WHAT-IF ANALYSIS THROUGH SIMULATION-OPTIMIZATION HYBRIDS

Marco GavanelliENDIF University of Ferrara, Italymarco.gavanelli@unife.it

Michela MilanoDEIS University of Bologna, Italymichela.milano@unibo.it

Alan Holland and Barry O’SullivanCork Constraint Computation Center, Ireland

{a.holland,b.osullivan}@4c.ucc.ie

ABSTRACTThis paper proposes to improve traditional what-if anal-ysis for policy making by a novel integration of differentcomponents. When a simulator is available, a human ex-pert, e.g., a policy maker, might understand the impact ofher choices by running a simulator on a set of scenariosof interest. In many cases, when the number of scenar-ios is exponential in the number of choices, identifyingthe scenarios of interest might be particularly challeng-ing. We claim that abandoning this generate and test ap-proach could greatly enhance the decision process andthe quality of political actions undertaken. In this pa-per we propose and experiment with one approach forcombining simulation with a combinatorial optimizationand decision making component. In addition, we proposetwo alternative approaches that can reasonably combinedecision making with simulation in a coherent way andavoid the generate and test behaviour.

KEYWORDSPOLICY MODELING SOCIAL SIMULATION COM-BINATORIAL OPTIMIZATION

INTRODUCTIONPublic policy issues are extremely complex, occur inrapidly changing environments characterized by uncer-tainty, and involve conflicts among different interests.Our society is ever more complex due to globalisation,enlargement and rapidly changing geo-political situation.This means that political activity and intervention be-come more widespread. Therefore, the effects of anysuch interventions become more difficult to assess. Ofcourse, it is becoming ever more important to ensure thatactions are effectively tackling the real challenges thatthis increasing complexity entails. Thus, those respon-sible for creating, implementing, and enforcing policiesmust be able to reach decisions about ill-defined problemsituations that are not well understood, have no one cor-rect answer, involve many competing interests, and inter-act with other policies at multiple levels. It is thereforemore important to ensure coherence across these com-plex issues.

The majority of policy models rely on agent-basedsimulation (Troitzsch et al., 1999; Matthews et al., 2007;

Gilbert, 2010) where agents represent the parties in-volved in the decision-making and implementation pro-cess. The hypothesis is that for modelling complex sys-tems, agent-based simulation is a suitable approach tounderstand such systems in a more natural way. In partic-ular, agent-based models enable the use of computer ex-periments to support a better understanding of the com-plexity of economic, environmental and social systems,structural changes, and endogenous adjustment reactionsin response to a policy change. In addition to agent-based simulation models, which provide individual levelmodels, we claim that the policy planning activity needsa global perspective that faces the problem at a globallevel and should tightly interact with the individual levelmodel. The policy maker must take decisions by perceiv-ing a set of (possibly conflicting) objectives, and satisfy-ing a set of constraints while at the same time reducingnegative impacts and enhancing positive impacts on theenvironment, society and economy. Simulation could betherefore used to understand the impact of her decisionsvia what-if analysis or scenario analysis.

Figure 1: Manual decision making

If a decision maker received no useful feedback re-garding the impact of decisions, this would be the worstoutcome of all. However, typically at present a policymaker devises a set of scenarios to be simulated and eval-uates the impact of the taken decision. The process iter-ates as soon as the policy maker finds a solution that sat-isfies her, as depicted in Figure 1. The simplest way toimprove this process is to aid the decision maker in thefirst step of her process, by designing a Decision SupportSystem (DSS) for the selection of (Pareto) optimal pointscorresponding to specific political actions, as depicted inFigure 2. In brief, the problem components that the pol-icy maker should take into account, namely impacts on

Figure 2: Decision support system for scenario selection

environment, economy, financial aspects, territory-basedconstraints, and objectives, can be cast as a combinato-rial optimization and decision problem and solved usingthe appropriate techniques, described e.g. in (Gavanelliet al., 2010, 2011). Despite being more sophisticatedthan the manual approach, this secondary process stillexhibits a generate-and-test behaviour. In other words,the decision making and optimization component oper-ates within the confines of a limited information set andis not guided toward simulation-reasonable solutions.

