Multi-agent Dynamic Algorithm Conﬁguration
Anonymous Author(s)
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Abstract
Automated algorithm conﬁguration relieves users from tedious, trial-and-error tuning tasks.
A popular algorithm conﬁguration tuning paradigm is dynamic algorithm conﬁguration (DAC), in which an agent learns dynamic conﬁguration policies across instances by reinforcement learning (RL).
However, in many complexalgorithms, there may exist different types of conﬁguration hyperparameters, andsuch heterogeneity may bring difﬁculties for classic DAC which uses a singleagent RL policy.
In this paper, we aim to address this issue and propose a multiagent DAC (MA-DAC) framework, with one agent working for one type of conﬁguration hyperparameters.
MA-DAC formulates the dynamic conﬁguration ofa complex algorithm with heterogeneous types of hyperparameters as a contextual multi-agent Markov decision process and solves it by a cooperative multiagent RL (MARL) algorithm.
To instantiate, we apply MA-DAC to a well-knownoptimization algorithm for multi-objective optimization problems.
Experimentalresults show the effectiveness of MA-DAC in not only achieving superior performance compared with other conﬁguration tuning approaches based on heuristicrules, multi-armed bandits, and single-agent RL, but also being capable of generalizing to different problems classes.
Furthermore, we release the environmentsin this paper as a benchmark for testing MARL algorithms, with the hope of facilitating the application of MARL.
Introduction
Finding right conﬁgurations of hyperparameters is critical for many learning and optimization algorithms.
Automated methods, such as algorithm conﬁguration (AC) [15, 22], emerge to search forright conﬁgurations, with the aim of relieving users from tedious, trial-and-error tuning tasks.
However, static conﬁguration policies obtained by AC may not necessarily yield optimal performance(compared with dynamic policies) since algorithms may require different conﬁgurations at differentstages of their execution [31].
Dynamic algorithm conﬁguration (DAC) [2] is a well-known paradigm for obtaining dynamic conﬁguration policies.
Unlike AC, DAC can dynamically adjust the algorithm’s conﬁguration duringthe optimization process, through formulating it as a contextual Markov decision process (MDP) andthen solving it by reinforcement learning (RL) [27].
DAC has been found to outperform static methods on many tasks, including the tuning learning rate of the deep neural network [6], the step-sizeadaptation of evolution strategy [29], and heuristic selection of planning [31].
The task of DAC typically focuses on a single type of conﬁguration hyperparameter(s), such as tuning the step-size in CMA-ES [29].
However, due to the increasing complexity of real-world problemmodeling, there are many algorithms whose performance rests on multiple types of hyperparameters.
Tuning one type while ﬁxing the rest may not produce promising results.
Take a popularevolutionary algorithm for multi-objective optimization problems, MOEA/D [41], as an example.
Ithas four types of conﬁguration hyperparameters: weights, neighborhood size, reproduction opera- tor type, and parameters associated with the reproduction operator used.
All of them are criticaland signiﬁcantly affect the performance of the algorithm [36].
Finding a near-optimal conﬁgurationcombination for even part of these hyperparameters requires massive manual effort [10].
In this paper, we attempt to extend DAC to dealing with tasks with multiple heterogeneous typesof conﬁguration hyperparameters.
We model this as a cooperative multi-agent problem [24], witheach agent handling one type of hyperparameters, for a shared goal (i.e., maximizing the teamreward).
Speciﬁcally, the proposed multi-agent DAC (MA-DAC) framework formulates the task asa contextual multi-agent MDP (MMDP) [4], and solves it by a common pay-off cooperative multiagent RL (MARL).
As an instantiation, we apply MA-DAC to the multi-objective evolutionaryalgorithm MOEA/D to learn the right conﬁgurations of its four types of hyperparameters by theclassic MARL algorithm called value-decomposition networks (VDN) [33].
Experiments on well-established multi-objective optimization problems show that MA-DAC outperforms other conﬁguration tuning methods based on heuristic rules [26], multi-armed bandits [17, 13]and single-agent RL [23].
Furthermore, we demonstrate the generalization of the learned MA-DACpolicy to both inner classes (different instances with the same number of objectives) and outer classes(different instances with different numbers of objectives).
Ablation studies demonstrate the importance of tuning every type of hyperparameter.
