Preference-inspired Co-evolutionary Algorithm Research Articles

Preference-inspired coevolutionary algorithm with sparse autoencoder for many-objective optimization

Preference-inspired coevolutionary algorithm with sparse autoencoder for many-objective optimization

Two-Stage Multi-Objective Stochastic Model on Patient Transfer and Relief Distribution in Lockdown Area of COVID-19.

The outbreak of an epidemic disease may cause a large number of infections and a slightly higher death rate. In response to epidemic disease, both patient transfer and relief distribution are significant to reduce corresponding damage. This study proposes a two-stage multi-objective stochastic model (TMS-PTRD) considering pre-pandemic preparedness measures and post-pandemic relief operations. The proposed model considers the following four objectives: the total number of untreated infected patients, the total transfer time, the overall cost, and the equity distribution of relief supplies. Before an outbreak, the locations of temporary relief distribution centers (TRDCs) and the inventory levels of established TRDCs should be determined. After an outbreak, the locations of temporary hospitals (THs), the locations of designated hospitals (DHs), the transfer plans for patients, and the relief distribution should be determined. To solve the TMS-PTRD model, we address an improved preference-inspired co-evolutionary algorithm named the PICEA-g-AKNN algorithm, which is embedded with a novel similarity distance and three different tailored evolutionary strategies. A real-world case study of Hunan of China and 18 test instances are randomly generated to evaluate the TMS-PTRD model. The finding shows that the PICEA-g-AKNN algorithm is better than some most widely used multi-objective algorithms.

Robust Optimization of the Multi-Objective Multi-Period Location-Routing Problem for Epidemic Logistics System With Uncertain Demand

The effective distribution of relief to an emergency logistics system plays a crucial role during the disaster response phase. Considering stochastic characteristics of relief demand, this study investigates the robust optimization of a multi-objective multi-period location-routing problem for epidemic logistics, a special emergency logistics, with uncertain scenarios. A corresponding robust multi-objective multi-period optimization model is proposed, which aims to determine the optimal location of temporary relief distribution centres and route planning simultaneously. The optimization objectives include the total travel time, the total cost, and the disutility of relief service. To solve the above optimization model, a preference-inspired co-evolutionary algorithm with Tchebycheff decomposition (PICEA-g-td) is given. The performance of the proposed PICEA-g-td is evaluated by comparing it with NSGA-II, MOEA/D and PICEA-g. The experimental results show that the proposed algorithm performs better than the other three algorithms in terms of the solution quality. Finally, some useful management insights are obtained.

Preference-inspired coevolutionary algorithm based on differentiated space for many-objective problems

Preference-inspired coevolutionary algorithm based on differentiated space for many-objective problems

Preference-inspired coevolutionary algorithm with active diversity strategy for multi-objective multi-modal optimization

Multi-objective multi-modal optimization problems have recently received increasing attention in the field of evolutionary computation. Addressing such problems is not easy for existing evolutionary multi-objective algorithms (EMOAs) since they require finding solutions with good convergence and diversity in both objective and decision spaces. This study therefore proposes a new algorithm, namely, the preference-inspired coevolutionary algorithm (PICEAg) with an active diversity strategy, to deal with multi-objective multi-modal optimization problems. The proposed algorithm, denoted as MMPICEAg, adopts the popular coevolutionary framework of PICEAg and introduces a diversity-aware fitness assignment and a double-diversity archive update strategy to promote diversity in objective and decision spaces simultaneously. The performance of MMPICEAg is compared with that of three general EMOAs as well as four state-of-the-art multi-modal EMOAs. The comparison results on three sets of widely used benchmarks clearly demonstrate the effectiveness of MMPICEAg for multi-objective multi-modal optimization.

Mathematical Optimization Method of Low-Impact Development Layout in the Sponge City

