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TABLE II. BUYER REQUIREMENTS AND CONSTRAINTS

Table 1 II. BUYER REQUIREMENTS AND CONSTRAINTS

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Figure 1. Multi-Objective CRA Initialization. We present here the parameters and characteristics of our multi-objective CRA.
Figure 1. Multi-Objective CRA Initialization. We present here the parameters and characteristics of our multi-objective CRA.
In the fitness assignment, we adopt the weighted sum approach. We remodel the fitness assignment procedure according to the requirements of our WD problem. Since we are following the priori approach, deducing weights from the requirements is necessary. We apply the Rank Sum Weights method [10] to obtain the relative weight of each attribute w. r. t. the buyer ranking. We also calculate the utility vectors according to buyer and seller constraints. Thus, the returned fitness value reflects the optimization of the solution based on all the attributes. The objectives are taken into account in the fifth equation when calculating the utility of a seller for an attribute of a certain product. The chromosomes are re- produced by following the Darwinian statement of “survival
In the fitness assignment, we adopt the weighted sum approach. We remodel the fitness assignment procedure according to the requirements of our WD problem. Since we are following the priori approach, deducing weights from the requirements is necessary. We apply the Rank Sum Weights method [10] to obtain the relative weight of each attribute w. r. t. the buyer ranking. We also calculate the utility vectors according to buyer and seller constraints. Thus, the returned fitness value reflects the optimization of the solution based on all the attributes. The objectives are taken into account in the fifth equation when calculating the utility of a seller for an attribute of a certain product. The chromosomes are re- produced by following the Darwinian statement of “survival
TABLE V. CHROMOSOMES IN FIRST GENERATION
TABLE V. CHROMOSOMES IN FIRST GENERATION
We have implemented the proposed WD algorithm in Java and executed it on an Intel (R) core (TM) i3-2330M CPU with 2.20 GHz processor speed and 4 GB of RAM. We conduct three experiments with artificial data. As shown in Table VIII, we randomly generate five instances of our multi-objective CRA problem by varying 4 parameters: the numbers of sellers, products, units and attributes.
We have implemented the proposed WD algorithm in Java and executed it on an Intel (R) core (TM) i3-2330M CPU with 2.20 GHz processor speed and 4 GB of RAM. We conduct three experiments with artificial data. As shown in Table VIII, we randomly generate five instances of our multi-objective CRA problem by varying 4 parameters: the numbers of sellers, products, units and attributes.
solution. As we can see, supplier S10 has been chosen to provide one unit for each of the three products.
solution. As we can see, supplier S10 has been chosen to provide one unit for each of the three products.
Figure 4. Computational time of WD by varying number of units and number of attributes The ranking and objectives of the attributes are also determined randomly. Regarding the constraints, the maximum value of each attribute is randomly produced from [100, 10000], and the minimum value from [10% of maximum value, 50% of maximum value]. Furthermore, we perform numerous parameter-tuning testing, and based on the results, we use the following best configuration, unless otherwise stated: ¢ = 500, 6 = 1000, a (crossover rate) = 0.6, B (mutation rate) = 0.01, y = ¢ and w = 0.2. All the results returned by the WD method represent the average values of 30 runs.
Figure 4. Computational time of WD by varying number of units and number of attributes The ranking and objectives of the attributes are also determined randomly. Regarding the constraints, the maximum value of each attribute is randomly produced from [100, 10000], and the minimum value from [10% of maximum value, 50% of maximum value]. Furthermore, we perform numerous parameter-tuning testing, and based on the results, we use the following best configuration, unless otherwise stated: ¢ = 500, 6 = 1000, a (crossover rate) = 0.6, B (mutation rate) = 0.01, y = ¢ and w = 0.2. All the results returned by the WD method represent the average values of 30 runs.
ABLE IX. COMPUTATION EXPENSE COMPARISON Table IX provides the processing time of IAC, EAB and GAMICRA,; the first two were taken from [16] and the last one from [20]. As we can see, our WD is significantly superior to all of them. Table IX also shows the results for the BnB-based method, taken from [20]. Even though BnB is evaluated on a computer with more processor speed (450 MHz for BnB, and 2.20 GHz for WD), it is clear that our WD greatly outperforms BnB. Since BnB is an exact algorithm, it searches the entire solution space and as a result it costs much more computation time.
ABLE IX. COMPUTATION EXPENSE COMPARISON Table IX provides the processing time of IAC, EAB and GAMICRA,; the first two were taken from [16] and the last one from [20]. As we can see, our WD is significantly superior to all of them. Table IX also shows the results for the BnB-based method, taken from [20]. Even though BnB is evaluated on a computer with more processor speed (450 MHz for BnB, and 2.20 GHz for WD), it is clear that our WD greatly outperforms BnB. Since BnB is an exact algorithm, it searches the entire solution space and as a result it costs much more computation time.
Figure 6. Statistical analysis of WD
Figure 6. Statistical analysis of WD
Related topics:
Combinatorial AuctionMultiobjective Evolutionary OptimizationOnline AuctionsWinner Determination
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