Both Multi-HDCS and Multi-Hyb (see section 6) use one centralised systematic search per agent, one distributed local search and one distributed systematic search. However, their overall approaches are substantially different as follows: (i) In Multi-HDCS all three types of searches run concurrently whereas in Multi-Hyb a two-phase strategy is used; (ii) In Multi-HDCS, the knowledge discovered during the distributed local search is regularly passed to the distributed systematic search; (iii) Multi-Hyb uses a fixed-order distributed systematic search whereas Multi-HDCS dynamically orders its agents in its distributed systematic search; (iv) Multi-Hyb adds solutions dynamically only to distributed local search whilst solutions are added dynamically to distributed local search and distributed systematic search in Multi-HDCS ; (v) the distributed local search and distributed sys- tematic search use complex variables in Multi-Hyb (i.e. one variable per agent containing all possible solutions for that agent) whilst only the distributed systematic search uses complex variables in Multi-HDCS. Multi-HDCS uses distributed local search for coarse- grained DisCSP algorithms so that the distributed local search has agents consisting of the number of variables which are externally relevant (i.e. have inter-agent constraints) for that agent. This was found to reduce the number of constraint checks over distributed local search with complex variables as there were less constraint checks performed when choosing a new value as the potential domain for the variable was much reduced. This wasn’t the case for distributed systematic search and so this still uses complex variables.
In terms of our problem areas, we have shown that Multi-HDCS is primarily effective at reducing NCCCs for randomly generated and sensor network problems. In addition, it can frequently also reduce the number of messages. Our graph colouring problems and scheduling problems tend to have symmetrical solutions (i.e. solutions spread equally over a large search space) in which case Multi-Hyb is the more effective algorithm. Multi-Hyb can find these solutions quickly without the additional overhead of concurrent searches which Multi-HDCS has.
7.6. Contributions 142
7.6
Contributions
The following contributions have been made:
1. The Multi-HDCS approach which finds the externally relevant solutions for each agent’s complex local problem whilst participating in a distributed local search and a distributed systematic search to find a global solution. The distributed local search periodically shares knowledge with the distributed systematic search.
2. Two implementations of the Multi-HDCS approach: Multi-HDCS-Pen using the penalty-on-values local search strategy and Multi-HDCS-DB using the breakout local search strategy.
3. InterDisPeL which revises the Multi-DisPeL approach specifically for considering inter-agent constraints and uses only solutions dynamically supplied by centralised systematic searches.
4. InterDisBO-wd which revises the DisBO-wd approach for inter-agent constraints and only considering solutions supplied dynamically by centralised systematic searches. 5. InterPODS, a dynamically ordered systematic search algorithm using complex vari-
ables which dynamically receives solutions from centralised systematic searches and knowledge from distributed local search.
7.7
Summary
Multi-HDCS is a new hybrid approach for solving DisCSPs with complex local problems where the problem solving is carried out by concurrent cooperative searches: (i) a set of centralised systematic searches (one per agent) finds all non-interchangeable solutions to each agent’s local problem; (ii) a distributed local search attempts to solve the inter- agent constraints using variable-value combinations approved by the centralised systematic searches. It also identifies local problems which are difficult to solve and passes this infor- mation to a distributed systematic search (see below); (iii) a distributed systematic search attempts to find a solution satisfying the inter-agent constraints using only variable-value
combinations approved by centralised systematic searches whilst dynamically prioritising agents acording to the level of difficulty of their local problems assigned by the distributed local search.
We have presented two implementations of our approach: Multi-HDCS-Pen and Multi- HDCS-DB. These approaches differ mainly in the algorithm used for distributed local search: Multi-HDCS-Pen uses a penalty-based algorithm (InterDisPeL) whereas Multi- HDCS-DB uses a breakout-based (i.e. weights on constraints) algorithm (Inter-DisBO- wd ). Both algorithms use SEBJ to solve the agent’s local problem and InterPODS as the distributed systematic search algorithm.
Substantial empirical results on several problem classes demonstrate that the Multi- HDCS approach (particularly in the Multi-HDCS-DB implementation) is generally com- petitive when compared to leading DisCSPs with complex local problems algorithms on both solvable problems and unsolvable problems.
Chapter 8
Conclusions and Future Work
This thesis has researched and developed hybrid algorithms for Distributed Constraint Satisfaction and their applicability on a number of problem classes. A number of new contributions to the Distributed Constraint Satisfaction community in the field of hybrid algorithms have been made through this thesis. This chapter outlines the contributions of this thesis and possible avenues for future work.
8.1
Contributions
A number of contributions have been made in this thesis (table 8.1 summarises the con- tributions):
1. In chapter 5, the DisHyb approach was presented. This novel hybrid approach for DisCSPs with one variable per agent runs a distributed local search algorithm for a bounded number of cycles. This local search algorithm learns important knowledge about difficult variables and the best values for those variables. If the distributed local search algorithm fails to solve the problem, a distributed systematic search runs guided by the knowledge learnt by distributed local search. Two implementations of this approach have been presented in this thesis: PenDHyb and DBHyb. We have derived a formula to predict the best number of cycles for distributed local search and also shown that much longer executions of local search may be beneficial for harder solvable problems. We have shown that PenDHyb and DBHyb outperform
systematic search on three problem classes (randomly generated problems, graph colouring problems and meeting scheduling problems).
2. In chapter 6, the Multi-Hyb approach was presented. This is a novel two-phase hybrid approach for DisCSPs with complex local problems. In the first phase, a centralised systematic search algorithm runs concurrently for each agent to find solutions for that agent’s complex local problem. Concurrently, a distributed local search algorithm runs which only considers constraints between agents and attempts to combine solutions to an agent’s complex local problem (i.e. partial solutions to the global problem) in order to find a global solution to the problem. This local search also learns about difficult variable and value combinations. If all solutions to an agent’s complex local problem are found before distributed local search finds a solution, a distributed systematic search runs which finds a solution or detects unsolvability. Two implementations of this approach have been presented in this thesis: Multi-Hyb-Pen and Multi-Hyb-DB. We have shown that Multi-Hyb-Pen and Multi-Hyb-DB often outperform leading algorithms for DisCSPs with complex local problems (Multi-ABT, Multi-AWCS, Multi-DisPeL, DisBO-wd) on randomly gener- ated problems, graph colouring problems, meeting scheduling problems (for number of messages) and sensor network problems.
3. In chapter 7, the Multi-HDCS approach was presented. This is a novel hybrid approach for DisCSPs with complex local problems. This algorithm also runs con- currently a centralised systematic search for each agent to detect all solutions to an agent’s complex local problem. In addition, two concurrent searches are run: (i) a distributed local search algorithm which learns about difficult variables and values in addition to attempting to finding a global solution to the problem; (ii) a dis- tributed systematic search which is guided by the distributed local search through synchronisation of information and finds a global solution to the problem or detects unsolvability. Two implementations of this approach have been presented in this thesis: Multi-HDCS-Pen and Multi-HDCS-DB. We have shown that Multi-HDCS is an important revision to Multi-Hyb which outperforms Multi-Hyb on randomly
8.2. Future Work 146