DEPSO, or called DEPS, is an algorithm for (constrained) numerical optimization problem (NOP), which hybridizes the advantages of both Particle Swarm Optimization (PSO) and Differential Evolution (DE).
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Basic Description  What’s New  Problem to be solved  Setting Parameters  Output Information  References  Contact 

License information: DEPSO is free software; you can redistribute it and/or modify it under the terms of the Creative Commons NonCommercial License 3.0.
System Requirements: DEPSO is a platformindependent software developed by JAVA version 1.4 or above.
Command line (examples): $ java DEPSO Problem=<Problem_Name> [NAME=VALUE] …
What’s New


Version: V1.0.001 [download]:
 Bug fixed (Reported by Miklos Espak, Nov 16, 2010): ProblemEncoder.java
 For boundaryhandling, the cycled version [3] instead of the periodic version [1] is considered, so that all new solutions are generated within the original search space, as well as the agents are searching within a virtually infinite space. In addition, the limitation of maximal velocity is no longer required.
 The adaptive constraints relaxing (ACR) rule [2] might tackle the problem with equality constraints more efficiently than the basic constrainthandling (BCH) rule does.
 Newly introduced parameters: isACR.
Version: V1.0.000 [download]:
 It implements the original DEPSO algorithm [1].
 Setting parameters: Problem, N, T, Tout, FACTOR, CR, c1, c2, weight.
Problem to be solved


The problem to be solved is (constrained) numerical optimization problem (NOP), or called the nonlinear programming problem.
Tips: 1) all the variable bounds must be specified, since optimal solution(s) might situate at anywhere; 2) it had better to avoid using any equality constraints, at least any unavoidable constraint should be relaxed by a small tolerance value (e.g., ε=1E4 for problem.constrained.Michalewicz_G3); and 3) problem.ProblemEncoder andproblem.UnconstrainedProblemEncoder are the parental classes of all constrained (e.g.,problem.constrained.Michalewicz_G1) and unconstrained (e.g., problem.unconstrained.GoldsteinPrice) problems, respectively.
Implemented problem instances: please download from the uptodate list of source files, which will be situated in the directories: 1) problem/constrained, and 2) problem/unconstrained.
Setting parameters [NAME=VALUE]


NAME VALUE_type Range Default_Value Description Problem String * <Problem_Name> The problem to be solved //For example: problem.constrained.Michalewicz_G2 is the default value  N integer >5 70 The number of agents T integer >1 2000 The maximum learning cycles //The total number of evaluation times is about N*T isACR boolean false Constrainthandling: BCH(false), ACR(true) //Basic constrainthandling (BCH) rule or adaptive constraints relaxing (ACR) rule Tout integer >0 100 The output interval (not important) //The program outputs runtime information of the best solution every "Tout" cycles. FACTOR real (0, 1.2] 0.5 DE: scale constant CR real [0, 1] 0.9 DE: crossover constant //The parameters of DE operator, there are two suggested settings for DE: // 1) FACTOR=0.5, CR=0.9; 2) FACTOR=0.5, CR=0.1 c1 real [0, 2] 1.494 PSO: learning factor for pbest c2 real [0, 2] 1.494 PSO: learning factor for gbest weight real [0, 1] 0.729 PSO: inertia weight //The parameters of PSO operator, default values: c1=c2=1.494, weight=0.729
Output Information


//Vopt: the value of objective function; Vcon: the weighted constraint violation value (≥0), which is not outputted if Vcon≡0 since there is no violation [Summary information]: At the end, it outputs the input variables, response values, and evaluation values <Vcon, Vopt> of the best solution.
References


[1] WenJun Zhang, XiaoFeng Xie^{*}. DEPSO: hybrid particle swarm with differential evolution operator. IEEE International Conference on Systems, Man, and Cybernetics (SMCC), Washington, DC, USA, 2003: 38163821. [DOI] (^{*} Corresponding Author)
[2] XiaoFeng Xie, WenJun Zhang, DeChun Bi. Handling equality constraints by adaptive relaxing rule for swarm algorithms. Congress on Evolutionary Computation (CEC), Portland, OR, USA, 2004: 20122016. [DOI]
[3] XiaoFeng Xie, Jiming Liu. A compact multiagent system based on autonomy oriented computing, IEEE/WIC/ACM International Conference on Intelligent Agent Technology (IAT), Compiégne, France, 2005: 3844. [DOI]
[4] XiaoFeng Xie, Jiming Liu, ZunJing Wang. A cooperative group optimization system. Soft Computing, 2014, 18(3): 469495. [DOI]