Container Handling Using Multi-agent Architecture

Transcription

1 Container Handling Using Multi-agent Architecture Meriam Kefi 1, Ouajdi Korbaa 2, Khaled Ghedira 1, and Pascal Yim 2 1 Ecole Nationale des Sciences de l Informatique Université de Manouba 2010 Manouba, Tunisie 2 Ecole Centrale de Lille BP 48, Cité scientifique, F59651Villeneuve d Ascq, France Meriem.Elkefi@ec-lille.fr, Khaled.Ghedira@isg.rnu.tn, {Ouajdi.Korbaa, Pascal.Yim@ec-lille.fr Abstract. Container terminals are essential intermodal interfaces in the global transportation network. Efficient container handling at terminals is important in reducing transportation costs and keeping shipping schedules. This paper discusses a multi-agent model to simulate, solve and optimize the amount of storage space for handling container departures within a fluvial or maritime port. The multi-agent model is developed to minimize the expected total number of rehandles while respecting spatio-temporal constraints. Experimental and numerical runs are given and illustrated. These runs carry out the proposed multi-agent model with comparison to the associated centralized version, basing on non-informed search algorithm and informed search algorithm. They show that the multi-agent model reduces rather the number of expected relocation movements especially when basing on informed search algorithm. Keywords: Container terminal, Space allocation, transportation, Container stacking, Multi-agent systems. 1 Introduction The improvement of customer service in fluvial or maritime ports constituted of container terminals becomes an important problem facing the big concurrence between ports. One of the measures of performance of this service is the berthing time of ships. This time is composed in major part of container loading and unloading time. To reduce loading duration, it is necessary to choose adequate storage slots either for the arriving containers or for the shifted containers after successive departures of others, in order to be loaded efficiently (minimization of the number of re-handles) within a vessel. This operation allying transfer, stacking and unstacking of containers is claimed to be an important problem among the decision problems met in container terminal [12]. In literature, few studies are dedicated to this problem which is known by "Container Stacking Problem". [6] proposed dynamic programming to attain an ideal configuration while minimizing the number of containers to move and the follow-on travelled distance. The problem is divided into two sub-problems: Bay matching and N.T. Nguyen et al. (Eds.): KES-AMSTA 2007, LNAI 4496, pp , Springer-Verlag Berlin Heidelberg 2007

2 686 M. Kefi et al. move planning problem, and moving tasks sequencing problem. A mathematical model is used for the resolution of each sub-problem. It is noted worthy that [10] used genetic algorithms in their study to reduce container transfer and handling times and thereafter the berthing time of ship at port quays. An interesting work, propounded by [7], dealt with the problem of determination of the best storage slot for containers with the aim of minimizing the number of expected relocation movements in loading operation. They deployed the weight of the container as criteria to define certain priority between the different containers to be stacked in the storage yard. [1] provided an empiric and comparative survey of the different strategies of container storage in a terminal port according to several parameters. Another work [8] proposed a cost model for determining the optimal storage position and the optimal number of cranes used for container handling. A recent work [9] has described a model to determine in real time the best slot of an arriving container in the storage yard, while minimizing the number of the expected relocation movements at the phase of loading containers in a ship. It should be noted that these studies often used the above-mentioned mathematical models to solve the underlined problem. These models were not very efficient and successful seen the complexity and the dynamicity of this problem. Besides, we observe that the multi - agent approach used in [2], [11] and [5] is applied very insufficiently to solve the problem of container stacking. In this paper, we focus on container handling when container departures occur, while the majority of related works are focused on container arrivals. Furthermore, we opt for the distributed resolution via the multi-agent systems. In fact, these systems prove to lend themselves to model phenomena in which the interactions between various entities are too complex to be apprehended by classic tools of mathematical modelling. Therefore, we set a multi- agent model to solve the problem of container storage. We refer to concepts that are exploited in a multi-agent context to solve combinatorial problems by Ghedira [4], and in eco-solving method applied to solve the Block world Problem [2]. The remainder of this paper is organized as follows. Section 2 presents parameters, hypotheses and objective of the considered problem. Section 3 describes the architecture of the proposed multi-agent model. Section 4 details the dynamic of this model. Section 5 provides corresponding numerical results. Some conclusions and perspectives are drawn in the last section 6. 2 Problem Description Our essential concern is to arrange the containers in adequate slots with respect to spatio-temporal constraints in order to minimize the relocation movements precisely the unproductive movements at the moment of their departure in order to be loaded on vessels (i.e., when an outside truck or vessel arrives in a random manner and requests a container, one of the difficult problems in the yard operation is that it takes too much handling effort to re-handle containers on the top of the requested container).