In this paper we propose an approach that enables atight interaction between a simulator and a decision mak-ing component based on machine learning. Machinelearning is used to synthesize constraints for the decisionmaking component from simulation results. We show anexample applied to the Italian Emilia-Romagna region,and in particular on its Regional Energy Plan. The defi-nition of the plans is provided by a decision support sys-tem by casting the problem in a mathematical model andsolving it through optimization techniques. On the otherhand, the implementation strategy, namely the definitionof the percentage of incentives to reach the objectives ofthe regional plan, can be only understood through agent-based simulation. The proper interaction between policyplanning and policy implementation should necessarilylead to an integration of decision support and simulationcomponents.

Also, we devise two alternative approaches thatmaintain close connections between simulation and thedecision-making components, and abandon the generateand test behaviour: one is based on Benders’ decomposi-tion, while the other is based on the game theoretic prin-ciples of Mechanism Design.

The paper is organized as follows: we first describe theconsidered case study, i.e. the regional energy plan, thenwe propose the first approach of optimization-simulationhybrids we experimented with, namely the one using ma-chine learning techniques. Then we propose two alterna-tive approaches that would reasonably improve the firstintegration scheme: one based on problem decomposi-tion and one on mechanism design.

THE REGIONAL ENERGY PLAN CASE STUDYThe Regional Energy Plan defines the strategic regionalobjectives for the energy production and energy effi-

ciency. The case study is based on data provided by theItalian Emilia-Romagna region. The region has strategicobjectives, financial and territorial constraints and envi-ronmental impacts. An example of an objective that theregion might have is to increase the production of energywhile at the same time increasing the share of renewableenergy sources in the regional energy balance.

For each energy source, the plan should provide: theinstalled power, in MW; the total energy produced in ayear, in kTOE (TOE stands for Tonne of Oil Equivalent);the total cost, in Me. The ratio between installed powerand total produced energy is mainly influenced by theavailability of the source: while a biomass plant can, atleast in theory, produce energy 24/7, the sun is availableonly during the day, and the wind only occasionally. Forunreliable sources an average for the whole year is taken.The cost of the plant, instead, depends mainly on the in-stalled power: a solar plant has an installation cost thatdepends on the surface area of installed panels, whichon their turn can provide some maximum power (peakpower).

The 20-20-20 EU directive imposes that 20% of totalenergy requirements for 2020 should be provided by re-newable sources. Technicians in the region proposed apercentage to be provided during the period 2011-2013of 177kTOE of electrical energy and 296kTOE of ther-mal energy. With this premise they developed plans forelectrical and thermal energy, respectively. In Table 1 weshow the electric plan based only on renewable energysources. The total private and public investment require-ment is 3014Me.

Table 1: Regional Energy plan 2011-2013

Power 2010 Power 2013 Energy 2013Power plants (MW) (MW) (kTOE)Hydroelectric 300 310 69.3Photovoltaic 230 850 87.7Th.dyn. solar 0 10 1Wind farms 20 80 10.3Biomasses 430 600 361.2Total 980 1850 529.5

In general, after a plan is created, the policy makerdefines actions for its implementation. A widely usedinstrument for supporting the renewable energy marketis monetary incentives. For example, in the Emilia-Romagna region, incentives for the photovoltaic energyare distributed to stakeholders by means of auctions thatindeed do not result from a specific strategy, but ratherfrom extemporaneous strategies. In these auctions thebids are ranked on the basis of various criteria (includ-ing the co-financing percentage), and the first n bids thatsatisfy the budget constraint are funded. However, thisstrategy may be far from optimal and further research isrequired to examine the efficacy of this approach.

Italian law considers four different methods for pro-

viding incentives, while in the auctions developed in thepast only one type was used. Finally, one should considercarefully how to spend the limited financial resourcesavailable: for example, should we provide higher incen-tives or spend more money into advertising the availabil-ity of incentives? As we can see, the number of possiblechoices, just for the implementation of the plan, is combi-natorial, which makes a hand-made process inapplicableor highly sub-optimal. Moreover, the outcome of a givenpolicy of incentives is not clear or easily foreseeable, andit can only be obtained through a social simulator.

In this paper, we propose to integrate in the plan-ning process a mechanism for defining a proper incentivestrategy that achieves the objectives of the plan. For thisreason we should devise a methodology for coupling adecision component with a simulator.