Our contributions are three-fold. 1)
To the best of our knowledge, the MA-DAC framework is theﬁrst one to address dynamic conﬁguration of algorithms with heterogeneous types of hyperparameters.
The contextual MMDP formulation of MA-DAC is analyzed, and experimental results showthat the presented formulation works well and has good generalization ability.
The instantiationof conﬁguring MOEA/D in this work can be used as a benchmark problem for MARL.
The heterogeneity of MOEA/D’s hyperparameters and the stochasticity of its search can promote the researchof the MARL algorithms.
Besides, the learned policies are useful for a speciﬁc type of optimizationtasks - multi-objective optimization, which will facilitate the application of MARL.
Background2.1 Dynamic algorithm conﬁguration
Different from the static conﬁguration of AC, DAC aims at dynamically adjusting the conﬁgurationhyperparameters of an algorithm during its optimization process.
Biedenkapp et al.
[2] formulated
DAC as a contextual MDP and applied RL to solve it.
Given a target algorithm A with its conﬁguration hyperparameters space Θ , a DAC policy π ∈ Π maps the state s ∈ S (e.g., history ofchanges in the objective value achieved by the target algorithm A ) to the action a ∈ A (i.e., a hyperparameter θ ∈ Θ of the target algorithm A ).
DAC aims at improving the performance of A on a setof instances (e.g., optimization functions).
Given a probability distribution p over the the space ofproblem instance set f ∈ F , the objective of DAC is to ﬁnd an optimal policy π ∗ .
That is,
[Equation]
where f ∈ F is a function to be optimized, and c ( π, f ) ∈ R is the cost function of the targetalgorithm with policy π on f .
It has been shown that DAC outperforms static policies in learning rateadaptation in SGD [6], step-size adaptation in CMA-ES [29], and heuristic selection in planning [31].
These applications all only involve a single type of hyperparameter(s).
Dynamic conﬁgurations ofcomplex algorithms with heterogeneous types of hyperparameters have been found to be difﬁcultfor current DAC methods [9].
2.2 Multi-agent reinforcement learning
A multi-agent system [40] under fully observable cooperative situation can be modeled as an
MMDP [4], which can be formalized as M := ⟨N , S , {A i } ni =1 , T , r ⟩ , where N is a set of n agents, 82 S is the state space, and A i is agent i ’s action space.
At each time-step, agent i ∈ N acquiress ∈ S
and then chooses the action a
i ∈ A i .
The joint action a = ⟨ a (1) , . .
. , a ( n ) ⟩ leads to next states ′ ∼ T ( · | s, a ) and all agents get a shared global reward r ( s, a ) .
The goal of an MMDP is to ﬁnd a joint policy that maps the states to probability distributions overjoint actions, π : S → ∆( A 1 × A 2 × · · · × A n ) , where ∆( A 1 × A 2 × · · · × A n ) stands for the distribution over joint actions, with the goal of maximizing the global value function: Q π ( s, a ) = 88 E π[-[ (cid:80) ∞ t =
-]
[ ∑ ∞ t =0 γ t r ( s t , a t ) | s 0 =
s, a 0 = a ] .
Multi-agent DAC framework
This section is devoted to the MA-DAC framework, where Section 3.1 is concerned with formulating
MA-DAC as a contextual MMDP and Section 3.2 is concerned with explaining detailed componentsof MA-DAC.
3.1 Problem formulation
We propose MA-DAC as a new paradigm for solving the dynamic conﬁguration of algorithmswith heterogeneous types of hyperparameters.
We formulate MA-DAC as a contextual MMDP 96 M I :=
{M i } i ∼I , where M i := ⟨N , S , {A j } nj =1 , T i , r i ⟩ is a single MMDP as deﬁned in Section 2.2.
The notion of context I induces multiple MMDPs.
Each M i stands for a speciﬁc instancei sampled from a given distribution I .
Different M i s have shared state and action spaces, but withdifferent transition and reward functions.
Algorithms are often tasked with solving different probleminstances from the same or similar domains.
Searching for well-performing parameter settings ona speciﬁc instance might achieve strong performance on that individual instance but might performpoorly in new instances.
Therefore, we explicitly take the instance distribution I as context intoaccount to facilitate generalization.
Given a parameterized algorithm A with a conﬁguration space Θ = { θ j } j ∈N , one agent in MA-DACis to handle one type of conﬁguration hyperparameter θ j ∈ Θ and all the agents work with the samegoal, i.e., maximizing the team reward.