3 Container Handling Using Multi-agent Architecture 687 It should be mentioned that in port s storage yard, distances are not very big. Therefore, the time that a reach stacker takes to transport a container from one slot to another is very similar whatever the position of the container is. For this reason, we focus on the relocation movements which induce delays. Thus, our study seeks to answer the following question: after every departure of some containers, how can we rearrange the containers unconcerned by this departure in most adequate manner? The rationale underlying this was to manage the next departures efficiently (i.e., retrieving easily the containers to load on vessel) as well as the next arrivals (i.e., determining easily the appropriate slots for the containers to stack). To clarify the problem raised, we present next its parameters, its hypotheses, its constraints and its objectives. 2.1 Parameters The following parameters were taken into account in our study: - A storage yard composed of M Slots, - N ISO Containers stocked in stacks, - H max : the maximal height of stacks, - initconfig: an initial arrangement of the N containers in the M available slots, - finconfig: a final possible arrangement of deranged containers after the departure of some ones. This arrangement must be attained from initconfig. 2.2 Hypotheses We adopt the following hypotheses: - Container arrival and a departure cannot coincide, - The departure order of different containers is known, while their arrival order is unknown, - Only one container arrives at once, - The containers of different dimensions (1 TEU, 2 TEU etc.) are stacked on two different storage yards, - A movement consists on removing a container and putting it somewhere, - Vessels are classified as A, B, C, D, E, and F according to the chronological order of their departure dates which are known in advance, - Vessels of which the exact departure dates are beyond F are called Y. - Vessels of which the departure dates is completely unknown are called Z, - We associate to every container the vessel whereby it is going to leave (A, B, C, D, E, F Y & Z) which determines implicitly its departure date t. For example, for two different containers C and C, if C is going to leave on vessel A and C is going to leave on vessel B, C, D,.. or Y then t (C) <t (C '), - The containers are categorized identically to the associated vessels. For example a container is of category A if it is going to leave on vessel A, - One container is prioritized to another container if the category of the former is less than the category of the latter (A<B<C<D<E<F).

4 688 M. Kefi et al. 2.3 Objectives The objective of the present study is to determine firstly a feasible sequence of successive unstacking stacking operations, and then approximate one that minimises container rehandles, considering temporal and spatial constraints. To achieve this objective, we have developed a multi-agent model implementing both non informed and informed algorithms. This model will be detailed in the next section. 3 Architecture of Multi-agent Model 3.1 Assumptions and Definitions - A Container agent corresponds to each container, - A Container agent cannot be placed on another one unless it is free. - Container agent j blocks another Container agent i, if its own category is greater than the category of i, - A Container agent is satisfied, if it is placed in a slot without blocking another one. - The state of a Container agent is either satisfied or unsatisfied. - A Container agent is free if he does not have Container agents above. 3.2 Architecture The agents defined in the proposed multi-agent model are: the Container agent and the Interface agent. The Container agent is defined by its acquaintances formed by the other Container agents and the agent Interface, its static knowledge: identifier, destination port, load, tare and dimension; and its dynamic knowledge: category, the Container agent under, the Container agent on and State. Its behaviour will be described in the following section. 4 Multi-Agent Dynamic Here, we provide a description of the dynamic of the set up multi-agent model: the main steps of the solving process, and the most important messages exchanged between the different agents and incorporated into their behaviour. 4.1 Solving Process The solving process associated to the multi-agent model is composed essentially of the following steps: - Setting the state of the Container agents which block the Container agents A to "Unsatisfied". - Departure of the Container agents A. - The Container agents which blocked the Container agents A are deranged, and then they search a new adequate slot by diffusing a message "Search-Place" to their acquaintances to request a new appropriate slot eventually. - Reception of messages: "I_m_Free" et "I_m_Sorry".

