Improved particle swarm optimizers with adaptive leadership features and their application in process water integration

• Main Author: Col-long, Kristine Joy
• Format: text
• Language: English
• Published: Animo Repository 2006
• Subjects: Chemical processes; Optimization techniques; Mathematical optimization; Water resources development; Process Control and Systems
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/3441; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/10279/viewcontent/CDTG004182_P__1_.pdf
• Institution: De La Salle University

Mismanagement of water resources is the main reason of water scarcity. Process Integration aims to optimize interrelationships of process units to improve performance in terms of cost minimization, energy efficiency or operability. Evolutionary search techniques have been studied extensively to approach these types of MINLP problems. A recently introduced algorithm called particle swarm optimization (PSO) has been applied in water network synthesis (Hul, 2006). This paper proposes enhancements to PSO technique. a-PSO incorporates the leader-follower concept into the algorithm to provide direction when searching for optimal positions. The leader holds the focal position in the swarm and knows the performance of all follower particles while the latter refers to the leader for direction. The velocity and position update functions are modified as follows: for the leader: vt a +1 = wvit + c1R1 ( pi best - xt a ) + c2R2 ( gbest - xt a ) (1) xt a 1 + = xt a + vit +1 (2) for the followers: vit +1 = vit + c1R1 ( pi best - xit ) + c2R2 ( xt a - xit ) (3) xit +1 = xit + vit +1 (4) Figure 1 (Above): a-PSO algorithm Figure 2 (Right): -PSO algorithm Is an optimum solution derived? Is the stdev below the threshold value? Initialize the position of the particles Update vt a +1 , xt a +1 , vit +1 and xit +1 Identify the leader START For every function evaluation Evaluate the objective function YES Reinitialize the followers END NO Determine stdev of the pbests YES NO Is an optimum solution derived? Initialize the position of the particles Update vt a +1 , xt a +1 , vit +1 and xit +1 Identify the leader START Evaluate the objective function YES END NO -PSO was developed from µ-GA, a small-population genetic algorithm with an adaptive reinitialization process which prevents loss of population diversity. The reset mechanism happens when the position of the particles falls below a standard deviation threshold at each iteration. A hypothetical plant from Polley and Polley (2000) was used to study the performance of the two novel algorithms. Initially, four processes require a total of 300t/h of water while discharging 280t/h of effluent. By adding just one interconnection from source 2 to sink 3, the freshwater input and wastewater generation are reduced by more than 25%. The figure on the left presents the optimal network with 1 link. Figure 3: Optimal water network for Polley and Polley (2000) case study The objective function is expressed as equation (5) while equations (6) to (8) show the mass balance and topological constraints. Min j wj F (5) Fwj + Fi, j - F j,k - F j,out = 0 (6) Fi, j (Ci out max , - Cj in max , ) - Fwj Cj in max , 0 (7) aij = N (8) where 1 if Fij rij > 0 aij = 0 if Fij rij = 0 Figure 4 shows that while three PSO variations result to satisfactory solutions, a-PSO and -PSO converge faster and provide quality solutions complying with the constraints. Figure 4: Comparison of results using a-PSO (A), PSO (B) and -PSO (C) 80 0 50 100 150 200 250 300 350 0 200 400 600 800 1000 1200 1400 1600 1800 2000 No. of iterations Water Budget A B C 50 20 70 60 D1 D4 D3 D2 S1 S2 S3 S4 100 50 70.