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In this study, a new bilateral equilibrium model was developed for the optimal bidding strategy of both price-taker generation companies (GenCos) and distribution companies (DisCos) that participate in a joint day-ahead energy and reserve electricity market. This model, from a new perspective, simultaneously takes into account such techno-economic-environmental measures as market power, security constraints, and environmental and loss considerations. The mathematical formulation of this new model, therefore, falls into a nonlinear, two-level optimization problem. The upper-level problem maximizes the quadratic profit functions of the GenCos and DisCos under incomplete information and passes the obtained optimal bidding strategies to the lower-level problem that clears a joint day-ahead energy and reserve electricity market. A locational marginal pricing mechanism was also considered for settling the electricity market. To solve this newly developed model, a competent multi-computational-stage, multi-dimensional, multiple-homogeneous enhanced melody search algorithm (MMM-EMSA), referred to as a symphony orchestra search algorithm (SOSA), was employed. Case studies using the IEEE 118-bus test system—a part of the American electrical power grid in the Midwestern U.S.—are provided in this paper in order to illustrate the effectiveness and capability of the model on a large-scale power grid. According to the simulation results, several conclusions can be drawn when comparing the unilateral bidding strategy: the competition among GenCos and DisCos facilitates; the improved performance of the electricity market; mitigation of the polluting atmospheric emission levels; and, the increase in total profits of the GenCos and DisCos. [ABSTRACT FROM AUTHOR]