INTEGRATING SIMULATION WITH LEARNINGWe report on some experiments we have conducted thatshow how a machine learning system can be integratedwith a simulator to assist in the policy-making processassociated with a regional energy planning task. Inthis case, the simulator generates a set of scenarios, re-lating decisions with observables as depicted in Fig-ure 3. The collected tuples 〈decision1, . . . , decisionn,observable1, . . . observablem〉 are stored as a trainingset for a learning component which in turn learns a rela-tion between decisions and observables. The relation canbe an objective function or a constraint or a cost function,the automated modeling of which can be framed as a re-gression problem. In any case it should have a form thatis compatible with the decision support system model.

Figure 3: Learning-Based Interaction

We consider now the learning based interaction. Whatwe want to learn is a function that relates the installedpower to the percentage of incentives provided by the re-gion. We have performed a large number of simulations

(1500) for each value of incentives from 1% to 30% insteps of 1% (for a total of 45,000 simulations). Each sim-ulation has 1000 agents, and we recorded, for each sim-ulation, the total installed power in MW of photo-voltaicplants. A plot of the results is shown in Figure 4 whereeach point represents an individual simulation.

Of course, an individual simulation does not provideuseful information, as can be seen from Figure 4, andone should try to extract some statistics from a signifi-cant number of simulations in order to get some insight.In order to learn a model of the dependency of the in-stalled power from the incentives, we average the resultsof all the simulations with the same amount of incen-tives. In this way we obtain a point for each value ofthe incentives from 1% to 30%. Then we learned a func-tion that relates the installed power to the incentives. Wetried various regression algorithms, including linear re-gression (Rousseeuw and Leroy, 1987), Gaussian pro-cesses (Mackay, 1998), least median squared linear re-gression (Rousseeuw and Leroy, 1987), multilayer per-ceptron (Mitchell, 1997), Gaussian radial basis functionnetworks (Mitchell, 1997) and support vector regression(Smola and Scholkopf, 2004).

Figure 4: Simulations

We evaluated the mean squared error of each algorithmusing ten-fold cross validation. The algorithm that gavethe lowest mean squared error was linear regression sowe applied it to the whole dataset and we obtained thefunction

GPV = mI% + q (1)

(where PV stands for photovoltaic) that is also shown inFigure 5. The values of the parameters we obtained arem = 2645MW and q = 405MW .

We inserted in the model the relationship of Equa-tion 1, in this way we were able to relate the incentivesgiven by the region with the obtained installed power ofphotovoltaic energy.

The region has a limited budget BPV for the incen-tives towards photovoltaic plants (PV), so this should beimposed as an upper bound to the total incentive:

ITotPV ≤ BPV (2)

The total incentive is given by the percentage of incen-tives given by the region multiplied by the total cost of

Figure 5: Learned function.

installed photovoltaic panels:

ITotPV = I%cTot

PV (3)

the cost is given by the unit cost cPV multiplied by themagnitude of the installed panels:

cTotPV = cPVGPV (4)

From the simulations and linear regression, we obtainedthe relationship between the provided percentage of in-centives and the expected magnitude (Eq. 1). Combiningequations (1), (3) and (4) we obtain:

ITotPV = I%cPV (mI

% + q) = cPVm(I%)2 + qI%

(5)The constraint of Eq. (2) can be rewritten (solving Eq. (5)for I% and excluding a trivial bound, since I% is non-negative), as:

I% ≤−q +

√q2 + 4mBPV /cPV

2m. (6)

By inserting this constraint into the decision sup-port system, we can define regional energy plans whoseincentives strategies are compatible with budget con-straints.

MORE SOPHISTICATED INTEGRATIONSIn this section we consider how more sophisticated hy-brids of optimisation and simulation can be developed.In the first case we consider an approach based on a clas-sic problem decomposition technique from the field ofoperations research. This technique can be used to linkthe multiple levels of abstraction needed in a complexpolicy-making setting. In the second scenario we con-sider how game theoretic concerns can be considered inthe process, by exploiting the utilities of agents to de-sign complex incentive schemes to motivate particularbehaviours that maximise overall efficiency of the sys-tem.