The action space of each agent j ∈ N is the hyperparameterspace of the corresponding θ j .
Note that MA-DAC can be seen as a common-payoff cooperative
MARL problem and can be solved by cooperative MARL algorithms.
3.2 Components of MA-DAC
Next, we introduce several important components of MA-DAC, including the state, action, transition,reward, and instance set.
State.
The state is used to describe the situation of the target algorithm, which is a key componentin MA-DAC.
We suggest that the state should have the following properties.
Accessibility.
The state should be accessible in each step during the optimization process.
Representation.
The state should reﬂect the information in the optimization process.
Generalization.
The learned policy is expected to generalize to inner and even outer classesof instances.
Thus, the state should consist of the common features across different instances.
Besides, it is better if the state can be easily obtained, reducing the computational cost.
Action.
Each agent in MA-DAC focuses on one type of conﬁguration hyperparameter.
Its actionis the value of the hyperparameter that should be adjusted, which can be discrete or continuous.
MA-DAC agents are heterogeneous because they have completely different action spaces and affectdifferent types of hyperparameters of the target algorithm.
Transition.
The transition function describes the dynamics of the problem.
For an iterative algorithm, each iteration can be deﬁned as a step.
Given state s t , each agent acts a ( i ) t , and the probabilityof reaching state s t +1 can be expressed as T ( s t +1 | s t , a t ) .
Different from the state and actionspaces, the transition function depends on the given instance f ∈ F .
Thus, the policy should identify the characteristics of the current instance and take the optimal action under it.
Reward.
The reward is used to guide the policy’s learning process, whose quality has a signiﬁcantimpact on the policy’s ﬁnal performance.
Many RL benchmark environments include a well-deﬁned reward function.
However, in many application scenarios, we must deﬁne the reward function manually based on a speciﬁc metric that can indicate the ﬁnal performance.
Given a metric f ( s t ) of the problem, assume the smaller the value, the better the performance. Anintuitive way to deﬁne the reward function is r t = max { f ( s t ) − f ( s t +1 ) , 0 } .
However, this typeof reward function can easily mislead agents, because higher rewards do not always imply betterperformance, e.g., repeated rewards obtained by switching back and forth between good and badstates. Furthermore, the policy’s learning process will be inﬂuenced by different scales of instances.
To address the issues above, we propose the following reward function at step t :
[Equation]
where p t = f
( s 0 ) − f ( s t +1 )
f ( s 0 ) if f ( s t +1 ) <
f ∗ t , and p t = p t − 1 otherwise; f ∗ t is the minimum metricvalue found until step t .
[Figure]
As shown in Figure 1, the isosceles right-angled triangle indicates the maximum rewards we can get.
The triangle’s leftside (colored by blue) indicates the cumulative rewards alreadyachieved, the middle part (colored by green) indicates the immediate rewards obtained when the best-found metric value isimproved, and the right side (colored by brown) indicates therewards that can still be obtained in the future.
The reward function deﬁned in this way can prevent the agentsfrom getting repeated rewards. The structure of the trianglealso helps the agents focus on long-term rewards, because thereward increment becomes larger from left to right.
Exampleexplanations and comparative experiments will be provided in
Appendix B. We believe that this design is applicable to a widerange of similar tasks.
Instance set.
Instance set deﬁnes the optimization problem instances that have to be solved bythe target algorithm.
Note that the instances should have similar properties, otherwise the goodgeneralization ability is hardly achievable [9].
Applying MA-DAC to dynamic conﬁguration tuning of MOEA/D
As an instantiation, we apply MA-DAC to a well-established evolutionary algorithm for multiobjective optimization problems, multi-objective evolutionary algorithm based on decomposition(MOEA/D)
As one of the most widely used multi-objective evolutionary algorithms, MOEA/Dhas several heterogeneous types of conﬁguration hyperparameters (e.g., weights, neighborhood size,and reproduction operator type), which is a good ﬁt for the proposed MA-DAC.
We ﬁrst brieﬂy introduce multi-objective optimization and MOEA/D in Section 4.1, followed by detailed explanationsof applying MARL to MOEA/D in Section 4.2, which results in an MARL benchmark, denoted by
MaMo.
