# A Population-Based Search Approach to Solve Continuous Distributed Constraint Optimization Problems
## 7 Discussions  
In recent years, the C-DCOPs have been widely studied as an extension framework of DCOPs. As a basic problem framework, there are many other extension frameworks of DCOPs that have become research hot-spots, such as _Asymmetric DCOPs_ (ADCOPs) [45], _Multi-objective DCOPs_ (MO-DCOPs) [46], _Dynamic DCOPs_ (D-DCOPs) [47], _Probabilistic DCOPs_ (P-DCOPs) [48], etc. Accordingly, many algorithms have been proposed for solving different DCOPs-based frameworks. Specifically, in contrast to DCOPs, the utility generated by one agent in ADCOPs from a utility function may differ from the utility generated by another agent from the same utility function. Therefore, the authors of reference [45] extend DSA and proposes _Asymmetric Coordinated Local Search_ (ACLS) to solve ADCOPs, which changes its value with a certain probability to escape from local minimums. The authors of reference [49] solve ADCOPs by employing the PT-ISABB algorithm, which adopts customized inference algorithms to provide strict upper and lower bounds and adopts a complete tree-based search to guarantee optimal performance. In [50], AsymDPOP is proposed to solve the privacy exposure problem in ADCOPs. For MO-DCOPs, the authors of reference [51] propose _Multi-objective Synchronous Branch and Bound_ (MO-SBB) to solve it; the agents in MO-SBB extend the _Current Partial Assignment_ (CPA) with their own assignments with the current utility vector. Once a non-dominated solution is found, it is broadcasted to all agents and the solution is added to the global bounding list. In addition, the authors of reference [52] adopt the concept of non-dominated bounded vectors and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Graph Type** & **Our Algorithms** & **HCMS (\(\sigma\))** & **PCD (\(\sigma\))** & **C-CCoA (\(\sigma\))** & **PCD-LD (\(\sigma\))** \\ \hline \multirow{2}{*}{Sparse random graphs} & PLSA & 19.68\% (\(\pm\)3.17\%) & 24.24\% (\(\pm\)8.53\%) & 13.61\% (\(\pm\)5.40\%) & 3.55\% (\(\pm\)2.00\%) \\  & PGSA & 23.68\% (\(\pm\)4.06\%) & 28.41\% (\(\pm\)9.25\%) & 17.42\% (\(\pm\)6.08\%) & 7.01\% (\(\pm\)2.58\%) \\ \hline \multirow{2}{*}{Dense random graphs} & PLSA & 26.57\% (\(\pm\)3.97\%) & 29.83\% (\(\pm\)6.94\%) & 49.03\% (\(\pm\)6.66\%) & 6.52\% (\(\pm\)3.56\%) \\  & PGSA & 28.70\% (\(\pm\)4.26\%) & 31.97\% (\(\pm\)6.43\%) & 51.50\% (\(\pm\)6.13\%) & 8.30\% (\(\pm\)3.49\%) \\ \hline \multirow{2}{*}{Scale-free networks} & PLSA & 20.43\% (\(\pm\)3.42\%) & 23.19\% (\(\pm\)8.47\%) & 20.65\% (\(\pm\)6.90\%) & 3.93\% (\(\pm\)1.94\%) \\  & PGSA & 25.44\% (\(\pm\)4.12\%) & 28.31\% (\(\pm\)9.02\%) & 25.65\% (\(\pm\)7.15\%) & 8.23\% (\(\pm\)2.14\%) \\ \hline \multirow{2}{*}{Small-world networks} & PLSA & 20.03\% (\(\pm\)3.08\%) & 22.18\% (\(\pm\)7.57\%) & 13.57\% (\(\pm\)1.99\%) & 2.06\% (\(\pm\)2.54\%) \\  & PGSA & 27.45\% (\(\pm\)2.31\%) & 27.57\% (\(\pm\)7.16\%) & 18.65\% (\(\pm\)3.28\%) & 6.59\% (\(\pm\)1.98\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average improvement rate (rounded to two decimals) of PLSA and PGSA compared to the competing algorithms on three benchmark problems with different numbers of agents, where \(\sigma\) represents the standard deviation of the improvement rates. retain only non-dominated vectors to solve MO-DCOPs. Then, the D-DCOPs are proposed to cope with environmental evolution over time. The authors of reference [53] introduces an inference-based approach and employ the _Hybrid Algorithm for Reconstructing Pseudo-trees_ (HARP) to solve D-DCOPs, which reuses previous DCOP information to accelerate the search for solutions. In addition [54], the authors employ a reinforcement learning approach to solve D-DCOPs. Finally, P-DCOPs are proposed to cope with environments with stochastic behavior, i.e., there are unexpected events that affect the agent's behavior.