 26.62 |

L | 25.68 | 25.75 | 26.01 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Soares, J.; Borges, N.; Vale, Z.; Oliveira, P.B.D.M.
Enhanced Multi-Objective Energy Optimization by a Signaling Method. *Energies* **2016**, *9*, 807.
https://doi.org/10.3390/en9100807

**AMA Style**

Soares J, Borges N, Vale Z, Oliveira PBDM.
Enhanced Multi-Objective Energy Optimization by a Signaling Method. *Energies*. 2016; 9(10):807.
https://doi.org/10.3390/en9100807

**Chicago/Turabian Style**

Soares, João, Nuno Borges, Zita Vale, and P.B. De Moura Oliveira.
2016. "Enhanced Multi-Objective Energy Optimization by a Signaling Method" *Energies* 9, no. 10: 807.
https://doi.org/10.3390/en9100807