Finally, we compare MaMo with other MARL benchmarks in Section 4.3.
4.1 Multi-objective optimization and MOEA/D
Multi-objective optimization refers to an optimization problem with more than one objective tobe considered simultaneously.
It is very common in the real world.
For example, in deep neuralnetworks, apart from the accuracy, one may also care about the model size, latency, and/or energyconsumption [21, 12].
A prominent feature of multi-objective optimization problems (MOPs) is that unlike single-objectiveoptimization problems, in MOPs there is no single optimal solution, but a set of Pareto optimalsolutions.
A solution is called Pareto optimal if there is no other solution in the search space thatdominates it 1 .
Unfortunately, the number of Pareto optimal solutions for a given MOP is typically prohibitively large or even inﬁnite.
Therefore, the goal of a multi-objective optimization algorithmis to ﬁnd a good approximation that well represents all the Pareto optimal solutions.
Evolutionary algorithms have demonstrated their effectiveness to solve MOPs.
Their populationbased nature can approximate the problem’s optimal solutions within one execution, with each solution in the population representing a unique trade-off between the objectives.
MOEA/D [41] is arepresentative multi-objective evolutionary algorithm.
Unlike other mainstream multi-objective evolutionary algorithms like NSGA-II [7], which compare solutions based on their Pareto dominancerelation and density in the population, MOEA/D converts an MOP into a number of single-objectivesub-problems through a number of weights, where neighboring solutions work cooperatively for theoptimal solutions for the single-objective sub-problems.
As such, MOEA/D entails different heterogeneous types of hyperparameters, e.g., weights and neighborhood size.
Such hyperparameterssigniﬁcantly affect the performance of the algorithm.
For example, different weight distributionsare suitable for MOPs with different Pareto front shapes as the weights are used to control the distribution of the ﬁnal population [19].
A large neighborhood has high search ability in the objectivespace while a small neighborhood is beneﬁcial for diversity maintenance in the decision space [16].
In short, ﬁnding right conﬁgurations for these hyperparameters requires massive manual effort anddifferent conﬁgurations work well on different MOPs.
Note that recently some efforts have been made to tune the hyperparameters of MOEA/D by heuristic rules [26], multi-armed bandit [17] and RL [35].
However, they all focus on a single type ofhyperparameters, and also very few of them work on the dynamic algorithm conﬁguration as well.
4.2 MA-DAC for MOEA/D
In this section, we show how to apply MA-DAC to learn the conﬁguration policy of MOEA/D andalso introduce the resulting environment MaMo.
Each generation in the evolutionary process of
MOEA/ D is one step in the MaMo.
The state of MaMO can be divided into three parts.
The ﬁrst part is the features of the instance,including the number of variables and objectives.
The second part includes the features of theoptimization process, i.e., how much computational budget has been used and how many steps of thealgorithm have not made any progress.
Besides, we use several indicators, i.e., hypervolume 2 [43],the ratio of non-dominated solutions in the population and the average distance of the solutions, toreﬂect the evolutionary progress of the current population.
Lastly, we use statistic metrics (the meanand variance) of the indicators in several recent steps and all steps from the beginning to measurethe short and long histories of the optimization, respectively.
Note that all the states are normalizedto [0 , 1] to ensure the generalization of the learned MA-DAC policy.
We consider four heterogeneous types of conﬁguration hyperparameters in MOEA/D as the actionsof different agents of MA-DAC.
Weights.
In MOEA/D, weights are used to maintain the diversity of the converted single-
objective sub-problems [26].
The action space is discrete with two dimensions,
i
e., adjust- ing (T) and not adjusting (N) the weights.
Furthermore, we limit the frequency of adjust- ment, because too frequent adjustment will lead to drastic changes in the sub-problems and
is detrimental to the optimization process.
Neighborhood size.
The neighborhood size is to control the distance between solutions inmating selection; a small size helps the search exploit the local area while a large size helps
the search explore a wide objective space [39].
We discretize the action space into four dimensions.
Types of the reproduction operators.
We consider four types of differential evolution (DE)
operators.
Each type has different search ability [17].
Parameters of the reproduction operators.
The parameters (e g., scaling factor) of the repro- duction operators in MOEA/D signiﬁcantly affect the algorithm’s performance [32], and
the action space has dimensions
We use the MOPs with similar properties from the well-known MOP benchmarks DTLZ [8] and
WFG [14] as the instance set of MaMo.