Benders DecompositionBenders (1962) decomposition is a method for solvingcombinatorial optimization problems that can be decom-posed into two components: a master problem and a sub-problem. Benders Decomposition was originally devised

in the field of Integer Linear Programming, but has beenextended for dealing with general solvers in the so calledLogic-Based Benders Decomposition (Hooker and Ot-tosson, 2003). In our case, the master problem is thedefinition of the regional energy plan that partitions theneeded energy into renewable sources. The master prob-lem is solved through Constraint Programming as de-scribed in (Gavanelli et al., 2012). The subproblem isthe definition of the incentive strategy to achieve the re-quired photovoltaic installed power, that is also consis-tent with the regional budget. The simulator is run to un-derstand which is the proper required incentive to obtainthe solution provided by the master problem. In case theincentives are not compatible with the regional budget aBenders cut is generated and another solution is providedby the master.

Figure 6: Benders Decomposition Interaction

The learning-based interaction, as described in previ-ous section, requires the execution of a very high numberof simulations in order to (1) get significant statistics foreach value of the incentives (or, in general, for each pos-sible decision in the policy) and (2) provide a wide set ofdata for the machine learning.

On the other hand, it may be the case that some val-ues of policy decision variables are not interesting, asthey would provide very bad values for the Decision Sup-port System that utilizes optimization. In principle, onewould like to simulate only the best values from the DSSviewpoint; unluckily these values are unknown and de-pend on the constraints provided by the machine learningcomponent. This shows that the architecture in Figure 3,with one-way communication from the simulator to theDSS, should be extended to a cycle, that provides bidirec-tional communication between the two main components(Figure 6).

The interaction starts from the DSS, that generates anoptimal solution of the master problem. This solutioncontains tentative values for the incentives, and for therequired outcome for photovoltaic energy. The tentativevalues are passed to the simulator, that executes a num-ber of simulations only for those values of the parame-

ters provided by the DSS, and provides the correspondentstatistics. These statistics might confirm or not the ten-tative values proposed by the DSS: if the (average) sim-ulated outcome is higher or equal to the correspondingtentative value, the iteration stops and the result is prov-ably optimal (Benders, 1962). Instead, if the tentativevalue of the outcome is higher than the simulated value,another iteration is required. So, a constraint (or nogood)is communicated from the simulator to the DSS, explain-ing that one cannot obtain the requested level of photo-voltaic power with the proposed value of incentives. TheDSS inserts the nogood into the constraint model, solvesit to optimality, and provides new tentative values to thesimulator.

The main challenge is determining the set of con-straints that are communicated between the two systems:if one excludes from the feasible set only the tentativevalues, the risk is to perform many interactions, leadingto exhaustive simulation of all the values of the param-eters, while if one excludes further values there is therisk to possibly discard promising solutions. This issueis subject of current research.

INCENTIVE COMPATIBLE MECHANISMS

We now consider an approach that supports What-IfAnalysis based upon the principles of Economic Theoryand, in particular, Game Theory. When one assumes thatagents are all self-interested and rational utility maximiz-ers, one can apply the solution concepts of Nash Equi-librium to predict expected outcomes. This is an attrac-tive concept for policy makers because it can aid the pre-dictability of novel economic policies or initiatives.

A seminal result known as the Revelation Principlestates that, no matter the mechanism, a designer con-cerned with efficiency need only consider equilibria inwhich agents truthfully report their “types” that signifytheir private valuation for an item (Gibbons, 1992). Clev-erly designed economic mechanisms (or auctions) canallocate resources and determine payments that are re-silient to manipulation. The design of subsidy schemesto support the construction of public goods is particu-larly challenging (Laffont, 1987). Our setting involvesa possibly large number of agents and a set of renewabletechnologies so tractability concerns must also be bornein mind (Nisan and Ronen, 2001). The key design chal-lenge concerns the free rider problem and consequent un-der provision of public goods. For example, in first priceauctions previously conducted in the Emilia-Romagnaregion, participants that wished to acquire a photovoltaicdevice without government aid had an incentive to under-report their valuation to receive a subsidy.