Aiming at the optimization layout of distributed low-impact development (LID) practices in the sponge city, a new mathematical method combining Stormwater Management Model (SWMM) and preference-inspired co-evolutionary algorithm using goal vectors (PICEA-g) was developed and was applied in the Ximen waterlogged area of Pingxiang City. Firstly, a block-scaled rainfall-runoff model was built in the study area by using SWMM. Then, an LIDs area optimization model was established by linking the SWMM and the PICEA-g based on the Matlab platform, which took the area ratios of various LIDs in each block as decision variables and took the total runoff, peak flow, suspended substance (SS) pollutant, and LIDs cost as objective functions. Thus, the problem of LIDs layout was turned into a mathematical optimization issue. So the cost-benefit optimal solutions with different emphases were found by using this algorithm, and the LIDs layout optimal scheme for this area was further analysed and verified by rainfall-runoff model. The results show that the total runoff reduction rates of the system reach a maximum of 21.8%, the peak flow reduction rates of the system are more than 10%, and the SS pollutant reduction rates are reduced by about 30% compared with before LIDs under the design storms of different return periods. The reduction rates of each runoff index are higher than the nondominated sorting genetic algorithm II (NSGA-II) method, and decision-makers can more effectively analyse the cost-benefit optimal solution from the Pareto solution sets. Therefore, the LIDs layout optimization method proposed in this paper has obvious advantages in solving similar many-objective optimization problems (MOOPs) in sponge city construction.

Preference-Inspired Coevolutionary Algorithm Based on Differentiated Resource Allocation Strategy

Preference-inspired co-evolutionary algorithms (PICEAs) consider the target vectors as the preferences, and then use the domination relationship between the candidate solutions and target vectors to increase their selection pressure. However, the size of dominating objective space varies with the different positions of candidate solutions and it leads to the imbalance of the evolutionary ability of whole population. To solve this problem, this paper proposes a preference-inspired coevolutionary algorithm based on a differentiated allocation strategy (PICEAg-DS). First, it sets up an external archive to save the nondominated solutions and then extracts the convergence and diversity information from it. Second, it divides the objective space into several subspaces and designs a space distance operator to evaluate their optimization difficulty. Finally, it dynamically assigns the target vectors and guides more computational resource to the difficult to optimize subspaces, and thus drives the whole population evolution. To prove the advantages of differentiated resource allocation strategy, the PICEAg-DS is compared with two classic coevolutionary algorithms (PICEAg, CMOPSO) and two classic MOEAs based on resource allocation strategy (EAG-MOEAD, MOEAD-DRA). The experimental results show that PICEAg-DS performs better than the other algorithms on many WFG test problems. To further analysis the effectiveness of PICEAg-DS, compare it with two MOEAs based on domination relationship (NSGAII, SPEA2) and two MOEAs based on decomposition (RVEA, MOEA/D-M2M) on MOP and UF test suite. The experimental results show the PICEAg-DS has a better convergence than the other comparison algorithms, especially on 3-objective MOP6-7 and UF8-9.

Multi-Objective Optimal Reactive Power Dispatch of Power Systems by Combining Classification-Based Multi-Objective Evolutionary Algorithm and Integrated Decision Making

For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming to minimize active power loss and voltage deviation is formulated. And then the two-step approach integrating decision-making into optimization is proposed to solve the model. Specifically speaking, the first step aims to seek the Pareto optimal solutions (POSs) with good distribution by using a multi-objective optimization (MOO) algorithm named classification and Pareto domination based multi-objective evolutionary algorithm (CPSMOEA). Furthermore, the reference Pareto-optimal front is generated to validate the Pareto front obtained using CPSMOEA; in the second step, integrated decision-making by combining fuzzy c-means algorithm (FCM) with grey relation projection method (GRP) aims to extract the best compromise solutions which reflect the preferences of decision-makers from the POSs. Based on the test results on the IEEE 30-bus and IEEE 118-bus test systems, it is demonstrated that the proposed approach not only manages to address the MORPD issue but also outperforms other commonly-used MOO algorithms including multi-objective particle swarm optimization (MOPSO), preference-inspired coevolutionary algorithm (PICEAg) and the third evolution step of generalized differential evolution (GDE3).

Multi-objective mean-semi-entropy model for optimal standalone micro-grid planning with uncertain renewable energy resources

Standalone renewable energy system holds the most promising solution to the electrification of remote areas without utility grid access as well as to reduce fossil fuel consumption and environmental pollution. However, the random volatility and unpredictability of renewable energy are key factors to restrict its large-scale accommodation. In the present study, a multi-objective mean-semi-entropy model is proposed for a standalone micro-grid with photovoltaic-wind-battery-diesel generator hybrid system, with the aim of providing a trade-off solution between maximum profits and minimum risk in consideration of photovoltaic and wind uncertainties. Then, the preference-inspired co-evolutionary algorithm, along with Pareto optimality concept, is used for the system techno-economic optimization, i.e., to maximize the profits defined as the mean value of the return and to minimize the risk defined as the semi-entropy simultaneously. Subsequently, the preference ranking organization method is used for decision making to determine the optimal trade-off dispatch solution. Simulation results show that the multi-objective mean-semi-entropy model is well applicable to deal with standalone micro-grid operation, considering the integration of uncertain renewable energy resources.