5 Container Handling Using Multi-agent Architecture When receiving messages "I_m_Free", then a Container agent sends the message "Migrate" to the free Container agent. - Sending "I_am_Leaving": one Container agent leaves its current slot only if it received a message "Confirm" from the Container agent which is accepting it to be on. - Finishing if all the containers are satisfied. 4.2 Exchanged Messages The solving process above described is based on a negotiation protocol that involves different types of messages exchanged between two different Container agents i and j: - "I_am_Blocked": i wants to be free to leave its slot; it is blocked in by j. - "Search_Place»: i is looking for an appropriate slot. - "I_am_Free»: i informs j that it is free and then proposes to j to take place on it. - "Apologize": i informs j that it can not accept it on because there is an other Container agent which takes the place. This is due to the asynchronous aspect of exchanging messages in a Multi-Agent model generally. - "Migration": i asks j if it possible to be above. - "Confirmation": i accepts definitively j to be on. - "Rejection»: i refuses the migration request of j. - "I_m_Leaving": i informs j that it goes away, so j becomes free. These messages are invoked through a global behavior procedure: Procedure Global_Behaviour() { ACLMessage msg = receive(aclmessage.inform); if (msg!= null) { if ( (msg == ("you_are_free")) { I_m_Free(Sender); if ( (msg ==("you_block_me")) { I_Block(); if ( (msg ==("Search_place")) { Search_place_for(Sender)); if ( (msg ==("on_you")) { On_me(Sender); if ( (msg ==("I_m_Free")) { It_is_Free(Sender); if ( (msg ==("appologize")) { It_applogizes(Sender);

6 690 M. Kefi et al. if ((msg == ("CIAO")){ dodelete(); if((msg == ("update")){ update_coordinates(msg); if((msg == ("confirm")){ It_confirms(Sender, SenderState); if((msg == ("reject")){ It_rejects(); 5 Experimental Results We used JADE platform: to implement the proposed multi-agent model. To evaluate our model, we have first developed the distributed version and the corresponding centralized version, and then we have associated to each one a non informed search algorithm and an informed search algorithm, i.e. in the former, the determination of a new slot for each Container agent is done randomly. By the opposite, in the latter a tested heuristic is applied locally to each Container agent who is searching an appropriate place. The following graphics show plots comparing these versions. We represent on axis Y the total number of unproductive movements in function of random-generated Fig. 1. This figure shows a comparison between the Distributed version DNIA "Distributed Non Informed Algorithm" and the centralized version CNIA "Centralized Non Informed Algorithm", both based on non informed algorithm

7 Container Handling Using Multi-agent Architecture 691 instances mentioned on Axis X. Each instance signifies an initial configuration with a certain number of containers. We note that the numerical results correspond to 10-run average for each generated instance. As shown (Fig. 1), the distributed version outperforms slightly the centralised version given a non informed algorithm to solve the underlying problem. This enhancement is due to cooperation between the agents of our Multi-agent model. In fact, cooperation helps to reach near values in ten runs of the same instance. Fig. 2. This figure shows a comparison between two Distributed versions: one based on non informed algorithm DNIA «Distributed Non Informed Algorithm» and the other based on informed algorithm DIA «Distributed Informed Algorithm " Fig. 3. This figure shows a comparison between the Distributed version DIA "Distributed Informed Algorithm" and the Centralized version CIA "Centralized Informed Algorithm", both based on informed algorithm

8 692 M. Kefi et al. To improve the previous results, we have introduced an intelligence degree on the behaviour of the Container agents using an informed algorithm, i.e. when searching a new place; each Container agent does not select randomly a new slot among received proposals, but it applies intelligibly a tested heuristic. Then, as shown (Fig. 2, Fig. 3), a significant improvement is noted particularly when the number of containers is increasing with comparison to the distributed version with non informed algorithm and the centralised version with an informed algorithm. Fig. 4. This figure shows a comparison between the Distributed version based on informed algorithm DIA "Distributed Informed Algorithm" and the Centralized version based on non informed algorithm CNIA: Centralized Non Informed Algorithm" As we clearly observe, the results (Fig. 4) show a larger enhancement which is due to the combination of distributed algorithm and informed algorithm. Indeed, introducing intelligence on Container agent behavior led to reduce significantly the total number of unproductive movements. We should notice that the number of containers is not sufficient to characterize a generated initial configuration (number of containers 18). We should determine a more significant parameter to evaluate the evolution of the unproductive movements. This constitutes one point of interest in our current works. 6 Conclusion In this paper, we described and developed a multi-agent model to solve and optimize the container handling on ports, especially the container stacking process after container departures. This model involves uniquely Container agents, which cooperate, coordinate and negotiate within a solving process. This paper provides empirical and comparative studies showing that multi-agent model where we are introducing intelligence degree within agent behaviour via informed algorithm outperforms considerably the multi-agent model with non

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