Abstract
As a popular approach to solve Multiobjective Optimization Problem (MOP), weighted-sum (WS) method obtains a series of weight-dependent Pareto Optimalities (i.e. multi-objective global optimums) forming Pateto Front. Each priori (preset) combination of single-objective (SO) weights stands for a certain way to compromise all of SO, e.g. a popular opinion is “Balanced weights lead to the equilibrium solution”. To verify this notion, this paper proposes a method to obtain adaptive posteriori weights derived from heuristic search rather than human-judged priori weights, so as to generate an unique Equilibrium Pateto Optimality (Equi-PO) out of the Pareto Front of multiobjective-function (MOFunc), where mutual interest of every single-objective- function (SOFunc) is achieved to a certain “equal” extent. The numerical example reveal that an unique Equi-PO is obtainable with adaptive weights converging towards an unique end, and: (1) For and only for the WS-MOP whose Pareto Front is symmetric to the Equiangular Utopia Ray, “balanced weights” results in “equilibrium solution”; (2) For other conditions, “balanced weights” can’t.
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Supported by National Key Technology R&D Program of China “Key Technologies and System Integration of Network-based Coordinated Control of Freeway Traffic Safety (Project No.: 2014BAG01B04)”, Key Laboratory of Road Traffic Safety of Ministry of Public Security of China.
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Wu, Y., Zhang, Z., Yuan, J., Ma, Q. (2017). Weight-Dependent Equilibrium Solution for Weighted-Sum Multiobjective Optimization. In: Lu, H. (eds) Proceedings of the Second International Conference on Intelligent Transportation. ICIT 2016. Smart Innovation, Systems and Technologies, vol 53. Springer, Singapore. https://doi.org/10.1007/978-981-10-2398-9_22
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DOI: https://doi.org/10.1007/978-981-10-2398-9_22
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