Multi-Objective Optimal Design of Renewable Energy Integrated CCHP System Using PICEA-g

The integration of renewable energies into combined cooling, heating, and power (CCHP) systems has become increasingly popular in recent years. However, the optimization of renewable energies integrated CCHP (RECCHP) systems (i.e., optimal component configurations) is far from being well addressed, especially in isolated mode. This study aims to fill this research gap. A multi-objective optimization model characterizing the system reliability, system cost, and environmental sustainability is constructed. In this model, the objectives include minimization of annual total cost (ATC), carbon dioxide emission (CDE), and loss of energy supply probability (LESP). The decision variables representing the configuration of the RECCHP system include the number of photovoltaic (PV) panels and wind turbines (WTs), the tilt angle of PV panels, the height of WTs, the maximum fuel consumption, and the capacity of battery and heat storage tanks (HSTs). The multi-objective model is solved by a multi-objective evolutionary algorithm, namely, the preference-inspired coevolutionary algorithm (PICEA-g), resulting in a set of Pareto optimal (trade-off) solutions. Then, a decision-making process is demonstrated, selecting a preferred solution amongst those trade-off solutions by further considering the decision-maker preferences. Furthermore, on the optimization of the RECCHP system, operational strategies (i.e., following electric load, FEL, and following thermal load, FTL) are considered, respectively. Experimental results show that the FEL and FTL strategies lead to different optimal configurations. In general, the FTL is recommended in summer and winter, while the FEL is more suitable for spring and autumn. Compared with traditional energy systems, RECCHP has better economic and environmental advantages.

Localized Weighted Sum Method for Many-Objective Optimization

Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori . The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, $\boldsymbol {\theta }$ -dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization.

Multi-objective design optimization for a two-stage transmission system under heavy load condition

A gear reducer is of critical importance to the performance of many transmission systems in automotive, marine, and aerospace applications. In the preliminary design phase, the pursuits of minimum volume, maximum surface fatigue life and maximum load capacity essentially becomes a multi-objective optimization problem. In this paper, a novel metaheuristics algorithm, Crow Search Algorithm (CSA), is extended to a multi-objective decision scenario based on the strategy embedded in the preference-inspired co-evolutionary algorithm using weights (PICEA-w). The proposed algorithm combines the nature of diversity, the rapid convergence of CSA and the efficient adaptive weights from PICEA-w. The genetic operator applied in the original PICEA-w aims to generate the offspring that is replaced by the food survey strategy of CSA with augmented efficiency. A hoisting transmission optimization problem from heavy cable shovel excavator is solved. Comparisons with other methods are provided to illustrate the effectiveness of the proposed optimization algorithm.

Optimal design of grid-connected hybrid renewable energy systems using multi-objective evolutionary algorithm

The optimal design of grid-connected Hybrid Renewable Energy Systems (HRESs) is studied by using multi-objective evolutionary algorithm in this paper. With the total system cost and fuel emissions to be minimized, a two-objective optimization model of the hybrid system is established. Then, a modifi ed preference-inspired co-evolutionary algorithm is, for the first time, applied to fi nd the optimal con guration of a grid-connectedhybrid system. As an example, a grid-connected hybrid system, including PV panels, wind turbines, and diesel generators, has been designed and good results are obtained which show that the proposed method is effective.

Optimal design of Fractional Order Digital Integrators – An Evolutionary Approach

The optimal design of grid-connected Hybrid Renewable Energy Systems (HRESs) is studied by using multi-objective evolutionary algorithm in this paper. With the total system cost and fuel emissions to be minimized, a two-objective optimization model of the hybrid system is established. Then, a modifi ed preference-inspired co-evolutionary algorithm is, for the first time, applied to fi nd the optimal con guration of a grid-connectedhybrid system. As an example, a grid-connected hybrid system, including PV panels, wind turbines, and diesel generators, has been designed and good results are obtained which show that the proposed method is effective.