Mechanism design is a game of private information inwhich a single central agent, the “center”, chooses thepayoff structure. Agents report a type to the center thatthey may choose strategically so that it is different fromtheir true value. After the reporting phase, the center de-termines an outcome. The outcome consists of an allo-

cation and a payoff. The center typically wishes to ful-fil a social choice function to map the true type profiledirectly to the allocation of goods transferred, whereas amechanism maps the reported type profile to an outcome.

A Subsidy Disbursement ExampleLet us consider a more specific example. There are mhouseholds whose suitability for receiving a subsidy for aphotovoltaic device depends upon the pitch of their roof,orientation, horizon profile and location. We reduce theseparameters to a single value describing the worth of a so-lar device per unit of power to value vi for agent i. Thisvalue reflects the day zero time-discounted value of theexpected stream of future cashflows given their circum-stances. The social choice function is to assign the pan-els pj , j ∈ {1, . . . , J} to agents in a manner that mini-mizes the maximum cost for any agent. The imposition(or cost) for agent i if panel j is received is the price ofthe device minus the value per unit of power multipliedby the power output of the device,

cij = rj − viφj ,∀i ∈ {1, . . . , I}, j ∈ {1, . . . , J}

where rj is the purchase price of an installed panel.This problem can be transposed to a makespan min-

imization problem denoted in the scheduling theory lit-erature as Q||Cmax, where Cmax refers to makespan inscheduling theory. We wish to to allocate device acquisi-tion and hosting responsibility (jobs) across houses (ma-chines) that each perceive a private cost associated withacceptance of that job. The minimization of the maxi-mum time to wait for all jobs to complete is comparableto the minimization of the maximum cost imposed on anyhouse-owner so that inconvenience is bounded as tightlyas possible.

Non-monotone Algorithm Consider the followingsimple algorithm: order the panels from highest to low-est power and greedily assign each device in turn tothe household that has received lowest cost impositionthus far in the partial allocation. This algorithm is a 2-approximation that is non-monotone. Consider an ex-ample with 3 devices {d1, d2, d3} and 2 agents {h1, h2}that illustrates non-monotonicity. Let the publicly knownpower ratings for the devices be φ1 = 10W and φ2 =φ3 = (9 + ε)W and all devices cost rj = 60e. Thisis common to all agents. However, let each house-owner’s value per unit of power be v1 = 5e/W andv2 = (5 − ε)e/W . This is the private information thatwe wish to elicit. Our greedy algorithm first assigns:d1 → h1, d2 → h2 and d3 → h2 resulting in costsc1 = 60 − 10 × 5 = 10e and c2 = 2(60 − (45 −4ε − ε2)) ∼= (30 + 8ε)e. But if we increase v2 so thatv2 = (5 + ε)e/W then it receives only the first device.The first (highest power device) will be assigned to thesecond agent because she now has a higher value per unitof power. The second (lower power) device is assignedto the first agent because this agent has received a lower

cost imposition thus far. The third (lower power) de-vice is also assigned to the first agent because this agenthas received a lower cost imposition thus far because theprevious lower power device imposed less cost than thehigh power device did for the agent that values renew-able power more. So this algorithm is not monotoneand a direct consequence of this is that it cannot be usedwithin any truthful mechanism for allocating devices toagents (Archer and Tardos, 2001).

Monotone Algorithm There exists a randomized 3-approximation that is truthful in expectation. Kovacs(2005) developed an approximation scheme for schedul-ing n jobs to m machines of different speeds so that themakespan is minimized. This problem is sometimes re-ferred to as (Q||Cmax) (Kovacs, 2005). A fast, deter-ministic monotone 3-approximation algorithm exists forthis problem. The importance of monotonicity is veryrelevant to our setting and the context of truthful mecha-nisms in general. When each agent knows its own valuefor hosting a device, it is necessary to design an incen-tive for declaration of true values to enable efficient al-location. Archer and Tardos (2001) demonstrated thatsuch motivation is possible only if the allocation algo-rithm within the mechanism is monotone.

