Winner Determination in Multi-Objective Combinatorial Reverse Auctions Shubhashis Kumar Shil and Samira Sadaoui Department of Computer Science University of Regina Regina, Canada {shil200s, sadaouis}@uregina.ca Abstract— This study introduces a new type of Combinatorial Reverse Auction (CRA), products with multi-units, multi- attributes and multi-objectives, which are subject to buyer and seller constraints. In this advanced CRA, buyers may maximize some attributes and minimize some others. To address the Winner Determination (WD) problem in the presence of multiple conflicting objectives, we propose an optimization approach based on genetic algorithms. To improve the quality of the winning solution, we incorporate our own variants of the diversity and elitism strategies. We illustrate the WD process based on a real case study. Afterwards, we validate the proposed approach through artificial datasets by generating large instances of our multi- objective CRA problem. The experimental results demonstrate on one hand the performance of our WD method in terms of three quality metrics, and on the other hand, its significant superiority to well-known heuristic and exact WD techniques that have been defined for simpler CRAs. Keywords- Combinatorial reverse auctions; winner determination; multi-objective optimization; evolutionary algorithms; genetic algorithms; diversity; elitism I. INTRODUCTION By adopting Combinatorial Reverse Auctions (CRAs), buyers can purchase several products all at once. In the literature, it has been shown that combinatorial procurement auctions yield to economic growth [14, 16]. Numerous studies in CRAs focused on products with multiple units and a single attribute [8, 12, 14], but others considered products with multiple attributes and a single unit [16]. Actually, multiple attributes along with multiple units have been ignored in both forward and reverse combinatorial auctions. Researchers limited the auction parameters for the sake of simplicity. In addition, determining the winners in CRAs is a NP-hard problem [16], and therefore is difficult to implement because of the issue of time complexity. Past research in combinatorial auctions endorsed exact algorithms to find the optimal winners but endured an exponential time cost. Besides, time increases exponentially with the size of the Winner Determination (WD) problem. That is why evolutionary algorithms have been introduced to tackle the time-efficiency issue. These algorithms are necessary for large-scale applications, and also for problems that require good solutions in a very short time, like resource allocation, flight scheduling, route planning and wireless communication. In our previous work [19], we determined the winners for a new CRA type: multiple products (heterogeneous) with multiple units and two quantitative attributes, price and delivery rate. We defined a WD approach based on Genetic Algorithms (GAs), powerful searching techniques, which returns near-optimal solution (sometimes optimal) with the least procurement cost and time. As demonstrated in another paper [20], our WD method outperforms in terms of execution time and solution quality other exact and evolutionary algorithms that have been defined for much simpler CRAs. In this paper, we address a more elaborated combinatorial procurement auction that involves multiple units, multiple attributes and multiple objectives all together with the constraints of buyers and sellers. More precisely, the CRA possesses the following features: • Products may have different attributes. • A buyer should elicit his requirements i.e., the products to be auctioned, their attributes and quantities as well as the ranking and objectives of attributes. • A buyer may have multiple conflicting objectives since he can maximize some attributes (like increasing the product quality) and minimize some others (like reducing the product price). • A buyer as well as each seller should provide their constraints on the selected attributes. • A seller competes on any combination of products. Still, if he bids on a given product, we assume he has a full stock of that product. We represent the proposed CRA as a Multi-Objective Optimization (MOO) problem for which we need to optimize (minimize and maximize) several conflicting criteria all at the same time. Since the WD problem we consider here depends on the requirements and constraints of buyers, we therefore follow the priori optimization approach [5]. The latter first elicits the user preferences, then performs the optimization process and produces a single near-optimal solution. Our ultimate goal is to elaborate a robust and efficient evolutionary WD approach. The target is to return one single near-optimal solution (sometimes optimal) in a very low computational time by satisfying all the elicited requirements and constraints. 2016 IEEE 28th International Conference on Tools with Artificial Intelligence 2375-0197/16 $31.00 © 2016 IEEE DOI 10.1109/ICTAI.2016.110 713 2016 IEEE 28th International Conference on Tools with Artificial Intelligence 2375-0197/16 $31.00 © 2016 IEEE DOI 10.1109/ICTAI.2016.110 714 2016 IEEE 28th International Conference on Tools with Artificial Intelligence 2375-0197/16 $31.00 © 2016 IEEE DOI 10.1109/ICTAI.2016.110 714