Solving a multi-objective dynamic stochastic districting and routing problem with a co-evolutionary algorithm

This study considers a multi-objective dynamic stochastic districting and routing problem in which the customers of a territory stochastically evolve over several periods of a planning horizon, and where the number of service vehicles, the compactness of the districts, the dissimilarity measure of the districts and an equity measure of vehicles profit are considered as objectives. The problem is modeled and solved as a two-stage stochastic program, where in each period, districting decisions are made in the first stage, and the Beardwood–Halton–Hammersley formula is used to approximate the expected routing cost of each district in the second stage. An enhanced multi-objective evolutionary algorithm (MOEA), i.e., the preference-inspired co-evolutionary algorithm using mating restriction, is developed for the problem. The algorithm is tested on randomly generated instances and is compared with two state-of-the-art MOEAs. Computational results confirm the superiority and effectiveness of the proposed algorithm. Moreover, a procedure for selecting a preferred design for the proposed problem is described.

Multi-objective optimal design of hybrid renewable energy systems using preference-inspired coevolutionary approach

As the increasing energy demand and rapid depletion of conventional fossil fuel resources, renewable energy has caused great attention of the public. The main drawback of the renewable resources is their unpredictable nature. A hybrid renewable energy system (HRES) that integrates different resources in proper combination is a promising solution to overcome this challenge. In this context, the preference-inspired coevolutionary algorithm (PICEA) has been applied for the first time to the design of multi-objective hybrid renewable energy system. We propose an enhanced fitness assignment method to improve the preference-inspired coevolutionary algorithm using goal vectors (PICEA-g) in the optimization process minimizing, simultaneously, the annualized cost of system (ACS), the loss of power supply probability (LPSP) and the fuel emissions. As an example of application, a stand-alone hybrid system including PV panels, wind turbines, batteries and diesel generators has been designed to find the best combination of components, achieving a set of non-dominated solutions from which the decision maker can select a most adequate one.

An enhanced preference-inspired co-evolutionary algorithm using orthogonal design and an ε-dominance archiving strategy

The concept of co-evolution of preferences and candidate solutions has proven effective for many-objective optimization. One realization of this concept, namely preference-inspired co-evolutionary algorithms using goal vectors (PICEA-g), is found to outperform many state-of-the-art multi-objective evolutionary algorithms for many-objective problems. However, PICEA-g is susceptible to unevenness in the solution distribution. This study seeks to tackle this issue and to improve the performance of PICEA-g further. Two established strategies are incorporated into PICEA-g: (i) an adaptive ε-dominance archiving strategy which is applied to obtain a set of well spread solutions online; and (ii) the orthogonal design method which is used to initialize candidate solutions. The improved algorithm, denoted as aε-ODPICEA-g, shows a better performance than PICEA-g on both 2- and 7-objective benchmark problems as well as a real-world problem.

Preference-inspired co-evolutionary algorithms using weight vectors

Abstract Decomposition based algorithms perform well when a suitable set of weights are provided; however determining a good set of weights a priori for real-world problems is usually not straightforward due to a lack of knowledge about the geometry of the problem. This study proposes a novel algorithm called preference-inspired co-evolutionary algorithm using weights (PICEA-w) in which weights are co-evolved with candidate solutions during the search process. The co-evolution enables suitable weights to be constructed adaptively during the optimisation process, thus guiding candidate solutions towards the Pareto optimal front effectively. The benefits of co-evolution are demonstrated by comparing PICEA-w against other leading decomposition based algorithms that use random, evenly distributed and adaptive weights on a set of problems encompassing the range of problem geometries likely to be seen in practice, including simultaneous optimisation of up to seven conflicting objectives. Experimental results show that PICEA-w outperforms the comparison algorithms for most of the problems and is less sensitive to the problem geometry.

Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization

The simultaneous optimization of many objectives (in excess of 3), in order to obtain a full and satisfactory set of tradeoff solutions to support a posteriori decision making, remains a challenging problem. The concept of coevolving a family of decision-maker preferences together with a population of candidate solutions is studied here and demonstrated to have promising performance characteristics for such problems. After introducing the concept of the preference-inspired coevolutionary algorithm (PICEA), a realization of this concept, PICEA-g, is systematically compared with four of the best-in-class evolutionary algorithms (EAs); random search is also studied as a baseline approach. The four EAs used in the comparison are a Pareto-dominance relation-based algorithm (NSGA-II), an e-dominance relation-based algorithm [ e-multiobjective evolutionary algorithm (MOEA)], a scalarizing function-based algorithm (MOEA/D), and an indicator-based algorithm [hypervolume-based algorithm (HypE)]. It is demonstrated that, for bi-objective problems, all of the multi-objective evolutionary algorithms perform competitively. As the number of objectives increases, PICEA-g and HypE, which have comparable performance, tend to outperform NSGA-II, e-MOEA, and MOEA/D. All the algorithms outperformed random search.