These MOPs can have different number of objectives,and those with the same number of objectives can be seen as inner classes because the number ofobjectives considerably affects the properties and difﬁculty level of MOPs.
We use the invertedgenerational distance (IGD) [3] as the metric in Eq.
(2), resulting in the reward function.
To learn the policy, we use a classical MARL algorithm named VDN [33], which is widely used incooperative multi-agent systems.
VDN learns to decompose the team value function into agent-wisevalue functions, alleviating the exponential growth of the action space.
It follows the IndividualGlobal-Max (IGM) principle [30], i.e., the consistency between joint and local greedy action selections by the joint value function Q tot ( s, a ) and individual value functions [ Q i ( s, a ( i ) ) ] n i =1 .
Allparameters in the framework are updated using the standard TD loss from the global Q-values Q tot ,which follows additivity to factorize the global value function, i.e., Q tot ( s, a ) =
∑ ni =1 Q i ( s, a ( i ) ) .
In the testing phase, each agent acts greedily with respect to its Q i .
4.3 Comparison among MARL benchmarks
There are many benchmarks [25, 34] emerged in recent years.
In order to clearly show the characteristics of MaMo, we compare it with some MARL benchmarks, as shown in Table 1.
Heterogeneityrefers to agents having different action spaces or skills [37].
For example, in MaMo, there are fourentirely different action spaces, i.e., weights, neighborhood size, types of the reproduction operatorsand their paramters.
Stochasticity means that performing the same action in the same state may leadto a different next state.
The high stochasticity of MaMo comes from the randomness of MOEA/D. [Table] [Table] MPE [20]
[Table]
MAgent [42]
[Table]
SMAC [28] [Table] Active Voltage Control [38] [Table]
MaMo (Ours)
[Table]
The primary benchmarks are designed to investigate different aspects of multi-agent systems.
Forexample, Matrix Games [5] and Multi-Agent Particle Environments (MPE) are popular and classicaltestbeds, to investigate cooperative or competitive behaviors in small scale settings (with 2–3 agents).
MAgent [42] is used to test the scalability of MARL methods, where the number of agents is up to1000.
SMAC [28] has attracted wide attention in recent years to test the coordination ability in cooperative MARL.
For the ﬁrst time, Active Voltage Control [38] creates an exciting yet challengingreal-world scenario for the application of MARL.
To the best of our knowledge, none of the knownbenchmarks has focused on highly heterogeneous and stochastic scenarios in MARL.
We hope ournew MaMo benchmark can offer a good supplement that could beneﬁt the MARL community.
Experiments
To examine the effectiveness of MA-DAC, we conduct experiments using MaMo.
We investigate thefollowing research questions (RQs).
RQ1: How does MA-DAC perform compared with the baselineand other tuning algorithms?
RQ2: How is the generalization ability of MA-DAC?
RQ3: How dothe different parts of MA-DAC affect the performance?
We introduce the experimental settings in
Section 5.1, and investigate the above RQs in Section 5.2.
5.1 Experimental settings
We consider several well-established multi-objective test functions (DTLZ2, DTLZ4, and WFG4WFG9) with 3, 5, and 7 objectives following the practice in Bezerra et al.
[1] to examine our method.
Several arbitrary functions (here DTLZ2, WFG4 and WFG6) from the function set are used as the
[Table]
training set, and all the functions are considered in the testing.
IGD [3] is considered as the metricto measure the performance of the algorithms.
The mean and standard deviation of the IGD valuesobtained by each algorithm on each MOP for 30 independent runs are reported.
We apply the Wilcoxon rank-sum test with conﬁdence level 0.05.
For a fair comparison, other parameters (such aspopulation size and computational budget) are set to be the same across all the compared algorithms.
More details about the settings can be found in Appendix B due to space limitations.
The code usedin this paper is provided in the supplementary material.
5.2 Experimental results
RQ1: How does MA-DAC perform compared with the baseline and other tuning algorithms?
We compare the MA-DAC policy with the original MOEA/D [41], DQN [23], and MA-UCB [13].
DQN is a single-agent RL algorithm that shares the same state, reward, and transition as our MADAC but has a different action space that is the concatenation of the four types of hyperparameters.
DQN can be seen as an instantiation of DAC in MaMo.