RELATED WORK

In the literature, simulation and optimization have beenmerged mainly in the so-called simulation optimizationfield. In this case optimization aids simulation for choos-ing optimal parameters to improve operations (Deng,2007). The goal of optimization routines is to seek im-proved settings of system parameters with respect to theperformance metrics. Similarly, Neuro-Dynamic Pro-gramming (NDP) (Bertsekas and Tsitsiklis, 1996) is anapproach to select agent decision making rules (feed-back policy) that optimize a certain performance crite-rion. NDP often relies on simulation, in the so calledvalue function approximation, to tune the parameters ofa value function that quantifies the relative desirability ofdifferent states in the problem space. Markov decisionprocesses have also been used in Reinforcement Learn-ing (RL) together with simulation, for learning directlythe policy parameters (Marbach and Tsitsiklis, 2001).Both NDP and RL are concerned with how a single agentought to take actions in an environment so as to maximizesome form of cumulative reward. On the contrary, in thispaper we are interested in understanding how global po-litical actions and interventions impact on a complex sys-tems (namely, the energy market) without changing theagent behavior. We aim to (1) observe/learn the causallink between agents behavior and high level decisionsand (2) cast these relations into a model component.

Simulation-aware optimization has been consideredin the context of Genetic Algorithms (GAs). The ba-sic integration technique consists in solving a numericalmodel to evaluate the fitness function (see for example

(Obayashi et al., 2000)). Although GAs encode someknowledge of the system behavior through the popula-tion individuals, these approaches learn no explicit rela-tion between decision variables and the system observ-ables. As a consequence, analytic properties of the con-trolled system cannot be discovered and exploited withthe typical means of combinatorial optimization.

Finally, the closest approaches to this paper are thoserelated to the governance of a simulated system. The tra-ditional way to cope with combinatorial (global) deci-sion making where a part of the model can be simulatedis rather trivial: the decisions are taken and the simula-tor evaluates their “quality”. This is the base of Simu-lation for Optimization (Fu, 1994) that is strongly basedon stochastic programming. The main idea is that can-didate solutions are presented to the stochastic discrete-event simulator that, in turn, provides performance esti-mates of the solutions via statistical analysis. In this casethe simulator model is another objective function gener-ator, but the way solutions are presented follows a puregenerate-and-test pattern. A similar approach is consid-ered in OptQuest (Glover et al., 1999), a system that in-tegrates in a closed loop simulation and metaheuristics toachieve good quality solutions. In the paper also a prim-itive form of learning is used, namely a neural networkaccelerator aimed at avoiding trivially bad solutions. Inthe same fashion, in (Bartolini et al., 2011), simulationhas been used to learn neuron constraints in a thermalaware dispatching application. This last paper is closeto the one presented here, with the difference that thelearning component aims at tuning parameters of neuralconstraints, while in this paper we learn a linear func-tion linking decision variables and observables that canbe evaluated and validated by domain experts.

CONCLUSION AND FUTURE WORKIn future work we aim to tackle the challenge of devisinga mechanism that will facilitate a tractable and budgetbalanced approach to allocation and payments. We planto consider alternative social choice functions that takesa more holistic view of agent types that considers bothwelfare and aggregate renewable energy generated.

We face in this paper the very challenging problem ofmixing a regional planning activity with the definition ofan implementation strategy. While the planning part canbe cast into a combinatorial optimization problem andsolved through optimization techniques, the implemen-tation strategy requires a simulator to be understood in-volving self interested decision making agents. We pro-pose here one technique for integrating optimization andsimulation and two alternative solutions to aid this pro-cess that are subject of current study in the context of theEU FP7 ePolicy Project.

ACKNOWLEDGEMENTSWe would like to thank Fabrizio Riguzzi for his help onthe machine learning part.

This work was partially supported by EU project ePol-icy, FP7-ICT-2011-7, grant agreement 288147. Possibleinaccuracies of information are under the responsibilityof the project team. The text reflects solely the views ofits authors. The European Commission is not liable forany use that may be made of the information containedin this paper.

REFERENCES

Archer, A. and Tardos, Eva. (2001). Truthful mechanisms forone-parameter agents. In Proceedings of FOCS.

Bartolini, A., Lombardi, M., Milano, M., and Benini, L. (2011).Neuron constraints to model complex real-world problems.In Principles and Practice of Constraint Programming.

Benders, J. F. (1962). Partitioning procedures for solvingmixed-variables programming problems. Numerische Math-ematik, 4:238–252.

Bertsekas, D. and Tsitsiklis, J. (1996). Neuro-Dynamic Pro-gramming. Athena Scientific.