MA-UCB is a simpliﬁed algorithm that usesfour UCB agents to adjust the four types of hyperparameters.
For MA-DAC and DQN, we performthe training and testing on the same number of objectives.
The results are shown in Table 2.
As can be seen in the table, MA-DAC is signiﬁcantly superior tothe other algorithms on almost all the 24 problems.
Furthermore, MA-DAC (which is trained only on
DTLZ2, WFG4, and WFG6) shows excellent performance on previously unseen problems during thetraining process, demonstrating its good generalization ability.
DQN policy is signiﬁcantly worsethan MA-DAC on all the problems, which is consistent with the previous observation that DQNperforms poorly in MARL tasks [11].
The superiority of MA-DAC over MA-UCB also demonstratesthe necessity of learning conﬁguration policy by an MARL algorithm.
We also compare our algorithm with two adaptive MOEA/D algorithms, i.e., MOEA/D-AWA [26]and MOEA/D-FRRMAB [17] which adjust the weights and reproduction operator type based onheuristic rules and MAB, respectively.
The results are in Appendix B due to space limitation.
RQ2: How is the generalization ability of MA-DAC?
We compare MA-DAC policies trainedfrom different training sets to test the generalization ability of MA-DAC policies.
MA-DAC (M)denotes that the policy is trained on the problems with all 3, 5, and 7 objectives.
Meanwhile, MADAC (3), (5), and (7) denote that the policies are trained on the problems with 3, 5, and 7 objectives,respectively.
As shown in Table 3, it is unsurprising that the results of average rank show that the MA-DAC (3),(5), and (7) policies have best performance on the problems with 3, 5, and 7 objectives, respectively.
For example, MA-DAC (3) has the best average rank (i.e., 1.625) on the problems with 3 objectivesbut has the worst average rank, i.e., 3.0 and 3.25, on the problems with 5 and 7 objectives, respectively.
To obtain a more robust policy, we mix the problems with multiple numbers of objectives astraining sets, resulting in the MA-DAC (M).
As can be seen in Table 3, MA-DAC (M) demonstratesits robustness.
Among all the policies, MA-DAC always takes the ﬁrst or second place in termsof its performance in all three types of problems.
Lastly, the last row of the table shows the outperformance of these MA-DAC policies compared with other policies – the IGD values of all thefour MA-DAC policies perform signiﬁcantly better than the best result obtained by the three peeralgorithms MOEA/D, DQN and MA-UCB in Table 2. , and almost equivalent to the best value except for MA-DAC in Table 2, respectively, according to the Wilcoxon rank-sum test with conﬁdence level 0. [Table]
RQ3: How do the different parts of MA-DAC affect the performance?
We conduct ablationstudies to show the importance of different types of hyperparameters, and the results are given in
Table 4.
We use MA-DAC (M) w/o i to denote the MA-DAC policy that does not include the i -thagent, and we use a reasonable setting as the default for each ablated agent; the detailed settingsare provided in Appendix B. That is, MA-DAC (M) w/o 1 , 2 , 3 , and 4 represent MA-DAC (M)without tuning weights, neighborhood size, types of reproduction operators, and parameters of thereproduction operators, respectively.
As can be seen in Table 4.
MA-DAC (M) outperforms all the ablations, demonstrating the importance of tuning every type of hyperparameter.
On the other hand, we notice that the importance ofhyperparameters varies.
For example, adaptive weights are in general more important as the performance of MA-DAC (M) w/o 1 drops signiﬁcantly.
In addition, we have conducted the ablationstudies for the reward; this can be found in Appendix B due to space limitations. [Table] + / − / ≈ 0/24/ 0/20/ 3/ [Table]
Conclusion
This paper considers the dynamic conﬁguration of algorithms with heterogeneous types of hyperparameters.
We propose the framework MA-DAC to solve it, where one agent works to handle onetype of conﬁguration hyperparameters.
Experimental results show that MA-DAC works well and hasgood generalization ability.
The instantiation of conﬁguring MOEA/D forms the benchmark MaMofor MARL, with the hope of facilitating the application of MARL.
In the future, we would like topropose a better contextual MMDP formulation and better cooperative MARL algorithm based onthe heterogeneity and stochasticity of MA-DAC.
It is also interesting to include more real-worldoptimization problems into MaMo.
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