Deng, G. (2007). Simulation-based Optimization. PhD thesis,University of Wisconsin - Madison.

Fu, M. (1994). Optimization via simulation: A review. Annalsof Operations Research, 53:199–248.

Gavanelli, M., Riguzzi, F., Milano, M., and Cagnoli, P. (2010).Logic-Based Decision Support for Strategic EnvironmentalAssessment. Theory and Practice of Logic Programming,10(4-6):643–658.

Gavanelli, M., Riguzzi, F., Milano, M., and Cagnoli, P. (2012).Constraint and optimization techniques for supporting pol-icy making. In Computational Intelligent Data Analysis forSustainable Development, chapter 16. Taylor & Francis.

Gavanelli, M., Riguzzi, F., Milano, M., Sottara, D., Cangini,A., and Cagnoli, P. (2011). An application of fuzzy logicto strategic environmental assessment. In Pirrone, R. andSorbello, F., editors, AI*IA, volume 6934 of LNCS. Springer.

Gibbons, R. (1992). Game theory for applied economists.Princeton University Press.

Gilbert, N. (2010). Computational Social Science. SAGE.

Glover, F., Kelly, J., and Laguna, M. (1999). New advances forwedding optimization and simulation. In Proc. of the WinterSimulation Conference.

Hooker, J. N. and Ottosson, G. (2003). Logic-based bendersdecomposition. Mathematical Programming, 96:33–60.

Kovacs, A. (2005). Fast monotone 3-approximation algorithmfor scheduling related machines. In Proceedings of the 13thannual European conference on Algorithms, ESA’05, pages616–627, Berlin, Heidelberg. Springer-Verlag.

Laffont, J.-J. (1987). Incentives and the allocation of publicgoods. Handbook of public economics, 2:537–569.

Mackay, D. J. (1998). Introduction to Gaussian processes.

Marbach, P. and Tsitsiklis, J. N. (2001). Simulation-based op-timization of markov reward processes. IEEE Transactionson Automatic Control, 46(2):191–209.

Matthews, R., Gilbert, N., Roach, A., Polhill, G., and Gotts, N.(2007). Agent-based land-use models: a review of applica-tions. Landscape Ecology, 22(10).

Mitchell, T. M. (1997). Machine Learning. McGraw-Hill, NewYork.

Nisan, N. and Ronen, A. (2001). Algorithmic mechanism de-sign. Games and Economic Behavior, 35:166–196.

Obayashi, S., Sasaki, D., Takeguchi, Y., and Hirose, N.(2000). Multiobjective evolutionary computation for super-sonic wing-shape optimization. IEEE Transactions on Evo-lutionary Computation, 4:182–187.

Rousseeuw, P. J. and Leroy, A. M. (1987). Robust regressionand outlier detection. Wiley.

Smola, A. J. and Scholkopf, B. (2004). A tutorial on supportvector regression. Statistics and Computing, 14:199–222.

Troitzsch, K. G., Mueller, U., Gilbert, G. N., and Doran, J.(1999). Social science microsimulation. J. Artificial Soci-eties and Social Simulation, 2(1).

AUTHOR BIOGRAPHIESMARCO GAVANELLI is Ricercatore (AssistantProfessor) in Computer Science at the Departiment ofEngineering, University of Ferrara, Italy. His researchinterests are on Logic Programming and Constraint Pro-gramming and their applications. His personal webpageis at http://www.ing.unife.it/docenti/MarcoGavanelli/.

BARRY O’SULLIVAN holds the Chair in ConstraintProgramming at University College Cork and is Directorof the Cork Constraint Computation Centre (4C) in theDepartment of Computer Science. His personal webpageat http://osullivan.ucc.ie.

ALAN HOLLAND is a Research Fellow special-ising in optimisation and electronic commerce inthe Cork Constraint Computation Centre (4C),Department of Computer Science, University Col-lege Cork, Ireland. His personal webpage athttp://4c.ucc.ie/˜aholland.

MICHELA MILANO is Associate Professor in In-telligent Systems at the Departiment of Electronic,Computer Science and Systems, University of Bologna,Italy. Her research interests span from ArtificialIntelligence to Operations Research to build hybrid op-timization techniques. Her personal webpage at http://ai.unibo.it/people/MichelaMilano.